CN106126795A - The Forecasting Methodology of the multi stage axial flow compressor perf ormance that feature based value is theoretical - Google Patents

Abstract

The present invention relates to the Forecasting Methodology of a kind of multi stage axial flow compressor perf ormance, including: according to the situation of rotating stall of axial flow compressor tendency, use small pertubation theory, set up the three dimensional compressible Euler equation portraying flow field；Use Harmonic Decomposition and dispersion relation, and set up boundary condition at the wheel hub and blade tip in each basin；Rotor and stator use three-dimensional half swash dish model and carries out modelling, and use mode matching technique, conservation law and the sign condition of compressor loss property in interface, obtain solving the eigenvalue problem in line flow field；Solve this feature value problem and obtain the characteristic disturbances frequency of compressibility, and judge system stability by characteristic disturbances frequency, it is judged that standard: forcing frequency ω is plural number, is expressed as ω=ω_R+iω_I；Imaginary part ω when frequency_IDuring ＞ 0, it is decay that disturbance develops in time, system stability；Otherwise ω_I< 0, disturbance is amplified in time, system unstability.The present invention can be used for the prediction of multi stage axial flow compressor rotating stall stability.

Description

The Forecasting Methodology of the multi stage axial flow compressor perf ormance that feature based value is theoretical

Technical field

The present invention relates to the Forecasting Methodology of a kind of multi stage axial flow compressor perf ormance, particularly relate to a kind of feature based value The Forecasting Methodology of theoretical multi stage axial flow compressor perf ormance, belongs to turbine technical field.

Background technology

In prior art, common rotating stall Stability Model is typically not consider the two dimensional model of Radial Perturbation.And Currently available three-dimensional stability model is very limited, and great majority are that three-dimensional can not press Stability Model, can not meet at a high speed The needs of compressor/fan.

In order to set up three-dimensional stability model, some researcheres have been also carried out a lot of trial.It is emphasized that: except mould Outside the difficulty of type own, its method of value solving also counteracts that the development of three-dimensional stability model, such as, although Ludiwig is The three-dimensional established can not press Stability Model, but owing to not having suitable method of value solving, the most also ends up with nothing definite. Because stability features equation is a Complex eigenvalues matrix determinant, there is no analytical expression, to the derivative of independent variable also without Method express, and use Newton-Raphson method,When the conventional iterative methods such as method solve, the convergence direction of solution is not subject to Control, often have the situation of many solutions due to characteristic equation, and some solution is also beyond the scope of physical significance, even if to repeatedly The initial value in generation adjusts, it is also difficult to control the convergence direction of result of calculation.

Summary of the invention

In sum, necessary offer is a kind of can consider that the three dimensional compressible rotating stall of arbitrary order Radial Perturbation is steady Qualitative model, this model may be used for the research of multi stage axial flow compressor rotating stall stability, and in theory, can process There is the Compressor Stability problem of treated casing situation.

A kind of Forecasting Methodology of multi stage axial flow compressor perf ormance, including:

According to the situation of rotating stall of axial flow compressor tendency, using small pertubation theory, the three-dimensional in flow field is portrayed in foundation can Compression Euler equation；

Use Harmonic Decomposition and dispersion relation, and set up boundary condition at the wheel hub and blade tip in each basin, its In, the solution in each basin is the whirlpool ripple by the pressure disturbance ripple can propagated along upstream and downstream and propagated with mainstream speed, entropy Wave component；

Rotor and stator use three-dimensional half swash dish model and carries out modelling, and use mode matching technique in interface, keep The sign condition of constant rule and compressor loss property, obtains solving the eigenvalue problem in line flow field；

Obtain the characteristic disturbances frequency of compressibility by solving this feature value problem, and sentenced by characteristic disturbances frequency Disconnected system stability, the criterion of system stability: suppose that in Stability Model all disturbance quantities all contain in time Change item e^iωt, wherein forcing frequency ω is plural number, is expressed as ω=ω_R+iω_I；ThereforeVoid when frequency Portion ω_I> 0 time, disturbance develop in time be decay, system stability；Otherwise ω_I< 0, disturbance is amplified in time, system unstability.

Multi stage axial flow compressor is divided into vane region and n omicronn-leaf section, and sets flowing as without viscous adiabatic compressible flows, master Stream is equal uniform flow, and is conceived to the situation of compressor stall tendency, and i.e. linear microvariations are assumed；In n omicronn-leaf section, principal flow velocity Degree is two-dimentional, ignores radially mainstream speed；Disturbance velocity is three-dimensional turbulence；In vane region, will there is the leaf of camber and torsion Sheet flat-plate cascade replaces, and internal mainstream speed is one-dimensional, and same ignores radially mainstream speed, it is considered to Radial Perturbation speed The impact of degree.

The governing equation of n omicronn-leaf section is mainly made up of quality continuity equation, the equation of momentum and energy equation.

The boundary condition be given in sclerine face is for without penetrating, without sliding and zero vibration condition, by application trigonometric function The form of progression, represents radially characteristic function.

The axial wave number propagated axially upstream or downstreamExpression formula is:

${\mathrm{\&alpha;}}_{mn}^{\&PlusMinus;j}=\frac{M_x({\mathrm{\&beta;}}_m{M}_y+\frac{\mathrm{\&omega;}}{a_0})\&PlusMinus;\sqrt{{({\mathrm{\&beta;}}_m{M}_y+\frac{\mathrm{\&omega;}}{a_0})}^2+(1-M_x^2)\&lsqb;{\mathrm{\&beta;}}_m^2+{\left(k_{mn}^{+j}\right)}^2\&rsqb;}}{(1-M_x^2)},$

Wherein, β_mExpression circumference wave number:

${\mathrm{\&beta;}}_m=\frac{m}{r_m};$

r_mIt is the mean radius in blade grid passage, M_x、M_yRefer to the Mach number component at axial and circumferential, a₀Expression sound The spread speed of sound.

Leaf area uses one-dimensional half to swash dish model, comprises one-dimensional tangential flowing, absolute coordinate system in blade path For (x, y, z), with moving coordinate system (x ', y ', z '), and the tangential coordinate system of servo-actuated leaf grating is that (ξ, η z), do not consider at vertical leaf The disturbance quantity change that grid are tangential, therefore the tangential coordinate system of leaf grating is that (ξ, z), the governing equation of vane region includes quality side continuously Journey, the tangential equation of momentum, radial momentum equation and energy equation composition.

Solve and obtain an equation group closed:

$Q_{mn}{\left(\mathrm{\&omega;}\right)}_{(9K\&times;9K)}\&CenterDot;{\stackrel{\&OverBar;}{X}}_{mn\left(9K\right)}=0,$

Wherein, K is leaf row；

For two stage compressor,

det[Q_mn(ω)]=0,

By solving above formula, obtain the forcing frequency of system, judge the steady of system by the imaginary part analyzing forcing frequency Qualitative.

Relative to prior art, the Forecasting Methodology of the multi stage axial flow compressor perf ormance that the present invention provides, with eigenvalue Based on theory, it is provided that a kind of three dimensional compressible rotating stall Stability Model that can consider arbitrary order Radial Perturbation, can For the prediction of multi stage axial flow compressor rotating stall stability, and can process that to there is the compressor of treated casing situation steady Qualitative question.

Accompanying drawing explanation

The half sharp dish method blade grid passage schematic diagram that Fig. 1 provides for the embodiment of the present invention.

The schematic diagram of the rotor leaf grating origin coordinate system transform that Fig. 2 provides for the embodiment of the present invention.

The multistage compressor leaf grating schematic diagram that Fig. 3 provides for the embodiment of the present invention.

The two stage compressor mode shape coefficients distribution schematic diagram that Fig. 4 provides for the embodiment of the present invention.

Fig. 5 is the schematic diagram of the passage of NASA two-stage fan.

Fig. 6 is the overall performance of NASA two-stage fan.

Fig. 7 is aerodynamic parameter during NASA two-stage fan 100% rotating speed, wherein (a) import axial velocity；B () import is quiet Pressure；The derivative of (c) loss coefficient (d) loss coefficient.

Fig. 8 is stability prediction result during NASA two-stage fan 100% rotating speed.

Fig. 9 is that time delay is on the impact of stability during NASA two-stage fan 100% rotating speed.

Detailed description of the invention

The multi stage axial flow compressor mistake of the feature based value theory of the embodiment of the present invention is described in detail below in conjunction with accompanying drawing The Forecasting Methodology on speed border.

The Forecasting Methodology of the multi stage axial flow compressor perf ormance that the feature based value that the embodiment of the present invention provides is theoretical, bag Include following steps:

First, according to the situation of rotating stall of axial flow compressor tendency, use small pertubation theory, set up and portray the three of flow field Dimension compressible Euler equations；

Secondly, use Harmonic Decomposition and dispersion relation, and set up perimeter strip at the wheel hub and blade tip in each basin Part, wherein, the solution in each basin is by the pressure disturbance ripple can propagated along upstream and downstream and only to pass with mainstream speed Whirlpool ripple, the entropy wave broadcast form；

Again, rotor and stator use three-dimensional half swash dish model and carries out modelling, and use mode vectors correlation skill in interface The sign condition of art, conservation law and compressor loss property, obtains solving the eigenvalue problem in line flow field；

Finally, obtain the characteristic disturbances frequency of compressibility by solving this feature value problem, and pass through characteristic disturbances Frequency judges system stability, the criterion of system stability: suppose in Stability Model all disturbance quantities all contain with The change item e of time^iωt, wherein forcing frequency ω is plural number, is expressed as ω=ω_R+iω_I；ThereforeWhen frequency Imaginary part ω of rate_I> 0 time, disturbance develop in time be decay, system stability；Otherwise ω_I< 0, disturbance is amplified in time, system Unstability.

