CN110848166A  Axial flow compressor surge frequency prediction method  Google Patents
Axial flow compressor surge frequency prediction method Download PDFInfo
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 CN110848166A CN110848166A CN201911106649.0A CN201911106649A CN110848166A CN 110848166 A CN110848166 A CN 110848166A CN 201911106649 A CN201911106649 A CN 201911106649A CN 110848166 A CN110848166 A CN 110848166A
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 F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
 F04—POSITIVE  DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
 F04D—NONPOSITIVEDISPLACEMENT PUMPS
 F04D27/00—Control, e.g. regulation, of pumps, pumping installations or pumping systems specially adapted for elastic fluids
 F04D27/001—Testing thereof; Determination or simulation of flow characteristics; Stall or surge detection, e.g. condition monitoring

 F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
 F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01F04
 F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NONPOSITIVEDISPLACEMENT MACHINES OR ENGINES, GASTURBINES OR JETPROPULSION PLANTS
 F05D2260/00—Function
 F05D2260/81—Modelling or simulation

 F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
 F05—INDEXING SCHEMES RELATING TO ENGINES OR PUMPS IN VARIOUS SUBCLASSES OF CLASSES F01F04
 F05D—INDEXING SCHEME FOR ASPECTS RELATING TO NONPOSITIVEDISPLACEMENT MACHINES OR ENGINES, GASTURBINES OR JETPROPULSION PLANTS
 F05D2260/00—Function
 F05D2260/82—Forecasts
Abstract
The invention discloses a method for predicting the surge frequency of an axial flow compressor, which is used for solving the technical problem of poor practicability of the conventional method for measuring the surge frequency of the axial flow compressor. The technical scheme includes that physical and geometric modeling is firstly carried out on an experiment table of the axial flow compressor to obtain a conservation control equation of a corresponding model, a numerical method is used for solving, and a Fourier is used for analyzing a numerical result under a stall passing working condition, so that the surge frequency of the axial flow compressor is obtained. The simulation model of the axial flow compressor system is established, so that the construction of an experiment platform and a data acquisition system is avoided, the experiment data measurement process is converted into the process of obtaining parameter values through a numerical solution, then the numerical results are directly used for data analysis and processing, the surge frequency of the compressor is analyzed by Fourier transform, a large amount of labor and material cost is saved, and the practicability is good.
Description
Technical Field
The invention belongs to the field of gas turbine engines, and particularly relates to a method for predicting the surge frequency of an axial flow compressor.
Background
The document "fast fourier transform and wavelet transform analysis of compressor surge sound signals, energy technology, 2010, Vol31, No.3, p 125128" discloses a method for analyzing and processing surge signal data obtained by experiments by using fast fourier transform and wavelet transform. The method is characterized in that on the basis of obtaining compressor surge data through experiments, after the frequency spectrum analysis is carried out on the test data through fast Fourier transform, the frequency of the compressor surge is proved to be below 50 hz. Then, the data is further processed by utilizing wavelet transformation, and a sound characteristic signal for representing that the compressor enters surge is obtained. The surge frequency obtained by the method is accurate and reliable, and a good theoretical basis and basis are provided for monitoring the state of the compressor and diagnosing faults by using sound signals in actual production. However, the method for obtaining the surge frequency in the document needs to design experiments in advance, a large number of sensors and equipment for acquiring signals, and depends on the experimental environment, and more importantly, the method has high cost of manpower and material resources and poor practicability.
Disclosure of Invention
In order to overcome the defect that the existing axial flow compressor surge frequency measuring method is poor in practicability, the invention provides a method for predicting the surge frequency of an axial flow compressor. The method comprises the steps of firstly, carrying out physical and geometric modeling on an experiment table of the axial flow compressor to obtain a conservation control equation of a corresponding model, solving by using a numerical method, and then analyzing a numerical result under a stall passing working condition by using Fourier, so as to obtain the surge frequency of the axial flow compressor. The simulation model of the axial flow compressor system is established, so that the construction of an experiment platform and a data acquisition system is avoided, the experiment data measurement process is converted into the process of obtaining parameter values through a numerical solution, then the numerical results are directly used for data analysis and processing, the surge frequency of the compressor is analyzed by Fourier transform, a large amount of labor and material cost is saved, and the practicability is good.
