CN111102215B - Method and device for predicting streamline flow stability of axial flow compressor - Google Patents
Method and device for predicting streamline flow stability of axial flow compressor Download PDFInfo
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
- F04D—NON-POSITIVE-DISPLACEMENT PUMPS
- F04D19/00—Axial-flow pumps
- F04D19/002—Axial flow fans
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- F04—POSITIVE - DISPLACEMENT MACHINES FOR LIQUIDS; PUMPS FOR LIQUIDS OR ELASTIC FLUIDS
- F04D—NON-POSITIVE-DISPLACEMENT PUMPS
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Abstract
In order to solve the problem of low stability prediction efficiency in the technical problems, the disclosure provides a method and a device for predicting the streamline flow stability of an axial flow compressor, which can improve the efficiency of predicting the streamline flow stability of the axial flow compressor. The method comprises the following steps: acquiring a two-dimensional steady background flow field inside the compressor; constructing a Navier-Stokes equation with a force source item; developing a Navier-Stokes equation under a streamline coordinate system to obtain a master control equation; the main control equation is linearized based on the linear superposition of the background flow and the small disturbance; substituting the small perturbation expression into the linearized main control equation to obtain a first characteristic value equation; obtaining a characteristic value imaginary part based on a first characteristic value equation and a two-dimensional steady background flow field in the compressor; and judging the streamline flow stability of the compressor according to the imaginary part of the characteristic value. The method and the device can be used for solving the problem of the flow stability of the gas compressor into the problem of the mathematical characteristic value, and judging the stability of the flow system according to the positive and negative of the imaginary part of the characteristic value, and the judgment is simple and clear, and the efficiency is high.
Description
Technical Field
The disclosure relates to the field of compressors of aircraft engines, in particular to a method and a device for predicting flow stability of a streamline of an axial flow compressor.
Background
At present, the rotating stall problem of the compressor is still a great technical problem in the field of turbine. Although researchers in various countries carry out a great deal of research on the occurrence mechanism of rotating stall, due to the lack of a rapid, effective and reliable prediction tool for the instability point of the air compressor, the stability margin of the air compressor still cannot be evaluated at the design stage of the air compressor, so that the flow stability problem of the designed air compressor is effectively considered, namely the stability design is included in an air compressor design system. When the design and the forming of the compressor are tested, a designer of the compressor can only passively receive the test result, and once the stability margin is insufficient, remedial measures such as casing treatment and adjustable stator are taken, or the compressor is redesigned, because the stability margin of the compressor directly determines whether the aero-engine can safely and stably operate. No matter which method is adopted for remediation, the method is time-consuming and labor-consuming, and the newly designed compressor has the possibility of the problem of insufficient margin, so that the design of the compressor in the aspect of stability margin can only be completed by depending on the experience accumulated in the research process. To solve this problem, it is necessary to develop a rapid and reliable prediction tool for compressor flow stability, and the design solution is evaluated at the design stage to indicate the deficiency to guide the design of the compressor stability margin.
At present, the traditional compressor stability prediction mainly comprises two methods, one is an analytical model represented by an Emmons model, a Stenning model, a Moore-Greitzer model and a Sun model, and the other is an unsteady numerical simulation for reducing the problem into a primary boundary value problem. The analytic model has clear physical concept and quick calculation, but greatly simplifies the geometry and the flow field of the gas compressor, and the blade row is treated as a swash plate or a semi-swash plate, so that the flow is not compressible, the background flow is segmented uniformly, and the like. Therefore, although the method has great significance to deepen the physical understanding of the rotating stall to some extent, the prediction accuracy of the method is difficult to guarantee under the requirement of fine design at the present stage. While the unsteady numerical simulation can contain more factors such as the geometric details of the compressor and the details of the flow field, the incredible calculation amount and the calculation time become the root cause of the failure of the unsteady numerical simulation in the compressor design. In order to overcome the defects of the two methods, researchers at home and abroad have published a lot of research work on a compressor flow stability prediction model in recent years, but the efficiency of the analysis of the compressor flow stability is still low.
Disclosure of Invention
In order to solve at least one of the above technical problems, the present disclosure provides a method and an apparatus for predicting the streamline flow stability of an axial compressor, which can improve the efficiency of predicting the streamline flow stability of the axial compressor.
In order to achieve the above object, in one aspect of the present disclosure, a method for predicting streamline flow stability of an axial flow compressor includes:
acquiring a two-dimensional steady background flow field inside the compressor;
constructing a Navier-Stokes equation with a force source item;
developing a Navier-Stokes equation under a streamline coordinate system to obtain a master control equation;
expressing transient physical quantity in a main control equation into linear superposition of background flow and small disturbance, and linearizing the main control equation based on the linear superposition of the background flow and the small disturbance;
based on the assumption of axial symmetry, obtaining a small disturbance quantity expression for expressing the relationship between the small disturbance quantity and the disturbance quantity amplitude, the characteristic value and the disturbance circumferential wave number;
substituting the small perturbation expression into the linearized main control equation to obtain a first characteristic value equation;
obtaining a characteristic value imaginary part based on a first characteristic value equation and a two-dimensional steady background flow field in the compressor;
and judging whether the imaginary part of the characteristic value is greater than zero, if so, judging that the streamline flow of the compressor is unstable, otherwise, judging that the streamline flow of the compressor is stable.