Seeing also Fig. 1 to Fig. 3, in a model, multi stage axial flow compressor will be divided into vane region and n omicronn-leaf section, it Each own different governing equation, and assume flowing for without viscous adiabatic compressible flows, main flow is equal uniform flow, and is conceived to pressure The situation of mechanism of qi stall precursor, i.e. linear microvariations are assumed.It addition, in n omicronn-leaf section, mainstream speed is two-dimentional, have ignored The radial direction mainstream speed that accounting weight is smaller, but disturbance velocity is three-dimensional turbulence；In vane region, will there be camber and torsion Blade flat-plate cascade replaces, and internal mainstream speed regards one-dimensional as, and same ignores radially mainstream speed, it is considered to radially The impact of disturbance velocity.

Set up n omicronn-leaf section governing equation:

The governing equation of n omicronn-leaf section is mainly made up of quality continuity equation, the equation of momentum and energy equation.

$\frac{\&part;\mathrm{\&rho;}}{\&part;t}+\&dtri;\&CenterDot;\left(\mathrm{\&rho;}\stackrel{\&RightArrow;}{V}\right)=0---\left(1\right)$

$\frac{D\stackrel{\&RightArrow;}{V}}{Dt}+\frac{1}{{\mathrm{\&rho;}}_0}\&dtri;p=0---\left(2\right)$

$\frac{1}{P_0}\frac{Dp}{Dt}-\frac{k}{{\mathrm{\&rho;}}_0}\frac{D\mathrm{\&rho;}}{Dt}=0---\left(3\right)$

In formula: " 0 " represents average magnitude, k is the specific heat ratio of air, and ρ is density,Representation speed, p is pressure.

Above partial differential equation can be solved by the form using the separation of variable and series expansion, finally give the most micro- Divide non trivial solution as follows:

$p^j(x,y,z,t)=\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\underset{n=1}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\&lsqb;{\stackrel{\&OverBar;}{p}}_{mn}^{+j}{e}^{{\mathrm{i\&alpha;}}_{mn}^{+j}(x-x^j)}{\mathrm{\&psi;}}_{mn}^{+j}\left(z\right)+{\stackrel{\&OverBar;}{p}}_{mn}^{-j}{e}^{{\mathrm{i\&alpha;}}_{mn}^{-j}(x-x^j)}{\mathrm{\&psi;}}_{mn}^{-j}\left(z\right)\&rsqb;e^{i({\mathrm{\&beta;}}_{m}y+\mathrm{\&omega;}t)}---\left(4\right)$

${\mathrm{\&rho;}}^j=\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\underset{n=1}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\left[\begin{array}{c}\frac{1}{{\left(a_0^j\right)}^2}\left({\mathrm{\&psi;}}_{mn}^{+j}\right(z)e^{{\mathrm{i\&alpha;}}_{mn}^{+j}(x-x^j)}{\stackrel{\&OverBar;}{p}}_{mn}^{+j}+{\mathrm{\&psi;}}_{mn}^{-j}(z\left)e^{{\mathrm{i\&alpha;}}_{mn}^{-j}(x-x^j)}{\stackrel{\&OverBar;}{p}}_{mn}^{-j}\right)\\ +{\stackrel{\&OverBar;}{\mathrm{\&rho;}}}_{vmn}^{+j}{\mathrm{\&psi;}}_{vmn}^{+j}\left(z\right)e^{-i\frac{\mathrm{\&omega;}+{\mathrm{\&beta;}}_{m}V}{U}(x-x^j)}\end{array}\right]e^{i({\mathrm{\&beta;}}_{m}y+\mathrm{\&omega;}t)}---\left(5\right)$

$u^j=\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\underset{n=1}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\left[\begin{array}{c}-\frac{1}{{\mathrm{\&rho;}}_0^j}(\frac{{\mathrm{\&alpha;}}_{mn}^{+j}{\mathrm{\&psi;}}_{mn}^{+j}\left(z\right)e^{{\mathrm{i\&alpha;}}_{mn}^{+j}(x-x^j)}{\stackrel{\&OverBar;}{p}}_{mn}^{+j}}{(\mathrm{\&omega;}+{\mathrm{\&alpha;}}_{mn}^{+j}{U}^j+{\mathrm{\&beta;}}_m{V}^j)}+\frac{{\mathrm{\&alpha;}}_{mn}^{-j}{\mathrm{\&psi;}}_{mn}^{-j}\left(z\right)e^{{\mathrm{i\&alpha;}}_{mn}^{-j}(x-x^j)}{\stackrel{\&OverBar;}{p}}_{mn}^{-j}}{(\mathrm{\&omega;}+{\mathrm{\&alpha;}}_{mn}^{-j}{U}^j+{\mathrm{\&beta;}}_m{V}^j)})\\ +(\frac{{\mathrm{\&beta;}}_{m}U{\stackrel{\&OverBar;}{v}}_{vmn}^{+j}}{\mathrm{\&omega;}+{\mathrm{\&beta;}}_{m}V}-\frac{{\mathrm{ik}}_{vmn}^{+j}U{\stackrel{\&OverBar;}{w}}_{vmn}^{+j}}{\mathrm{\&omega;}+{\mathrm{\&beta;}}_{m}V}){\mathrm{\&psi;}}_{vmn}^{+j}\left(z\right)e^{-i\frac{\mathrm{\&omega;}+{\mathrm{\&beta;}}_{m}V}{U}(x-x^j)}\end{array}\right]e^{i({\mathrm{\&beta;}}_{m}y+\mathrm{\&omega;}t)}---\left(6\right)$

$v^j=\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\underset{n=1}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\left[\begin{array}{c}-\frac{1}{{\mathrm{\&rho;}}_0^j}(\frac{{\mathrm{\&beta;}}_m{\mathrm{\&psi;}}_{mn}^{+j}\left(z\right)e^{{\mathrm{i\&alpha;}}_{mn}^{+j}(x-x^j)}{\stackrel{\&OverBar;}{p}}_{mn}^{+j}}{(\mathrm{\&omega;}+{\mathrm{\&alpha;}}_{mn}^{+j}{U}^j+{\mathrm{\&beta;}}_m{V}^j)}+\frac{{\mathrm{\&beta;}}_m{\mathrm{\&psi;}}_{mn}^{-j}\left(z\right)e^{{\mathrm{i\&alpha;}}_{mn}^{-j}(x-x^j)}{\stackrel{\&OverBar;}{p}}_{mn}^{-j}}{(\mathrm{\&omega;}+{\mathrm{\&alpha;}}_{mn}^{-j}{U}^j+{\mathrm{\&beta;}}_m{V}^j)})\\ +{\stackrel{\&OverBar;}{v}}_{vmn}^{+j}{\mathrm{\&psi;}}_{vmn}^{+j}\left(z\right)e^{-i\frac{\mathrm{\&omega;}+{\mathrm{\&beta;}}_{m}V}{U}(x-x^j)}\end{array}\right]e^{i({\mathrm{\&beta;}}_{m}y+\mathrm{\&omega;}t)}---\left(7\right)$

$w^j=\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\underset{n=1}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\left[\begin{array}{c}\frac{1}{{\mathrm{\&rho;}}_0^j}(\frac{k_{mn}^{+j}{\mathrm{\&phi;}}_{mn}^{+j}\left(z\right)e^{{\mathrm{i\&alpha;}}_{mn}^{+j}(x-x^j)}{\stackrel{\&OverBar;}{p}}_{mn}^{+j}}{i(\mathrm{\&omega;}+{\mathrm{\&alpha;}}_{mn}^{+j}{U}^j+{\mathrm{\&beta;}}_m{V}^j)}+\frac{k_{mn}^{-j}{\mathrm{\&phi;}}_{mn}^{-j}\left(z\right)e^{{\mathrm{i\&alpha;}}_{mn}^{-j}(x-x^j)}{\stackrel{\&OverBar;}{p}}_{mn}^{-j}}{i(\mathrm{\&omega;}+{\mathrm{\&alpha;}}_{mn}^{-j}{U}^j+{\mathrm{\&beta;}}_m{V}^j)})\\ +{\stackrel{\&OverBar;}{w}}_{vmn}^{+j}{\mathrm{\&phi;}}_{vmn}^{+j}\left(z\right)e^{-i\frac{\mathrm{\&omega;}+{\mathrm{\&beta;}}_{m}V}{U}(x-x^j)}\end{array}\right]e^{i({\mathrm{\&beta;}}_{m}y+\mathrm{\&omega;}t)}---\left(8\right)$

Wherein, " m " is circumference mode, and " n " is radial mode shape；" ω " is the forcing frequency of compressibility to be asked, and it is One Complex frequency, its real part ω_rRepresent the actual frequency of disturbance, imaginary part ω_iRepresent the damping of disturbance, be also that this model judges The key parameter of compressibility stability.P, ρ, u, v, w and U, V, α_mn、β_mRepresent pressure, density, axial velocity, circumference respectively Speed, the microvariations amount of radial velocity and axial mainstream speed, circumference mainstream speed, axial wave number, circumference wave number.