The technical scheme adopted by the invention for solving the technical problems is as follows: the method for predicting the surge frequency of the axial flow compressor is characterized by comprising the following steps of:
step one, establishing a physical and geometric model of an axial flow compressor;
measuring the geometric dimension of the actual axial flow compressor, replacing the compressor with a swash plate to generate pressure rise, replacing an inlet pipeline and an outlet pipeline of the compressor with a pipeline with a uniform section, simulating a backpressure environment by a gas collection cavity, controlling the flow by a throttle valve, and setting the Mach number of an inlet to obtain an axial flow compressor simulation model.
Step two, writing a control equation according to the established axial flow compressed air simulation model:
a. flow disturbances in the compressor;
pressure rise of a single blade row by unsteady flow:obtaining the pressure rise of the Nstage compressor as follows:then define the circumferential average of φ:here, the circumferential flow coefficient Φ and the tangential velocity coefficient h are represented as Φ (ξ) + g (ξ, θ), h ═ h (ξ, θ), where θ represents the circumferential angle, ξ represents the rotor rotation radian, Φ represents the axial flow coefficient, Φ represents the circumferential average of the axial flow coefficient, F (Φ) represents the axisymmetric steadystate performance of the blade row, τ represents the hysteresis constant, a ≡ R/(N τ U) represents the reciprocal of the blade passage time hysteresis parameter, U represents the rotation speed at the average radius, Δ P represents the outlet pressure minus the inlet pressure, h represents the circumferential velocity coefficient, and t represents time.
b. Flow disturbances in the inlet duct and the guide vanes;
introducing a velocity potentialAnd disturbance velocity potentialThen velocity potentialExpressed as:the pressure rise far upstream to the guide vane inlet at this time is expressed as:wherein P is_{T}The total pressure at the inlet is shown,the potential of the speed is represented by,representing the disturbance velocity potential, η axial position coordinates, ξ rotor radian, phi axial flow coefficient, phi circumferential average value of the axial flow coefficient, l_{1}The inlet duct length is indicated.
c. Flow disturbances in the outlet duct and the outlet guide vanes;
definition of pressure coefficientThen at the downstream pipe outlet (η ═ l)_{E}) Comprises the following steps:then introducing a parameter m to obtain the static pressure change in the outlet pipeline:wherein p is_{s}Representing the static pressure in the collecting chamber, p representing the static pressure in the outlet duct, l_{E}Representing the dimensionless length, l, of the downstream pipe_{T}The outlet duct length is indicated and m is the compressor duct flow parameter.
d. Static pressure rise to the tail end of the outlet of the compressor;
the static pressure rise from the inlet to the end of the outlet pipe is:
defining the effective length l of compressor and its upstream and downstream pipelines_{C}And a:due to the disturbance velocity potential at the upstream of the compressorSatisfies the laplace equation:then, when it is expanded into a fourier series and only the first order term is considered, there are:and introducing a variable Y:the total pressure rise was obtained as:
wherein p is_{s}Representing the static pressure in the gascollecting chamber, p_{T}Representing total inlet pressure, N representing compressor stage number, phi representing axial flow coefficient, phi representing circumferential average value of axial flow coefficient, l_{E}Representing the dimensionless length, l, of the downstream pipe_{1}Inlet duct length, m representing a compressor duct flow parameter, a ≡ R/(Ntau U) representing the inverse of a vane passage time lag parameter, Y representing compressor inlet disturbance potential, K_{G}The inlet guide vane loss coefficient is expressed.