Optionally, the obtaining of the two-dimensional steady background flow field inside the compressor includes: obtaining a three-dimensional steady flow field, and performing circumferential density weighted average on the three-dimensional steady flow field according to the following formula to obtain a two-dimensional steady background flow field inside the compressor;
wherein q represents a steady background flow physical quantity, ρ represents a fluid density,
represents the background flow physical quantity after circumferential averaging,
indicating the fluid average density, theta the circumferential coordinate, and subscripts s and p the suction and pressure surfaces of the blade, respectively.
Optionally, the Navier-Stokes equation includes:
the continuous equation:
the momentum equation:
energy equation:
where p represents the fluid density, t represents time,
representing the velocity vector in an absolute coordinate system, pi representing the surface stress tensor of the fluid micelle,
representing the blade force vector and e representing the internal energy.
Optionally, the surface stress tensor of the fluid micelle is expressed by the following formula;
Π＝-pδ
wherein p represents the surface pressure of the fluid micro-cluster, and delta is a 3-order unit matrix.
Optionally, based on the assumption of axial symmetry, obtaining a small disturbance quantity expression for expressing a relationship between the small disturbance quantity and the disturbance quantity amplitude, the eigenvalue, and the disturbance circumferential wave number includes:
based on the assumption of axial symmetry, a small perturbation expression is obtained,
wherein q' represents a small disturbance amount,
representing the disturbance magnitude, ω representing a characteristic value, m representing the disturbance circumferential wave number, θ representing a circumferential coordinate, t representing time, r representing a radial coordinate, and z representing an axial coordinate.
Optionally, substituting the small-perturbation expression into the linearized master control equation to obtain the first characteristic value equation includes:
substituting the small-disturbance-quantity expression into the linearized control equation to obtain a first characteristic value equation as follows:
wherein X (omega) is a coefficient matrix with a variable omega,
is a column vector formed by the disturbance quantity amplitudes.
Optionally, the first eigenvalue equations of the compressors in different stages are integrated into a complete second eigenvalue equation based on the disturbance quantity continuity and the first-order partial derivative continuity of the disturbance quantity along the streamline as matching conditions, and a second eigenvalue is obtained based on the second eigenvalue equation and the constant background flow field inside the compressor.
Optionally, the method further comprises:
extracting the amplitude of the disturbance quantity of the streamline on the interface between the stages from the second characteristic value;
obtaining the disturbance quantity on the interface between the stages based on the amplitude of the disturbance quantity on the interface between the stages and the corresponding second characteristic value;
taking the disturbance quantity on the interstage interface as the boundary condition of the inlet and the outlet of each stage of the gas compressor to independently analyze the stability of each stage of the multi-stage gas compressor, and obtaining the quantitative distribution of the radial flow stability of each streamline of each stage of the gas compressor;
and comparing and judging to obtain the most unstable radial streamline of the compressor according to the quantitative distribution of the stability between the stages.
Optionally, the method further comprises: carrying out non-dimensionalization on the imaginary part of the characteristic value through the rotor rotating speed by the following formula to obtain a non-dimensional attenuation factor, and judging the streamline stability of the compressor according to the non-dimensional attenuation factor;
wherein DF is a dimensionless attenuation factor, omega is the rotor speediFor the imaginary part of the characteristic value,
as another aspect of the present disclosure, an axial flow compressor streamline flow stability prediction apparatus includes:
the acquisition module is used for acquiring a two-dimensional steady background flow field in the compressor;
the Navier-Stokes equation building module is used for building a Navier-Stokes equation with a force source item;
the master control equation acquisition module is used for developing the Navier-Stokes equation under a streamline coordinate system to obtain a master control equation;
the master control equation linearization module is used for expressing the transient physical quantity in the master control equation into linear superposition of background flow and small disturbance, and linearizing the master control equation based on the linear superposition of the background flow and the small disturbance;
the small disturbance quantity expression acquisition module is used for acquiring a small disturbance quantity expression for expressing the relation between the small disturbance quantity and the disturbance quantity amplitude, the characteristic value and the disturbance circumferential wave number based on the axial symmetry hypothesis;
the first characteristic value equation obtaining module is used for substituting the small disturbance quantity expression into the linearized main control equation to obtain a first characteristic value equation;
the characteristic value calculation module is used for obtaining a characteristic value imaginary part based on a first characteristic value equation and a two-dimensional steady background flow field in the gas compressor;
and the stability judging module is used for judging whether the imaginary part of the characteristic value is greater than zero, judging that the streamline flow of the compressor is unstable if the imaginary part of the characteristic value is greater than zero, and otherwise, judging that the streamline flow of the compressor is stable.