During the solution of derivation n omicronn-leaf section governing equation, need to combine boundary condition.First, be given in sclerine face Boundary condition for without penetrating, without sliding and zero vibration condition, by the form of application trigonometric function progression, footpath can be represented To characteristic function, following ψ and φ:

${\mathrm{\&psi;}}_{mn}^{\&PlusMinus;j}\left(z\right)={\mathrm{\&psi;}}_{vmn}^{\&PlusMinus;j}\left(z\right)=cos\left(k_{vmn}^{\&PlusMinus;j}z\right)---\left(9\right)$

${\mathrm{\&phi;}}_{mn}^{\&PlusMinus;j}\left(z\right)={\mathrm{\&phi;}}_{vmn}^{\&PlusMinus;j}\left(z\right)=sin\left(k_{vmn}^{\&PlusMinus;j}z\right)---\left(10\right)$

Radially wave number is:

$k_{mn}=\frac{n\mathrm{\&pi;}}{h},(n=0,1,2,...N)---\left(11\right).$

Circumference at compressor should meet periodicity condition, can use circumference wave numberForm.Wherein β_mRepresent circumference Wave number, expression formula is:

${\mathrm{\&beta;}}_m=\frac{m}{r_m}---\left(12\right)$

r_mIt it is the mean radius in blade grid passage.

It addition, " j " represents jth on-bladed region, "+" represent disturbance and downstream propagate, "-" represents disturbance and upstream passes Broadcast.Representing the axial wave number propagated axially upstream or downstream, its expression formula is:

${\mathrm{\&alpha;}}_{mn}^{\&PlusMinus;j}=\frac{M_x({\mathrm{\&beta;}}_m{M}_y+\frac{\mathrm{\&omega;}}{a_0})\&PlusMinus;\sqrt{{({\mathrm{\&beta;}}_m{M}_y+\frac{\mathrm{\&omega;}}{a_0})}^2+(1-M_x^2)\&lsqb;{\mathrm{\&beta;}}_m^2+{\left(k_{mn}^{+j}\right)}^2\&rsqb;}}{(1-M_x^2)}---\left(13\right)$

Wherein, M_x、M_yRefer to the Mach number component at axial and circumferential, a₀Represent the spread speed of sound.

See also Fig. 4, so far, single modal waves (m, n) corresponding disturbance quantity in an on-bladed region will be determined Size, need to obtain following 5 mode shape coefficients:

${\stackrel{\&OverBar;}{p}}_{mn}^{+j},{\stackrel{\&OverBar;}{p}}_{mn}^{-j},{\stackrel{\&OverBar;}{v}}_{vmn}^{+j},{\stackrel{\&OverBar;}{w}}_{vmn}^{+j},{\stackrel{\&OverBar;}{\mathrm{\&rho;}}}_{vmn}^{+j}---\left(14\right)$

Wherein,It is the mode shape coefficients of pressure wave,It is the mode shape coefficients of whirlpool ripple,It it is the mould of entropy wave State coefficient.

Set up vane region governing equation:

Leaf area can use one-dimensional half to swash dish model, tangential flowing the most one-dimensional in blade path.Absolute coordinate System is for (x, y, z), with moving coordinate system (x ', y ', z '), and the tangential coordinate system of servo-actuated leaf grating is that (ξ, η, z), owing to model is not examined Consider vertical leaf grating tangential disturbance quantity change, the most again it may be said that the tangential coordinate system of leaf grating be (ξ, z).

Be given below line Eulerian equation be built upon relative coordinate system (ξ, z) under, if Ω=0, be stator, otherwise For rotor.

As the composition of n omicronn-leaf section governing equation, the governing equation of vane region is by quality continuity equation, tangential dynamic Amount equation, radial momentum equation and energy equation composition.Can be with W_cRepresenting tangential average speed, q represents tangential disturbance velocity, W represents Radial Perturbation speed, and the governing equation of the vane region of foundation is as follows:

$\frac{\&part;\mathrm{\&rho;}}{\&part;t}+W_c\frac{\&part;\mathrm{\&rho;}}{\&part;\mathrm{\&xi;}}+{\mathrm{\&rho;}}_0(\frac{\&part;q}{\&part;\mathrm{\&xi;}}+\frac{\&part;w}{\&part;z})=0---\left(15\right)$

$\frac{\&part;q}{\&part;t}+W_c\frac{\&part;q}{\&part;\mathrm{\&xi;}}=-\frac{1}{{\mathrm{\&rho;}}_0}\frac{\&part;p}{\&part;\mathrm{\&xi;}}---\left(16\right)$

$\frac{\&part;w}{\&part;t}+W_c\frac{\&part;w}{\&part;\mathrm{\&xi;}}=-\frac{1}{{\mathrm{\&rho;}}_0}\frac{\&part;p}{\&part;z}---\left(17\right)$

$\frac{1}{P_0}(\frac{\&part;p}{\&part;t}+W_c\frac{\&part;p}{\&part;\mathrm{\&xi;}})+k(\frac{\&part;q}{\&part;\mathrm{\&xi;}}+\frac{\&part;w}{\&part;z})=0---\left(18\right).$

As the method solving n omicronn-leaf section governing equation, vane region pressure, density, tangential speed may finally be obtained With the solution of radial velocity disturbance quantity it is:

$p_c^k(x,y^{\&prime;},z,t)=\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\underset{n=1}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\&lsqb;e^{{\mathrm{i\&alpha;}}_{cmn}^{+k}(x-x^k)}{\mathrm{\&psi;}}_{cmn}^{+k}\left(z\right){\stackrel{\&OverBar;}{p}}_{cmn}^{+k}+e^{{\mathrm{i\&alpha;}}_{cmn}^{-k}(x-x^k)}{\mathrm{\&psi;}}_{cmn}^{-k}\left(z\right){\stackrel{\&OverBar;}{p}}_{cmn}^{-k}\&rsqb;e^{i(\mathrm{\&omega;}-m\mathrm{\&Omega;})t+{\mathrm{i\&beta;}}_m{y}^{\&prime;}}---\left(19\right)$

${\mathrm{\&rho;}}_c^k(x,y^{\&prime;},z,t)=\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\underset{n=1}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\left[\begin{array}{c}\frac{1}{{\left(a_0^k\right)}^2}\left({\mathrm{\&psi;}}_{cmn}^{+k}\left(z\right)e^{{\mathrm{i\&alpha;}}_{cmn}^{+k}(x-x^k)}{\stackrel{\&OverBar;}{p}}_{cmn}^{+k}+{\mathrm{\&psi;}}_{cmn}^{-k}\left(z\right)e^{{\mathrm{i\&alpha;}}_{cmn}^{-k}(x-x^k)}{\stackrel{\&OverBar;}{p}}_{cmn}^{-k}\right)\\ +{\stackrel{\&OverBar;}{\mathrm{\&rho;}}}_{cvmn}^{+k}{\mathrm{\&phi;}}_{cvmn}^{+k}\left(z\right)e^{-i\frac{(\mathrm{\&omega;}-m\mathrm{\&Omega;})+{\mathrm{\&beta;}}_m{W_c}^k{\mathrm{sin\&theta;}}^k}{{W_c}^k{\mathrm{cos\&theta;}}^k}(x-x^k)}\end{array}\right]e^{i(\mathrm{\&omega;}-m\mathrm{\&Omega;})t+{\mathrm{i\&beta;}}_m{y}^{\&prime;}}---\left(20\right)$

$q_c^k(x,y^{\&prime;},z,t)=\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\underset{n=1}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\left[\begin{array}{c}-\frac{1}{{\mathrm{\&rho;}}_0^k}\left(\begin{array}{c}\frac{({\mathrm{\&alpha;}}_{cmn}^{+k}\cos \mathrm{\&theta;}+{\mathrm{\&beta;}}_m\sin \mathrm{\&theta;})e^{{\mathrm{i\&alpha;}}_{cmn}^{+k}(x-x^k)}{\mathrm{\&psi;}}_{cmn}^{+k}\left(z\right){\stackrel{\&OverBar;}{p}}_{cmn}^{+k}}{\&lsqb;(\mathrm{\&omega;}-m\mathrm{\&Omega;})+W_c({\mathrm{\&alpha;}}_{cmn}^{+k}\cos \mathrm{\&theta;}+{\mathrm{\&beta;}}_m\sin \mathrm{\&theta;})\&rsqb;}\\ +\frac{({\mathrm{\&alpha;}}_{cmn}^{-k}\cos \mathrm{\&theta;}+{\mathrm{\&beta;}}_m\sin \mathrm{\&theta;})e^{{\mathrm{i\&alpha;}}_{cmn}^{-k}(x-x^k)}{\mathrm{\&psi;}}_{cmn}^{-k}\left(z\right){\stackrel{\&OverBar;}{p}}_{cmn}^{-k}}{\&lsqb;(\mathrm{\&omega;}-m\mathrm{\&Omega;})+W_c({\mathrm{\&alpha;}}_{cmn}^{-k}\cos \mathrm{\&theta;}+{\mathrm{\&beta;}}_m\sin \mathrm{\&theta;})\&rsqb;}\end{array}\right)\\ -\frac{{\mathrm{ik}}_{cvmn}^{+k}{W_c}^k}{(\mathrm{\&omega;}-m\mathrm{\&Omega;})}{e}^{-i\frac{(\mathrm{\&omega;}-m\mathrm{\&Omega;})+{\mathrm{\&beta;}}_m{W_c}^k{\mathrm{sin\&theta;}}^k}{{W_c}^k{\mathrm{cos\&theta;}}^k}(x-x^k)}{\mathrm{\&psi;}}_{cvmn}^{+k}\left(z\right){\stackrel{\&OverBar;}{w}}_{cvmn}^{+k}\end{array}\right]e^{i(\mathrm{\&omega;}-m\mathrm{\&Omega;})t+{\mathrm{i\&beta;}}_m{y}^{\&prime;}}---\left(21\right)$