e. Flow in the gas collection cavity and the exhaust valve pipeline;
the flow equation in the gas collection cavity and the exhaust pipeline is as follows:
and using parabolic equationsTo represent the pressure drop characteristic of the throttle valve. The axial flow coefficient phi of the downstream pipe_{T}Expressed as:then, integrating in the circumferential direction:wherein F_{T}Representing a function of the throttle characteristic, [ phi ]_{T}Represents the flow coefficient of the throttle pipe,/_{c}The effective length of the pipeline upstream and downstream of the compressor is shown, and psi represents the total static pressure rise coefficient.
f. A total set of governing equations;
and (3) the equations are arranged to obtain a complete control equation set of the compression system model:
and (3) carrying out order reduction processing on the equation set by using a Galerkin method, namely carrying out Fourier expansion on the variable Y, and replacing the variable Y by using a first order term to obtain a 1order differential equation set related to time:
where Ψ represents the total static pressure rise coefficient, Φ_{T}Expressing the flow coefficient of the throttling pipeline, Y expressing the disturbance potential of the inlet of the compressor, H and W expressing the relevant parameters of the axisymmetric characteristic line, F_{T}To representA throttling characteristic function, phi represents the axial flow coefficient of the compressor, J represents the square of the circumferential amplitude of the axial flow coefficient, l_{c}Indicating the effective length of the upstream and downstream conduits of the compressor, psi_{c0}The total static pressure rise coefficient under zero flow conditions is shown.
Solving a control equation set by utilizing a fourorder Runge Kutta method;
selecting a threedimensional axisymmetric characteristic line as an initial characteristic line of the compressor, and then solving a control equation set of a simulation model of the compression system by using a fourorder RK numerical method, wherein the formula is as follows:
after solving the control equation set, the B parameter is continuously changed until the critical B parameter is found. And then selecting a plurality of different parameters B on the side larger than the critical parameter B, and calculating the change condition of the flow coefficient or the total static pressure rise coefficient of the compressor along with time under the surge working condition.
Step four, calculating surge frequency;
and D, processing the change data of the compressor flow coefficient or the total static pressure rise coefficient along with time under the surge working conditions corresponding to the different B parameters obtained in the step three by utilizing discrete Fourier transform to obtain the surge frequency under the different B parameters.
The invention has the beneficial effects that: the method comprises the steps of firstly, carrying out physical and geometric modeling on an experiment table of the axial flow compressor to obtain a conservation control equation of a corresponding model, solving by using a numerical method, and then analyzing a numerical result under a stall passing condition by using Fourier, so as to obtain the surge frequency of the axial flow compressor. The simulation model of the axial flow compressor system is established, so that the construction of an experiment platform and a data acquisition system is avoided, the experiment data measurement process is converted into the process of obtaining parameter values through a numerical solution, then the numerical results are directly used for data analysis and processing, the surge frequency of the compressor is analyzed by Fourier transform, a large amount of labor and material cost is saved, and the practicability is good.
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
Drawings
FIG. 1 is a schematic view of an axial flow compressor experimental bench for the method of the present invention.
Fig. 2 is a schematic diagram of a physical and geometric model of the axial flow compression system constructed according to fig. 1.
Fig. 3 is a graph of the total static coefficient of the compressor over time for different B parameters calculated according to the simulation model of the compression system shown in fig. 2.
Fig. 4 is a graphical representation of frequency results after discrete fourier transformation from the data of fig. 3.
Detailed Description
Reference is made to fig. 14. The method for predicting the surge frequency of the axial flow compressor comprises the following specific steps:
1. establishing a physical and geometric model of the axial flow compressor;
the geometric dimensions of an actual axial flow compressor are measured firstly, and comprise the length of an inlet and outlet pipeline, the section area, the lengthdiameter ratio of the compressor, the volume of a gas collection cavity and the like, and then the geometric dimensions are simplified into a compression system model, namely a swash plate is used for replacing the compressor to generate pressure rise, the uniformsection pipeline is used for replacing the inlet and outlet pipeline of the compressor, a large gas collection cavity is used for simulating a backpressure environment, and a throttle valve is used for controlling the flow. Then, assuming that the mach number at the inlet is low and the gas in the compressor duct is incompressible, the process can be summarized as a simulation model from the actual compression system of fig. 1 to the compression system of fig. 2.
b) Column writing a model control equation set;
after a compression system model is established, a control equation set is established according to the MooreGreitzer theory. The main process is as follows:
① flow disturbances in the compressor;
first, all parameters are dimensionless to obtain a tangential coordinate θ, an axial coordinate η, and a dimensionless time coordinate ξ.