$w_c^k(x,y^{\&prime;},z,t)=\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\underset{n=1}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\left[\begin{array}{c}\frac{1}{{\mathrm{\&rho;}}_0}\left(\begin{array}{c}\frac{k_{cmn}^{+k}{e}^{-{\mathrm{i\&alpha;}}_{cmn}^{+k}(x-x^k)}{\mathrm{\&phi;}}_{cmn}^{+k}\left(z\right){\stackrel{\&OverBar;}{p}}_{cmn}^{+k}}{i\&lsqb;(\mathrm{\&omega;}-m\mathrm{\&Omega;})+W_c({\mathrm{\&alpha;}}_{cmn}^{+k}\cos \mathrm{\&theta;}+{\mathrm{\&beta;}}_m\sin \mathrm{\&theta;})\&rsqb;}\\ +\frac{k_{cmn}^{+k}{e}^{-{\mathrm{i\&alpha;}}_{cmn}^{-k}(x-x^k)}{\mathrm{\&phi;}}_{cmn}^{-k}\left(z\right){\stackrel{\&OverBar;}{p}}_{cmn}^{-k}}{i\&lsqb;(\mathrm{\&omega;}-m\mathrm{\&Omega;})+W_c({\mathrm{\&alpha;}}_{cmn}^{-k}\cos \mathrm{\&theta;}+{\mathrm{\&beta;}}_m\sin \mathrm{\&theta;})\&rsqb;}\end{array}\right)\\ +{\stackrel{\&OverBar;}{w}}_{cvmn}^{+k}{\mathrm{\&phi;}}_{cvmn}^{+k}\left(z\right)e^{-i\frac{(\mathrm{\&omega;}-m\mathrm{\&Omega;})+{\mathrm{\&beta;}}_m{W_c}^k{\mathrm{sin\&theta;}}^k}{{W_c}^k{\mathrm{cos\&theta;}}^k}(x-x^k)}\end{array}\right]e^{i(\mathrm{\&omega;}-m\mathrm{\&Omega;})t+{\mathrm{i\&beta;}}_m{y}^{\&prime;}}---\left(22\right)$

Wherein, in formulaIt is the velocity of sound in k row's leaf grating, M_cBeing Mach number tangential under relative coordinate system, Ω represents rotor Turn frequency, W_cRepresent the mainstream speed that leaf grating is tangential, axial wave number α_cmnExpression formula be:

${\mathrm{\&alpha;}}_{cmn}^{\&PlusMinus;k}cos\mathrm{\&theta;}+{\mathrm{\&beta;}}_{m}sin\mathrm{\&theta;}=\frac{\frac{M_c}{a_{0c}^k}(\mathrm{\&omega;}-m\mathrm{\&Omega;})\&PlusMinus;\sqrt{\frac{{(\mathrm{\&omega;}-m\mathrm{\&Omega;})}^2}{{\left(a_{0c}^k\right)}^2}-(1-{M_c}^2){\left(k_{cmn}^{\&PlusMinus;k}\right)}^2}}{(1-{M_c}^2)}---\left(23\right)$

Wherein, k_cmnIt is radial direction characteristic function ψ_cmnThe eigenvalue of (z).Radially the relational expression between characteristic function is as follows:

${\mathrm{\&psi;}}_{cmn}^{\&PlusMinus;k}={\mathrm{\&psi;}}_{cvmn}^{+k}=cos\left(k_{cmn}^{+k}z\right)---\left(24\right)$

${\mathrm{\&phi;}}_{cmn}^{\&PlusMinus;k}={\mathrm{\&phi;}}_{cvmn}^{+k}=sin\left(k_{cvmn}^{+k}z\right)---\left(25\right)$

Radially wave number is:

$k_{cmn}=\frac{n\mathrm{\&pi;}}{h},(n=0,1,2,...N)---\left(26\right).$

For rotor and stator, only difference is that Ω.Equally, if disturbance quantity is big in blade territory to be determined Little, it is also necessary to all mode shape coefficients of each perturbation wave will be obtained, for a leaf grating, determine the coefficient of a mode altogether There are four, it may be assumed that

Interphase match

After obtaining the analytic solutions of fundamental equation, interface uses mode matching technique, conservation law and permissible Characterize the condition of compressor loss property, the microvariations analytic solutions on interface are set up contact.

Owing to total pressure loss and traffic steering characteristic are extremely important, in this model to predicting the outcome, it is assumed that Flowing turns to and loss occurrence edge in front of the blade.Therefore, the leading edge matching condition be finally given is as follows:

${\mathrm{\&rho;}}^j{U}^j+{\mathrm{\&rho;}}_0^j{u}^j=({\mathrm{\&rho;}}^k{U}^k+{\mathrm{\&rho;}}_0^k{q}^k){\mathrm{cos\&theta;}}^k---\left(27\right)$

$T_t^{\&prime;j}=\frac{p^j}{{\mathrm{R\&rho;}}_0}-\frac{{\left(a_0^j\right)}^2}{{\mathrm{kR\&rho;}}_0}{\mathrm{\&rho;}}^j+\frac{1}{c_p}(U^j{u}^j+V_r^j{v}^j)=\frac{p^k}{{\mathrm{R\&rho;}}_0}-\frac{{\left(a_0^k\right)}^2}{{\mathrm{kR\&rho;}}_0}{\mathrm{\&rho;}}^k+\frac{W_c^k{q}^k}{c_p}=T_t^{\&prime;k}---\left(28\right)$

w^k=w^j+1 (29)

${p_t}^j-{p_t}^k=\frac{1}{1+{\mathrm{i\&omega;\&tau;}}_{loss}}\left[\begin{array}{c}\frac{1}{2}{\mathrm{\&xi;}}_s^k{\mathrm{\&rho;}}^j{\left(W^j\right)}^2+{\mathrm{\&xi;}}_s^k{\mathrm{\&rho;}}_0^j\&lsqb;U^j{u}^j+V_r^j{v}^j\&rsqb;\\ +\frac{1}{2U^j}\frac{\&part;{\mathrm{\&xi;}}_s^k}{\&part;{\mathrm{tan\&beta;}}^k}{\mathrm{\&rho;}}_0^j{\left(W^j\right)}^2(v^j-u^j{\mathrm{tan\&beta;}}^k)\end{array}\right]---\left(30\right)$

Wherein, T_t' representing stagnation temperature disturbance, R is air constant,For relative circumferential speed, τ_lossIt is time delay,It is Total pressure loss coefficient relatively:

${\mathrm{\&xi;}}_s^k=\frac{P_t^j-P_t^{j+1}}{{\mathrm{\&rho;}}^j{\left(W^j\right)}^2/2}---\left(31\right)$

The stagnation pressure disturbance of n omicronn-leaf section is:

$p_t^j=(S_1^j-\frac{k{\left(M^j\right)}^2}{2}{S}_2^j)p^j+\frac{{\left(W^j\right)}^2}{2}{S}_2^j{\mathrm{\&rho;}}^j+{\mathrm{\&rho;}}_0^j{U}^j{S}_2^j{u}^j+{\mathrm{\&rho;}}_0^j{S}_2^j{V}_r^j{v}^j---\left(32\right)$

Wherein, M represents Mach number,WithIt is respectively as follows:

$\begin{array}{cc}{S}_1^j={\&lsqb;1+\frac{\mathrm{\&kappa;}-1}{2}{\left(M^j\right)}^2\&rsqb;}^{\frac{\mathrm{\&kappa;}}{\mathrm{\&kappa;}-1}}& S_2^j={\&lsqb;1+\frac{\mathrm{\&kappa;}-1}{2}{\left(M^j\right)}^2\&rsqb;}^{\frac{1}{\mathrm{\&kappa;}-1}}\end{array}---\left(33\right)$

The stagnation pressure disturbance of vane region is:

$p_t^k=(S_1^k-\frac{k{\left(M_c^k\right)}^2}{2}{S}_2^k)p^k+\frac{{\left(W_c^k\right)}^2}{2}{S}_2^k{\mathrm{\&rho;}}^k+{\mathrm{\&rho;}}_0^k{S}_2^k{W}_c^k{q}^k---\left(34\right)$

Wherein,

$\begin{array}{cc}{S}_1^k={\&lsqb;1+\frac{\mathrm{\&kappa;}-1}{2}{\left(M_c^k\right)}^2\&rsqb;}^{\frac{\mathrm{\&kappa;}}{\mathrm{\&kappa;}-1}}& S_2^k={\&lsqb;1+\frac{\mathrm{\&kappa;}-1}{2}{\left(M_c^k\right)}^2\&rsqb;}^{\frac{1}{\mathrm{\&kappa;}-1}}\end{array}---\left(35\right)$

In Stability Model, it is assumed that the deflection do not flowed at trailing edge and loss occurrence, so 5 trailing edges couplings Condition is as follows:

p^k=p^j+1 (36)

ρ^k=ρ^j+1 (37)

w^k=w^j+1 (38)

q^kCos θ=u^j+1 (39)

q^kSin θ=v^j+1 (40)

Assuming that flow undistorted undisturbed, outlet areflexia:

${\stackrel{\&OverBar;}{p}}_{mn}^{+1}={\stackrel{\&OverBar;}{\mathrm{\&rho;}}}_{vmn}^{+1}={\stackrel{\&OverBar;}{v}}_{vmn}^{+1}={\stackrel{\&OverBar;}{w}}_{vmn}^{+1}=0,(n=1,2,3...N)---\left(41\right)$

${\stackrel{\&OverBar;}{p}}_{mn}^{-(J+1)}=0,(n=1,2,3...N)---\left(42\right)$

Finally give one close equation group:

$Q_{mn}{\left(\mathrm{\&omega;}\right)}_{(9K\&times;9K)}\&CenterDot;{\stackrel{\&OverBar;}{X}}_{mn\left(9K\right)}=0---\left(43\right)$

Wherein, K is leaf row.

For two stage compressor, Q_mn(ω) andRespectively:

$Q_{mn}\left(\mathrm{\&omega;}\right)={\left[\begin{array}{cccccccccccccc}{C}_{1,1}& C_{1,2}& \mathrm{...}& C_{1,5}& & & & & & & & & & \\ .& .& & .& & & & & & & & & & \\ .& .& & .& & & & & & & & & & \\ .& .& & .& & & & & & & & & & \\ C_{4,1}& C_{4,2}& \mathrm{...}& C_{4,5}& & & & & & & & & & \\ & C_{5,2}& \mathrm{...}& C_{5,5}& C_{5,6}& \mathrm{...}& C_{5,10}& & & & & & & \\ & .& & .& .& & .& & & & & & & \\ & .& & .& .& & .& & & & & & & \\ & .& & .& .& & .& & & & & & & \\ & C_{9,2}& \mathrm{...}& C_{9,5}& C_{9,6}& \mathrm{...}& C_{9,10}& & & & & & & \\ & & & & & & \mathrm{...}& \mathrm{...}& \mathrm{...}& & & & & \\ & & & & & & & .& & & & & & \\ & & & & & & & .& & & & & & \\ & & & & & & & .& & & & & & \\ & & & & & & & .& & & & & & \\ & & & & & & & .& & & & & & \\ & & & & & & & .& & & & & & \\ & & & & & & & & C_{32,29}& \mathrm{...}& C_{32,32}& C_{32,33}& \mathrm{...}& C_{32,36}\\ & & & & & & & & .& & .& .& & .\\ & & & & & & & & .& & .& .& & .\\ & & & & & & & & .& & .& .& & .\\ & & & & & & & & C_{36,29}& \mathrm{...}& C_{36,32}& C_{36,33}& \mathrm{...}& C_{36,36}\end{array}\right]}_{mn}---\left(44\right)$

${\stackrel{\&OverBar;}{X}}_{mn}={\left[\begin{array}{ccccc}{\stackrel{\&OverBar;}{p}}_{mn}^{-1}& {\stackrel{\&OverBar;}{p}}_{cmn}^{+1}& \mathrm{...}& {\stackrel{\&OverBar;}{v}}_{vmn}^{+5}& {\stackrel{\&OverBar;}{w}}_{vmn}^{+5}\end{array}\right]}^T---\left(45\right)$

Due toCertainly exist, and be not zero, therefore:

det[Q_mn(ω)]=0 (46)

Therefore, one is finally given about the eigenvalue problem solving line flow field.By solving above formula, can be The forcing frequency of system, judges the stability of system by the imaginary part analyzing forcing frequency.

The physical problem of two stage compressor stability is converted into during model inference and has solved line flow field Eigenvalue problem.

det[Q_mn(ω)]_36×36=0

Owing to this equation is often not common consolidation algebraic equation or general simple complex number type transcendental equation, but One complex matrix determinant, therefore, can use the method for singular value decomposition to solve.Singular value decomposition method not only can be accurate The singularity source of diagnostic characteristic matrix, it is also possible to process ill-condition matrix problem and most least square problem, therefore, For the eigenmatrix of two stage compressor stability, the method using singular value decomposition to obtain Matrix condition number is selected to judge square Battle array singularity.

The linear algebra that singular value decomposition method is based on is theoretical:

If X is M × N rank complex matrix, therefore X can be decomposed into M × M rank unitary matrice U, M × N rank diagonal matrix The product of the transposed matrix of S and N × N rank unitary matrice V, i.e.

(X)=(U) * S* (V^T)

Wherein, S=diag (σ 1, σ 2 ..., σ i), σ i >=0 (i=1 ..., r), r=rank (A)；U and V is X respectively Singular vector, S is the singular value of X.If one or more in σ i is zero or the least, then can be determined that Singular Value.Cause This singular value decomposition method can the singularity of clearly judgment matrix.In form, the conditional number of matrix can be defined as maximum Ratio with minimum singular value.In theory, during conditional number infinity, this Singular Value.Conditional number is the biggest, and matrix morbid state is the most serious. Solving this model feature value equation is i.e. to find correct σ i value so that matrix X is unusual.

As specific embodiment, to NASA two-stage fan stability Example Verification.

In order to assess this model to multistage compressor stability stall precursor point prediction ability, this model is applied to first The research of stall inception point when level rotor is NASA two-stage fan (such as Fig. 5) 100% rotating speed of low aspect ratio.Wherein, NASA two Level fan stall experiment carrys out research design rotating speed from 50% by the data gathering radially 11 differences at different erect-positions simultaneously To the perf ormance of 100%.In design conditions, mass flow is 33.248kg/s, and overall pressure ratio is 2.399 and adiabatic efficiency It is 0.849.Table 1 shows that some design parameters and Fig. 6 show overall performance.The geometry of NASA two-stage fan and performance The details of parameter is in NASA reports, detailed experimental data is provided by Urasek et al..

Table 1NASA two-stage fan design parameter

Model needs to input the geometric data of some multi stage axial flow compressors and flow field data, including calming the anger when calculating The derivative etc. of relative inlet angle is joined by the radius of machine, the chord length of blade and pressure, speed, relative total pressure loss coefficient with it Number.NASA experiment gives the flow field data of difference radial position at 11 on each erect-position of passage, owing to model has all Uniform flow, it is assumed that therefore first have to the flow field of each channel cross-section needed is obtained its meansigma methods, comes by mean flow field data Characterize the flow field of channel cross-section.Radial velocity speed to axial and circumferential speed is can be seen that relatively in the experimental result of NASA Little, can ignore, this is consistent with the hypothesis of model, and result of calculation can be made the most accurate.Relatively entering of mode input data Length velocity relation in bicker and use flow field, opposite outlet angle is obtained；It addition, the data that experiment is given are all at two stage compressor Data under lower state, in order to problem is better described, need to extrapolate to verify model to experimental data Reasonability.The extrapolation mode that this research uses is that the variation relation between loss coefficient and flow velocity can pass through known 7 experiments Out, the loss coefficient then reducing flow velocity can solve out from this relation in data matching.

Fig. 7 shows the aerodynamic data variation relation with mass flow of NASA two-stage fan, such as import axial velocity, enters Mouth static pressure, loss and derivative thereof are with the variation relation of flow.It can be seen that along with the reduction of mass flow, import axial velocity Also reducing, pressure slowly rises, and loss coefficient becomes big.

Fig. 8 show the two-stage fan of NASA 100% the predicting the outcome of design work speed.Wherein, x-axle table Showing that mass flow, y-axis represent decay factor DF, it is defined as r_mω_I/(mU₀) or represent relative velocity RS, it is defined as 60 ω_r/(2πmΩ).It should be noted that, along with the carrying out of throttling, mass flow reduces, decay factor is also reducing.Work as flow When being 33.9kg/s, decay factor is through stable marginal value, and the relative rotation speed of the numerical result of this model is 52.5% Design work speed.The relative error of stall starting point is 0.9%, and compared with the result of experiment, this is to close more accurately Reason prediction.

It addition, be investigated the time delay of the impact on stability.Under normal circumstances, it should when experiment measurement obtains Between the accurate value that postpones.And in the present embodiment, can define time delay is:

τ_loss=c/W_c

Wherein, c is the chord length of blade, W_cIt is air-flow at the tangential mean flow of leaf grating.

The research time delay of the impact on two stage compressor stability, shows NASA two stage compressor in figure further Under 100% design work rotating speed, the attenuation quotient of perturbation wave and relative circumferential speed are in the result of calculation of different time delays.Figure 9 represent in not free delay, and in the case of the difference that given time delay and dual-time postpone, NASA two-stage fan exists The perturbation wave decay factor of the design work speed of 100% and the result of calculation of relative circular velocity.Can from result of calculation Going out, the attenuation quotient of perturbation wave is had little to no effect by time delay, and the impact on relative circumferential speed is not the biggest.

It addition, those skilled in the art also can do other changes in spirit of the present invention, certainly, these are according to present invention essence The change that god is done, within all should being included in scope of the present invention.

Claims (10)

1. a Forecasting Methodology for multi stage axial flow compressor perf ormance, including:

According to the situation of rotating stall of axial flow compressor tendency, use small pertubation theory, set up the three dimensional compressible portraying flow field Euler equation；

Use Harmonic Decomposition and dispersion relation, and at the wheel hub and blade tip in each basin, set up boundary condition, wherein, often The solution in one basin is the whirlpool ripple by the pressure disturbance ripple can propagated along upstream and downstream and propagated with mainstream speed, entropy wave group Become；

Rotor and stator use three-dimensional half swash dish model and carries out modelling, and use in interface mode matching technique, conservation fixed Rule and the sign condition of compressor loss property, obtain solving the eigenvalue problem in line flow field；

Obtain the characteristic disturbances frequency of compressibility by solving this feature value problem, and judge system by characteristic disturbances frequency System stability, the criterion of system stability: suppose that in Stability Model all disturbance quantities all contain over time Item e^iωt, wherein forcing frequency ω is plural number, is expressed as ω=ω_R+iω_I；ThereforeImaginary part ω when frequency_I > 0 time, disturbance develop in time be decay, system stability；Otherwise ω_I< 0, disturbance is amplified in time, system unstability.