In which there is also a nonstationarity between the individual rotor and stator, it can be expressed as:
then, the pressure rise of the Nstage compressor under the unsteady condition can be obtained as follows:
next, the circumferential average of φ is defined as:
the circumferential flow coefficient phi and the tangential velocity coefficient h can be expressed as phi (ξ) + g (ξ, theta), h (ξ, theta), where theta represents the circumferential angle, η represents the axial coordinate value, ξ represents the rotor turning camber, phi represents the axial flow coefficient, phi represents the circumferential average of the axial flow coefficient, F (phi) represents the axisymmetric steadystate performance of the blade row, tau represents the hysteresis constant, a ≡ R/(N tau U) represents the inverse of the blade passage time lag parameter, U represents the rotational speed at the mean radius, deltap represents the port pressure minus the inlet pressure, and h represents the circumferential velocity coefficient.
② flow disturbances within the inlet duct and vanes;
the pressure difference between the inlet and the outlet of the guide vane can be expressed as:because the upstream pipeline of the inlet guide vane is in nonrotational flow, the velocity potential is introducedFrom the far upstream integration to the director inlet, one then obtains, according to bernoulli's equation:
introducing disturbance velocity potentialThe original velocity potential may then be expressed as The pressure rise far upstream to the guide vane inlet at this time can be expressed as:
wherein P is_{T}The total pressure at the inlet is shown,the potential of the speed is represented by,representing the disturbance velocity potential,/_{1}Inlet duct length.
③ flow disturbances within the outlet duct and outlet guide vanes;
definition of pressure coefficientThen at the downstream pipe outlet (η ═ l)_{E}) Comprises the following steps:then introducing a parameter m to obtain the static pressure change in the outlet pipeline:wherein p is_{s}Representing the static pressure in the collecting chamber, p representing the static pressure in the outlet duct, l_{E}Representing the dimensionless length, l, of the downstream pipe_{T}The outlet duct length is indicated and m is the compressor duct flow parameter.
④ static pressure rise to the compressor outlet end;
far forward atmospheric conditions p from the system inlet_{T}To the end of the outlet duct there may be a variation in static pressure in the circumferential direction, while the flow in the collecting volume and the downstream exhaust throttle valve duct contains only axial disturbances. At this time, the static pressure rise from the inlet to the end of the outlet pipe can be expressed as:
defining the effective length l of compressor and its upstream and downstream pipelines_{C}：If the flow dynamic response in the compressor is considered to be lagged to be pure inertia, then:wherein L is_{R}Is the blade row axial length, k is the coefficient that accounts for the blade row clearance effect, and γ is the effective stagger angle of the blade row. At this point, the total pressure rise can be written as:
disturbance velocity potential upstream of compressorSatisfies the laplace equation:and then expanded into a fourier series. When only the first order term is considered, there are:introducing a variable Y:then there are:
the variable Y satisfies at this time: h is Y_{θ}；g＝Y_{θθ}Y (ξ, θ +2 pi) ═ Y (ξ, θ) andwherein N represents the compressor stage number, Y represents the compressor inlet disturbance potential, K_{G}The inlet guide vane loss coefficient is expressed.
⑤ flow in the plenum and exhaust valve conduit;
the flow in the gas collection cavity and the exhaust pipeline is onedimensional unsteady flow, and the control equation is as follows:
wherein, F_{T}(Φ_{T}) For the pressure drop characteristic of the throttle valve, a parabolic equation is used for expression, namely:at this time, the axial flow coefficient phi of the downstream pipeline_{T}Can be expressed as:integration in the circumferential direction using the properties of Y yields:wherein F_{T}Representing a function of the throttle characteristic, [ phi ]_{T}Represents the flow coefficient of the throttle pipe,/_{c}The effective length of the pipeline upstream and downstream of the compressor is shown, and psi represents the total static pressure rise coefficient.