2. the Forecasting Methodology of multi stage axial flow compressor perf ormance as claimed in claim 1, it is characterised in that multistage axial flow pressure Mechanism of qi is divided into vane region and n omicronn-leaf section, and sets flowing for without viscous thermal insulation compressible flows, and main flow is equal uniform flow, and is conceived to The situation of compressor stall tendency, i.e. linear microvariations are assumed；In n omicronn-leaf section, mainstream speed is two-dimentional, ignores radially Mainstream speed；Disturbance velocity is three-dimensional turbulence；In vane region, the blade flat-plate cascade having camber and torsion is replaced, interior The mainstream speed in portion is one-dimensional, and same ignores radially mainstream speed, it is considered to the impact of Radial Perturbation speed.

3. the Forecasting Methodology of multi stage axial flow compressor perf ormance as claimed in claim 2, it is characterised in that n omicronn-leaf section Governing equation is mainly made up of quality continuity equation, the equation of momentum and energy equation.

$\frac{\&part;\mathrm{\&rho;}}{\&part;t}+\&dtri;\&CenterDot;\left(\mathrm{\&rho;}\stackrel{\&RightArrow;}{V}\right)=0,$

$\frac{D\stackrel{\&RightArrow;}{V}}{Dt}+\frac{1}{{\mathrm{\&rho;}}_0}\&dtri;p=0,$

$\frac{1}{P_0}\frac{DP}{Dt}-\frac{k}{{\mathrm{\&rho;}}_0}\frac{D\mathrm{\&rho;}}{Dt}=0,$

In formula: " 0 " represents average magnitude, k is the specific heat ratio of air, and ρ is density,Representation speed, p is pressure.

4. the Forecasting Methodology of multi stage axial flow compressor perf ormance as claimed in claim 3, it is characterised in that use and separate change Mensuration and series expansion form solves partial differential equation, and the solution obtaining partial differential equation is as follows:

$p^j(x,y,z,t)=\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\underset{n=1}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\&lsqb;{\stackrel{\&OverBar;}{p}}_{mn}^{+j}{e}^{{\mathrm{i\&alpha;}}_{mn}^{+j}(x-x^j)}{\mathrm{\&psi;}}_{mn}^{+j}\left(z\right)+{\stackrel{\&OverBar;}{p}}_{mn}^{-j}{e}^{{\mathrm{i\&alpha;}}_{mn}^{-j}(x-x^j)}{\mathrm{\&psi;}}_{mn}^{-j}\left(z\right)\&rsqb;e^{i({\mathrm{\&beta;}}_{m}y+\mathrm{\&omega;}t)},$

${\mathrm{\&rho;}}^j=\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\underset{n=1}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\left[\begin{array}{c}\frac{1}{{\left(a_0^j\right)}^2}\left({\mathrm{\&psi;}}_{mn}^{+j}\right(z)e^{{\mathrm{i\&alpha;}}_{mn}^{+j}(x-x^j)}{\stackrel{\&OverBar;}{p}}_{mn}^{+j}+{\mathrm{\&psi;}}_{mn}^{-j}(z\left)e^{{\mathrm{i\&alpha;}}_{mn}^{-j}(x-x^j)}{\stackrel{\&OverBar;}{p}}_{mn}^{-j}\right)\\ +{\stackrel{\&OverBar;}{\mathrm{\&rho;}}}_{vmn}^{+j}{\mathrm{\&psi;}}_{vmn}^{+j}\left(z\right)e^{-i\frac{\mathrm{\&omega;}+{\mathrm{\&beta;}}_{m}V}{U}(x-x^j)}\end{array}\right]e^{i({\mathrm{\&beta;}}_{m}y+\mathrm{\&omega;}t)},$

$u^j=\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\underset{n=1}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\left[\begin{array}{c}-\frac{1}{{\mathrm{\&rho;}}_0^j}(\frac{{\mathrm{\&alpha;}}_{mn}^{+j}{\mathrm{\&psi;}}_{mn}^{+j}\left(z\right)e^{{\mathrm{i\&alpha;}}_{mn}^{+j}(x-x^j)}{\stackrel{\&OverBar;}{p}}_{mn}^{+j}}{(\mathrm{\&omega;}+{\mathrm{\&alpha;}}_{mn}^{+j}{U}^j+{\mathrm{\&beta;}}_m{V}^j)}+\frac{{\mathrm{\&alpha;}}_{mn}^{-j}{\mathrm{\&psi;}}_{mn}^{-j}\left(z\right)e^{{\mathrm{i\&alpha;}}_{mn}^{-j}(x-x^j)}{\stackrel{\&OverBar;}{p}}_{mn}^{-j}}{(\mathrm{\&omega;}+{\mathrm{\&alpha;}}_{mn}^{-j}{U}^j+{\mathrm{\&beta;}}_m{V}^j)})\\ +(\frac{{\mathrm{\&beta;}}_{m}U{\stackrel{\&OverBar;}{v}}_{vmn}^{+j}}{\mathrm{\&omega;}+{\mathrm{\&beta;}}_{m}V}-\frac{{\mathrm{ik}}_{vmn}^{+j}U{\stackrel{\&OverBar;}{w}}_{vmn}^{+j}}{\mathrm{\&omega;}+{\mathrm{\&beta;}}_{m}V}){\mathrm{\&psi;}}_{vmn}^{+j}\left(z\right)e^{-i\frac{\mathrm{\&omega;}+{\mathrm{\&beta;}}_{m}V}{U}(x-x^j)}\end{array}\right]e^{i({\mathrm{\&beta;}}_{m}y+\mathrm{\&omega;}t)},$

$v^j=\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\underset{n=1}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\left[\begin{array}{c}-\frac{1}{{\mathrm{\&rho;}}_0^j}(\frac{{\mathrm{\&beta;}}_m{\mathrm{\&psi;}}_{mn}^{+j}\left(z\right)e^{{\mathrm{i\&alpha;}}_{mn}^{+j}(x-x^j)}{\stackrel{\&OverBar;}{p}}_{mn}^{+j}}{(\mathrm{\&omega;}+{\mathrm{\&alpha;}}_{mn}^{+j}{U}^j+{\mathrm{\&beta;}}_m{V}^j)}+\frac{{\mathrm{\&beta;}}_m{\mathrm{\&psi;}}_{mn}^{-j}\left(z\right)e^{{\mathrm{i\&alpha;}}_{mn}^{-j}(x-x^j)}{\stackrel{\&OverBar;}{p}}_{mn}^{-j}}{(\mathrm{\&omega;}+{\mathrm{\&alpha;}}_{mn}^{-j}{U}^j+{\mathrm{\&beta;}}_m{V}^j)})\\ +{\stackrel{\&OverBar;}{v}}_{vmn}^{+j}{\mathrm{\&psi;}}_{vmn}^{+j}\left(z\right)e^{-i\frac{\mathrm{\&omega;}+{\mathrm{\&beta;}}_{m}V}{U}(x-x^j)}\end{array}\right]e^{i({\mathrm{\&beta;}}_{m}y+\mathrm{\&omega;}t)},$

$w^j=\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\underset{n=1}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\left[\begin{array}{c}\frac{1}{{\mathrm{\&rho;}}_0^j}(\frac{k_{mn}^{+j}{\mathrm{\&phi;}}_{mn}^{+j}\left(z\right)e^{{\mathrm{i\&alpha;}}_{mn}^{+j}(x-x^j)}{\stackrel{\&OverBar;}{p}}_{mn}^{+j}}{i(\mathrm{\&omega;}+{\mathrm{\&alpha;}}_{mn}^{+j}{U}^j+{\mathrm{\&beta;}}_m{V}^j)}+\frac{k_{mn}^{-j}{\mathrm{\&phi;}}_{mn}^{-j}\left(z\right)e^{{\mathrm{i\&alpha;}}_{mn}^{-j}(x-x^j)}{\stackrel{\&OverBar;}{p}}_{mn}^{-j}}{i(\mathrm{\&omega;}+{\mathrm{\&alpha;}}_{mn}^{-j}{U}^j+{\mathrm{\&beta;}}_m{V}^j)})\\ +{\stackrel{\&OverBar;}{w}}_{vmn}^{+j}{\mathrm{\&phi;}}_{vmn}^{+j}\left(z\right)e^{-i\frac{\mathrm{\&omega;}+{\mathrm{\&beta;}}_{m}V}{U}(x-x^j)}\end{array}\right]e^{i({\mathrm{\&beta;}}_{m}y+\mathrm{\&omega;}t)},$

Wherein, " m " is circumference mode, and " n " is radial mode shape；" ω " is the forcing frequency of compressibility to be asked, and it is one Complex frequency, its real part ω_rRepresent the actual frequency of disturbance, imaginary part ω_iRepresent the damping of disturbance, be also that this model judges compression The key parameter of system stability；P, ρ, u, v, w and U, V, α_mn、β_mRepresent respectively pressure, density, axial velocity, circumferential speed, The microvariations amount of radial velocity and axial mainstream speed, circumference mainstream speed, axial wave number, circumference wave number, " j " represents jth On-bladed region, "+" represent disturbance and downstream propagate, "-" represents disturbance and upstream propagates.

5. the Forecasting Methodology of multi stage axial flow compressor perf ormance as claimed in claim 4, it is characterised in that give in sclerine face The boundary condition gone out is for without penetrating, without sliding and zero vibration condition, by applying the form of trigonometric function progression, representing radially Characteristic function, following ψ and φ:

${\mathrm{\&psi;}}_{mn}^{\&PlusMinus;j}\left(z\right)={\mathrm{\&psi;}}_{vmn}^{\&PlusMinus;j}\left(z\right)=\cos \left(k_{vmn}^{\&PlusMinus;j}z\right);$

${\mathrm{\&phi;}}_{mn}^{\&PlusMinus;j}\left(z\right)={\mathrm{\&phi;}}_{vmn}^{\&PlusMinus;j}\left(z\right)=sin\left(k_{vmn}^{\&PlusMinus;j}z\right);$

Radially wave number is:

$k_{mn}=\frac{n\mathrm{\&pi;}}{h},(n=0,1,2,...N).$

6. the Forecasting Methodology of multi stage axial flow compressor perf ormance as claimed in claim 5, it is characterised in that axially upward Trip or the axial wave number downstream propagatedExpression formula is:

${\mathrm{\&alpha;}}_{mn}^{\&PlusMinus;j}=\frac{M_x({\mathrm{\&beta;}}_m{M}_y+\frac{\mathrm{\&omega;}}{a_0})\&PlusMinus;\sqrt{{({\mathrm{\&beta;}}_m{M}_y+\frac{\mathrm{\&omega;}}{a_0})}^2+(1-M_x^2)\&lsqb;{\mathrm{\&beta;}}_m^2+{\left(k_{mn}^{+j}\right)}^2\&rsqb;}}{(1-M_x^2)},$

Wherein, β_mExpression circumference wave number:

${\mathrm{\&beta;}}_m=\frac{m}{r_m};$

r_mIt is the mean radius in blade grid passage, M_x、M_yRefer to the Mach number component at axial and circumferential, a₀Represent the biography of sound Broadcast speed.

7. the Forecasting Methodology of multi stage axial flow compressor perf ormance as claimed in claim 6, it is characterised in that leaf area is adopted Swashing dish model with one-dimensional half, comprise one-dimensional tangential flowing in blade path, absolute coordinate system is that (x, y, z), with moving axes System (x ', y ', z '), and the tangential coordinate system of servo-actuated leaf grating is that (ξ, η z), do not consider in the disturbance quantitative change that vertical leaf grating is tangential Changing, therefore the tangential coordinate system of leaf grating is that (ξ, z), the governing equation of vane region includes quality continuity equation, the tangential equation of momentum, footpath Form to the equation of momentum and energy equation, with W_cRepresenting tangential average speed, q represents tangential disturbance velocity, and w represents that radial direction is disturbed Dynamic speed, the governing equation of the vane region of foundation is as follows:

$\frac{\&part;\mathrm{\&rho;}}{\&part;t}+W_c\frac{\&part;\mathrm{\&rho;}}{\&part;\mathrm{\&xi;}}+{\mathrm{\&rho;}}_0(\frac{\&part;q}{\&part;\mathrm{\&xi;}}+\frac{\&part;w}{\&part;z})=0;$

$\frac{\&part;q}{\&part;t}+W_c\frac{\&part;q}{\&part;\mathrm{\&xi;}}=-\frac{1}{{\mathrm{\&rho;}}_0}\frac{\&part;p}{\&part;\mathrm{\&xi;}};$

$\frac{\&part;w}{\&part;t}+W_c\frac{\&part;w}{\&part;\mathrm{\&xi;}}=-\frac{1}{{\mathrm{\&rho;}}_0}\frac{\&part;p}{\&part;z};$

$\frac{1}{P_0}(\frac{\&part;p}{\&part;t}+W_c\frac{\&part;p}{\&part;\mathrm{\&xi;}})+k(\frac{\&part;q}{\&part;\mathrm{\&xi;}}+\frac{\&part;w}{\&part;z})=0.$

8. the Forecasting Methodology of multi stage axial flow compressor perf ormance as claimed in claim 7, it is characterised in that vane region is pressed The solution of power, density, tangential speed and radial velocity disturbance quantity is:

$p_c^k(x,y^{\&prime;},z,t)=\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\underset{n=1}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\&lsqb;e^{{\mathrm{i\&alpha;}}_{cmn}^{+k}(x-x^k)}{\mathrm{\&psi;}}_{cmn}^{+k}\left(z\right){\stackrel{\&OverBar;}{p}}_{cmn}^{+k}+e^{{\mathrm{i\&alpha;}}_{cmn}^{-k}(x-x^k)}{\mathrm{\&psi;}}_{cmn}^{-k}\left(z\right){\stackrel{\&OverBar;}{p}}_{cmn}^{-k}\&rsqb;e^{i(\mathrm{\&omega;}-m\mathrm{\&Omega;})t+{\mathrm{i\&beta;}}_m{y}^{\&prime;}};$

${\mathrm{\&rho;}}_c^k(x,y^{\&prime;},z,t)=\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\underset{n=1}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\left[\begin{array}{c}\frac{1}{{\left(a_0^k\right)}^2}\left({\mathrm{\&psi;}}_{cmn}^{+k}\left(z\right)e^{{\mathrm{i\&alpha;}}_{cmn}^{+k}(x-x^k)}{\stackrel{\&OverBar;}{p}}_{cmn}^{+k}+{\mathrm{\&psi;}}_{cmn}^{-k}\left(z\right)e^{{\mathrm{i\&alpha;}}_{cmn}^{-k}(x-x^k)}{\stackrel{\&OverBar;}{p}}_{cmn}^{-k}\right)\\ +{\stackrel{\&OverBar;}{\mathrm{\&rho;}}}_{cvmn}^{+k}{\mathrm{\&phi;}}_{cvmn}^{+k}\left(z\right)e^{-i\frac{(\mathrm{\&omega;}-m\mathrm{\&Omega;})+{\mathrm{\&beta;}}_m{W_c}^k{\mathrm{sin\&theta;}}^k}{{W_c}^k{\mathrm{cos\&theta;}}^k}(x-x^k)}\end{array}\right]e^{i(\mathrm{\&omega;}-m\mathrm{\&Omega;})t+{\mathrm{i\&beta;}}_m{y}^{\&prime;}};$

$q_c^k(x,y^{\&prime;},z,t)=\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\underset{n=1}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\left[\begin{array}{c}-\frac{1}{{\mathrm{\&rho;}}_0^k}\left(\begin{array}{c}\frac{({\mathrm{\&alpha;}}_{cmn}^{+k}\cos \mathrm{\&theta;}+{\mathrm{\&beta;}}_m\sin \mathrm{\&theta;})e^{{\mathrm{i\&alpha;}}_{cmn}^{+k}(x-x^k)}{\mathrm{\&psi;}}_{cmn}^{+k}\left(z\right){\stackrel{\&OverBar;}{p}}_{cmn}^{+k}}{\&lsqb;(\mathrm{\&omega;}-m\mathrm{\&Omega;})+W_c({\mathrm{\&alpha;}}_{cmn}^{+k}\cos \mathrm{\&theta;}+{\mathrm{\&beta;}}_m\sin \mathrm{\&theta;})\&rsqb;}\\ +\frac{({\mathrm{\&alpha;}}_{cmn}^{-k}\cos \mathrm{\&theta;}+{\mathrm{\&beta;}}_m\sin \mathrm{\&theta;})e^{{\mathrm{i\&alpha;}}_{cmn}^{-k}(x-x^k)}{\mathrm{\&psi;}}_{cmn}^{-k}\left(z\right){\stackrel{\&OverBar;}{p}}_{cmn}^{-k}}{\&lsqb;(\mathrm{\&omega;}-m\mathrm{\&Omega;})+W_c({\mathrm{\&alpha;}}_{cmn}^{-k}\cos \mathrm{\&theta;}+{\mathrm{\&beta;}}_m\sin \mathrm{\&theta;})\&rsqb;}\end{array}\right)\\ -\frac{{\mathrm{ik}}_{cvmn}^{+k}{W_c}^k}{(\mathrm{\&omega;}-m\mathrm{\&Omega;})}{e}^{-i\frac{(\mathrm{\&omega;}-m\mathrm{\&Omega;})+{\mathrm{\&beta;}}_m{W_c}^k{\mathrm{sin\&theta;}}^k}{{W_c}^k{\mathrm{cos\&theta;}}^k}(x-x^k)}{\mathrm{\&psi;}}_{cvmn}^{+k}\left(z\right){\stackrel{\&OverBar;}{w}}_{cvmn}^{+k}\end{array}\right]e^{i(\mathrm{\&omega;}-m\mathrm{\&Omega;})t+{\mathrm{i\&beta;}}_m{y}^{\&prime;}};$

$w_c^k(x,y^{\&prime;},z,t)=\underset{m=-\mathrm{\&infin;}}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\underset{n=1}{\overset{+\mathrm{\&infin;}}{\&Sigma;}}\left[\begin{array}{c}\frac{1}{{\mathrm{\&rho;}}_0}\left(\begin{array}{c}\frac{k_{cmn}^{+k}{e}^{-{\mathrm{i\&alpha;}}_{cmn}^{+k}(x-x^k)}{\mathrm{\&phi;}}_{cmn}^{+k}\left(z\right){\stackrel{\&OverBar;}{p}}_{cmn}^{+k}}{i\&lsqb;(\mathrm{\&omega;}-m\mathrm{\&Omega;})+W_c({\mathrm{\&alpha;}}_{cmn}^{+k}\cos \mathrm{\&theta;}+{\mathrm{\&beta;}}_m\sin \mathrm{\&theta;})\&rsqb;}\\ +\frac{k_{cmn}^{+k}{e}^{-{\mathrm{i\&alpha;}}_{cmn}^{-k}(x-x^k)}{\mathrm{\&phi;}}_{cmn}^{-k}\left(z\right){\stackrel{\&OverBar;}{p}}_{cmn}^{-k}}{i\&lsqb;(\mathrm{\&omega;}-m\mathrm{\&Omega;})+W_c({\mathrm{\&alpha;}}_{cmn}^{-k}\cos \mathrm{\&theta;}+{\mathrm{\&beta;}}_m\sin \mathrm{\&theta;})\&rsqb;}\end{array}\right)\\ +{\stackrel{\&OverBar;}{w}}_{cvmn}^{+k}{\mathrm{\&phi;}}_{cvmn}^{+k}\left(z\right)e^{-i\frac{(\mathrm{\&omega;}-m\mathrm{\&Omega;})+{\mathrm{\&beta;}}_m{W_c}^k{\mathrm{sin\&theta;}}^k}{{W_c}^k{\mathrm{cos\&theta;}}^k}(x-x^k)}\end{array}\right]e^{i(\mathrm{\&omega;}-m\mathrm{\&Omega;})t+{\mathrm{i\&beta;}}_m{y}^{\&prime;}};$