⑥ general control equations;
to this end, the complete control equation set for the compression system model described above may be written:
the system of equations is of order 3 for angle and 1 for time and is not easily solved. Then, using a galileo method to perform order reduction processing on the equation set (performing fourier expansion on the variable Y and using a firstorder term for substitution), obtaining (phi represents a circumferential average flow coefficient, psi represents a total static pressure rise coefficient, and J represents the square of circumferential disturbance amplitude):
wherein H and W represent parameters related to axisymmetric characteristic line, J represents square of circumferential amplitude of axial flow coefficient, ψ_{c0}Representing the total static pressure rise coefficient at zero flow.
c) Solving a control equation set by utilizing a fourorder Runge Kutta method;
in order to solve the control equation system, an initial value and an initial characteristic line of the compressor are required to be given. From Koff's studies, it is known that the threefold axisymmetric characteristic line can be used to better describe the pressure rise characteristics of the compressor over the entire flow range. Therefore, the model selects the cubic axisymmetric characteristic line as the initial characteristic line.
After part of initial values and initial characteristic lines of the compressor are given, solving a control equation set of a simulation model of the compression system by adopting a fourorder RK numerical method, wherein the formula is as follows:
after solving the control equation set, the critical B parameter can be found by continuously changing the B parameter. And then, the B parameter is larger than the critical B parameter, and the flow coefficient, the total static pressure rise coefficient and the change situation of the working point along with the time of the compressor under the surge working condition under different B parameters are calculated (see figure 3).
d) Calculating the surge frequency;
and analyzing the change process of the flow coefficient of the compressor or the total static pressure rise coefficient of the compressor along with time under the different B parameters obtained in the fourth step by utilizing Fourier analysis, obtaining the corresponding surge frequency under the B parameters, and providing a surge frequency range. Here, it is necessary to use a fourier method to analyze discrete data points, and the specific method is as follows:i.e. transforming the discrete points in the time domain to the frequency domain, thereby obtaining the frequency, which is the surge frequency.
e) Error analysis
The calculated surge frequency is compared with the surge frequency obtained from the actual compressor experimental data and a prediction error is given (see fig. 4).
Claims (1)
1. The method for predicting the surge frequency of the axial flow compressor is characterized by comprising the following steps of:
step one, establishing a physical and geometric model of an axial flow compressor;
measuring the geometric dimension of an actual axial flow compressor, replacing the compressor with a swash plate to generate pressure rise, replacing an inlet pipeline and an outlet pipeline of the compressor with a pipeline with a uniform section, simulating a backpressure environment by a gas collection cavity, controlling the flow by a throttle valve, and setting the Mach number of an inlet to obtain an axial flow compressor simulation model;
step two, writing a control equation according to the established axial flow compressed air simulation model:
a. flow disturbances in the compressor;
pressure rise of a single blade row by unsteady flow:obtaining the pressure rise of the Nstage compressor as follows:then define the circumferential average of φ:at this time, the circumferential flow coefficient phi and the tangential velocity coefficient h are expressed as phi (ξ) + g (ξ, theta), h as h (ξ, theta), where theta represents the circumferential angle, ξ represents the rotor turning radian, phi represents the axial flow coefficient, phi represents the circumferential average of the axial flow coefficient, F (phi) represents the axisymmetric steadystate performance of the blade row, tau represents the hysteresis constant, a ≡ R/(Ntau U) represents the reciprocal of the blade passage time hysteresis parameter, U represents the rotation speed at the average radius, deltaP represents the outlet pressure minus the inlet pressure, h represents the circumferential velocity coefficient, and t represents the time;
b. flow disturbances in the inlet duct and the guide vanes;
introducing a velocity potentialAnd disturbance velocity potentialThen velocity potentialExpressed as:the pressure rise far upstream to the guide vane inlet at this time is expressed as:wherein P is_{T}The total pressure at the inlet is shown,the potential of the speed is represented by,representing the disturbance velocity potential, η axial position coordinates, ξ rotor radian, phi axial flow coefficient, phi circumferential average value of the axial flow coefficient, l_{1}Represents the inlet duct length;
c. flow disturbances in the outlet duct and the outlet guide vanes;
definition of pressure coefficientThen at the downstream pipe outlet (η ═ l)_{E}) Comprises the following steps:then introducing a parameter m to obtain the static pressure change in the outlet pipeline:wherein p is_{s}Representing the static pressure in the collecting chamber, p representing the static pressure in the outlet duct, l_{E}Representing the dimensionless length, l, of the downstream pipe_{T}Representing the length of an outlet pipeline, and m represents a compressor pipeline flow parameter;
d. static pressure rise to the tail end of the outlet of the compressor;
the static pressure rise from the inlet to the end of the outlet pipe is:
defining the effective length l of compressor and its upstream and downstream pipelines_{C}And a:due to the disturbance velocity potential at the upstream of the compressorSatisfies the laplace equation:then, when it is expanded into a fourier series and only the first order term is considered, there are:and introducing a variable Y:the total pressure rise was obtained as:
wherein p is_{s}Representing the static pressure in the gascollecting chamber, p_{T}Representing total inlet pressure, N representing compressor stage number, phi representing axial flow coefficient, phi representing circumferential average value of axial flow coefficient, l_{E}Representing the dimensionless length, l, of the downstream pipe_{1}Inlet duct length, m representing a compressor duct flow parameter, a ≡ R/(Ntau U) representing the inverse of a vane passage time lag parameter, Y representing compressor inlet disturbance potential, K_{G}Representing the inlet guide vane loss coefficient;
e. flow in the gas collection cavity and the exhaust valve pipeline;
the flow equation in the gas collection cavity and the exhaust pipeline is as follows:
and isUsing parabolic equationsTo represent the pressure drop characteristic of the throttle valve; the axial flow coefficient phi of the downstream pipe_{T}Expressed as:then, integrating in the circumferential direction:wherein F_{T}Representing a function of the throttle characteristic, [ phi ]_{T}Represents the flow coefficient of the throttle pipe,/_{c}Representing the effective length of an upstream pipeline and a downstream pipeline of the compressor, and psi represents a total static pressure rise coefficient;
f. a total set of governing equations;
and (3) the equations are arranged to obtain a complete control equation set of the compression system model:
and (3) carrying out order reduction processing on the equation set by using a Galerkin method, namely carrying out Fourier expansion on the variable Y, and replacing the variable Y by using a first order term to obtain a 1order differential equation set related to time:
where Ψ represents the total static pressure rise coefficient, Φ_{T}Expressing the flow coefficient of the throttling pipeline, Y expressing the disturbance potential of the inlet of the compressor, H and W expressing the relevant parameters of the axisymmetric characteristic line, F_{T}Expressing a throttling characteristic function, phi expressing an axial flow coefficient of the compressor, J expressing the square of the circumferential amplitude of the axial flow coefficient, l_{c}Indicating the effective length of the upstream and downstream conduits of the compressor, psi_{c0}Represents the total static pressure rise coefficient under the condition of zero flow;
solving a control equation set by utilizing a fourorder Runge Kutta method;
selecting a threedimensional axisymmetric characteristic line as an initial characteristic line of the compressor, and then solving a control equation set of a simulation model of the compression system by using a fourorder RK numerical method, wherein the formula is as follows:
continuously changing the B parameter until finding out a critical B parameter after solving the control equation set; then selecting a plurality of different parameters B on one side larger than the critical parameter B, and calculating the change condition of the flow coefficient or the total static pressure rise coefficient of the compressor along with time under the surge working condition;
step four, calculating surge frequency;
and D, processing the change data of the compressor flow coefficient or the total static pressure rise coefficient along with time under the surge working conditions corresponding to the different B parameters obtained in the step three by utilizing discrete Fourier transform to obtain the surge frequency under the different B parameters.
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