Wherein, in formulaIt is the velocity of sound in k row's leaf grating, M_cBeing Mach number tangential under relative coordinate system, Ω represents turning of rotor Frequently, W_cRepresent the mainstream speed that leaf grating is tangential, axial wave number α_cmnExpression formula be:

${\mathrm{\&alpha;}}_{cmn}^{\&PlusMinus;k}cos\mathrm{\&theta;}+{\mathrm{\&beta;}}_{m}sin\mathrm{\&theta;}=\frac{\frac{M_c}{a_{0c}^k}(\mathrm{\&omega;}-m\mathrm{\&Omega;})\&PlusMinus;\sqrt{\frac{{(\mathrm{\&omega;}-m\mathrm{\&Omega;})}^2}{{\left(a_{0c}^k\right)}^2}-(1-{M_c}^2){\left(k_{cmn}^{\&PlusMinus;k}\right)}^2}}{(1-{M_c}^2)};$

Wherein, k_cmnIt is radial direction characteristic function ψ_cmnThe eigenvalue of (z)；Radially the relational expression between characteristic function is as follows:

${\mathrm{\&psi;}}_{cmn}^{\&PlusMinus;k}={\mathrm{\&psi;}}_{cvmn}^{+k}=cos\left(k_{cmn}^{+k}z\right);$

${\mathrm{\&phi;}}_{cmn}^{\&PlusMinus;k}={\mathrm{\&phi;}}_{cvmn}^{+k}=sin\left(k_{cvmn}^{+k}z\right);$

Radially wave number is:

$k_{cmn}=\frac{n\mathrm{\&pi;}}{h},(n=0,1,2,...N).$

9. the Forecasting Methodology of multi stage axial flow compressor perf ormance as claimed in claim 8, it is characterised in that assuming that flowing Turn to and loss occurrence edge in front of the blade, then leading edge matching condition is as follows:

${\mathrm{\&rho;}}^j{U}^j+{\mathrm{\&rho;}}_0^j{u}^j=({\mathrm{\&rho;}}^k{U}^k+{\mathrm{\&rho;}}_0^k{q}^k){\mathrm{cos\&theta;}}^k;$

$T_t^{\&prime;j}=\frac{p^j}{{\mathrm{R\&rho;}}_0}-\frac{{\left(a_0^j\right)}^2}{{\mathrm{kR\&rho;}}_0}{\mathrm{\&rho;}}^j+\frac{1}{c_p}(U^j{u}^j+V_r^j{v}^j)=\frac{p^k}{{\mathrm{R\&rho;}}_0}-\frac{{\left(a_0^k\right)}^2}{{\mathrm{kR\&rho;}}_0}{\mathrm{\&rho;}}^k+\frac{W_c^k{q}^k}{c_p}=T_t^{\&prime;k};$

w^k=w^j+1；

${p_t}^j-{p_t}^k=\frac{1}{1+{\mathrm{i\&omega;\&tau;}}_{loss}}\left[\begin{array}{c}\frac{1}{2}{\mathrm{\&xi;}}_s^k{\mathrm{\&rho;}}^j{\left(W^j\right)}^2+{\mathrm{\&xi;}}_s^k{\mathrm{\&rho;}}_0^j\&lsqb;U^j{u}^j+V_r^j{v}^j\&rsqb;\\ +\frac{1}{2U^j}\frac{\&part;{\mathrm{\&xi;}}_s^k}{\&part;{\mathrm{tan\&beta;}}^k}{\mathrm{\&rho;}}_0^j{\left(W^j\right)}^2(v^j-u^j{\mathrm{tan\&beta;}}^k)\end{array}\right];$

Wherein, T_t' representing stagnation temperature disturbance, R is air constant,For relative circumferential speed, τ_lossIt is time delay,It is relative Total pressure loss coefficient:

${\mathrm{\&xi;}}_s^k=\frac{P_t^j-P_t^{j+1}}{{\mathrm{\&rho;}}^j{\left(W^j\right)}^2/2};$

The stagnation pressure disturbance of n omicronn-leaf section is:

$p_t^j=(S_1^j-\frac{k{\left(M^j\right)}^2}{2}{S}_2^j)p^j+\frac{{\left(W^j\right)}^2}{2}{S}_2^j{\mathrm{\&rho;}}^j+{\mathrm{\&rho;}}_0^j{U}^j{S}_2^j{u}^j+{\mathrm{\&rho;}}_0^j{S}_2^j{V}_r^j{v}^j;$

Wherein, M represents Mach number,WithIt is respectively as follows:

$\begin{array}{cc}{S}_1^j={\&lsqb;1+\frac{\mathrm{\&kappa;}-1}{2}{\left(M^j\right)}^2\&rsqb;}^{\frac{\mathrm{\&kappa;}}{\mathrm{\&kappa;}-1}}& S_2^j={\&lsqb;1+\frac{\mathrm{\&kappa;}-1}{2}{\left(M^j\right)}^2\&rsqb;}^{\frac{1}{\mathrm{\&kappa;}-1}}\end{array};$

The stagnation pressure disturbance of vane region is:

$p_t^k=(S_1^k-\frac{k{\left(M_c^k\right)}^2}{2}{S}_2^k)p^k+\frac{{\left(W_c^k\right)}^2}{2}{S}_2^k{\mathrm{\&rho;}}^k+{\mathrm{\&rho;}}_0^k{S}_2^k{W}_c^k{q}^k;$

Wherein,

$\begin{array}{cc}{S}_1^k={\&lsqb;1+\frac{\mathrm{\&kappa;}-1}{2}{\left(M_c^k\right)}^2\&rsqb;}^{\frac{\mathrm{\&kappa;}}{\mathrm{\&kappa;}-1}}& S_2^k={\&lsqb;1+\frac{\mathrm{\&kappa;}-1}{2}{\left(M_c^k\right)}^2\&rsqb;}^{\frac{1}{\mathrm{\&kappa;}-1}}\end{array}.$

10. the Forecasting Methodology of multi stage axial flow compressor perf ormance as claimed in claim 9, it is characterised in that solve and obtain One equation group closed:

$Q_{mn}{\left(\mathrm{\&omega;}\right)}_{(9K\&times;9K)}.{\stackrel{\&OverBar;}{X}}_{mn\left(9K\right)}=0,$

Wherein, K is leaf row；

For two stage compressor, Q_mn(ω) andRespectively:

$Q_{mn}\left(\mathrm{\&omega;}\right)={\left[\begin{array}{cccccccccccccc}{C}_{1,1}& C_{1,2}& \mathrm{...}& C_{1,5}& & & & & & & & & & \\ .& .& & .& & & & & & & & & & \\ .& .& & .& & & & & & & & & & \\ .& .& & .& & & & & & & & & & \\ C_{4,1}& C_{4,2}& \mathrm{...}& C_{4,5}& & & & & & & & & & \\ & C_{5,2}& \mathrm{...}& C_{5,5}& C_{5,6}& \mathrm{...}& C_{5,10}& & & & & & & \\ & .& & .& .& & .& & & & & & & \\ & .& & .& .& & .& & & & & & & \\ & .& & .& .& & .& & & & & & & \\ & C_{9,2}& \mathrm{...}& C_{9,5}& C_{9,6}& \mathrm{...}& C_{9,10}& & & & & & & \\ & & & & & & \mathrm{...}& \mathrm{...}& \mathrm{...}& & & & & \\ & & & & & & & .& & & & & & \\ & & & & & & & .& & & & & & \\ & & & & & & & .& & & & & & \\ & & & & & & & .& & & & & & \\ & & & & & & & .& & & & & & \\ & & & & & & & .& & & & & & \\ & & & & & & & & C_{32,29}& \mathrm{...}& C_{32,32}& C_{32,33}& \mathrm{...}& C_{32,36}\\ & & & & & & & & .& & .& .& & .\\ & & & & & & & & .& & .& .& & .\\ & & & & & & & & .& & .& .& & .\\ & & & & & & & & C_{36,29}& \mathrm{...}& C_{36,32}& C_{36,33}& \mathrm{...}& C_{36,36}\end{array}\right]}_{mn},$

${\stackrel{\&OverBar;}{X}}_{mn}={\left[\begin{array}{ccccc}{\stackrel{\&OverBar;}{p}}_{mn}^{-1}& {\stackrel{\&OverBar;}{p}}_{cmn}^{+1}& \mathrm{...}& {\stackrel{\&OverBar;}{v}}_{vmn}^{+5}& {\stackrel{\&OverBar;}{v}}_{vmn}^{+5}\end{array}\right]}^T,$

Due toCertainly exist, and be not zero, therefore:

det[Q_mn(ω)]=0,

By solving above formula, obtain the forcing frequency of system, judged the stability of system by the imaginary part analyzing forcing frequency.