The implementation of the technical scheme of the present disclosure has the following beneficial effects:
the technical scheme disclosed by the invention avoids the difficulty of generating and calculating the fit grid by constructing the Navier-Stokes equation with the force source item. The force source term is expressed as a function of local flow state parameters to depict the action of the blades on the flow field, thereby not only considering the influence of the blade geometry and ensuring the accuracy of analysis, but also improving the calculation efficiency.
The technical scheme disclosed by the invention is based on the small disturbance hypothesis, transient quantities in a flow field are expressed as the sum of steady-state quantities and small disturbance quantities, a control equation is linearized, the small disturbance quantities are regularly expanded, and finally the control equation is sorted, so that the problem of the flow stability of the gas compressor is solved as a mathematical characteristic value problem, the stability of a flow system is judged according to the positive and negative of an imaginary part of the characteristic value, the criterion is simple and clear, and the efficiency is high.
Drawings
The accompanying drawings, which are included to provide a further understanding of the disclosure and are incorporated in and constitute a part of this specification, illustrate exemplary embodiments of the disclosure and together with the description serve to explain the principles of the disclosure.
FIG. 1 is a flow chart of a method in an embodiment of the present disclosure;
FIG. 2 is a schematic diagram of a multi-stage axial flow compressor flow line and a flow line coordinate system;
FIG. 3 is a graph of the attenuation factor DF along each streamline at each flow point;
FIG. 4 is a graph of the attenuation factor DF versus flow for each radial streamline;
fig. 5 is a block diagram of prediction of streamline flow stability of an axial compressor in an embodiment of the disclosure.
Detailed Description
The present disclosure will be described in further detail with reference to the drawings and embodiments. It is to be understood that the specific embodiments described herein are for purposes of illustration only and are not to be construed as limitations of the present disclosure. It should be further noted that, for the convenience of description, only the portions relevant to the present disclosure are shown in the drawings.
It should be noted that the embodiments and features of the embodiments in the present disclosure may be combined with each other without conflict. The present disclosure will be described in detail below with reference to the accompanying drawings in conjunction with embodiments.
Example 1:
as shown in fig. 1, the method for predicting the streamline flow stability of the axial flow compressor includes:
step S1: acquiring a two-dimensional steady background flow field inside the compressor;
step S2: constructing a Navier-Stokes equation with a force source item;
step S3: developing a Navier-Stokes equation under a streamline coordinate system to obtain a master control equation;
step S4: expressing transient physical quantity in a main control equation into linear superposition of background flow and small disturbance, and linearizing the main control equation based on the linear superposition of the background flow and the small disturbance;
step S5: based on the assumption of axial symmetry, obtaining a small disturbance quantity expression for expressing the relationship between the small disturbance quantity and the disturbance quantity amplitude, the characteristic value and the disturbance circumferential wave number;
step S6: substituting the small perturbation expression into the linearized main control equation to obtain a first characteristic value equation;
step S7: obtaining a characteristic value imaginary part based on a first characteristic value equation and a two-dimensional steady background flow field in the compressor;
step S8: and judging whether the imaginary part of the characteristic value is greater than zero, if so, judging that the streamline flow of the compressor is unstable, otherwise, judging that the streamline flow of the compressor is stable.
The method comprises the steps of constructing a Navier-Stokes equation (a Navier-Stokes equation) with a force source item, expressing transient physical quantity in a main control equation into linear superposition of background flow and small disturbance, and linearizing the main control equation; obtaining a small-disturbance-quantity expression based on an axisymmetric hypothesis, and obtaining a first characteristic value equation according to the linearized main control equation and the small-disturbance-quantity expression; obtaining an imaginary part of the characteristic value based on the first characteristic value equation and a two-dimensional steady background flow field in the gas compressor; and judging the streamline flow stability of the compressor based on the imaginary part of the characteristic value.
According to the technical scheme, the blade geometry inside the compressor is replaced by the distributed force source item through blade force modeling based on the immersion boundary theory, so that the difficulty of generating and calculating a body-fitting grid is avoided. The force source term is expressed as a function of local flow state parameters to characterize the effect of the blades on the flow field, thereby not only considering the influence of the blade geometry, but also improving the calculation efficiency.
The technical scheme disclosed by the invention is based on a small disturbance hypothesis, transient quantity in a flow field is expressed as the sum of steady-state quantity and small disturbance quantity, a control equation is linearized, the small disturbance quantity is regularly expanded, and finally the control equation is sorted, so that the problem of the flow stability of the gas compressor is solved as a mathematical characteristic value problem, the stability of a flow system is judged according to the positive and negative of an imaginary part of the characteristic value, and the criterion is simple and clear.
The technical scheme disclosed by the invention can predict the flow stability of the compressor under the uniform air intake condition and can predict the flow stability of the compressor under the distorted air intake condition.
In step S1, for the compressor in the design process, a two-dimensional steady background flow field inside the compressor can be directly obtained through two-dimensional through-flow calculation, that is, the compressor can be combined with the compressor in the true sense. For the designed compressor, the method can be obtained by three-dimensional steady compressible viscous numerical simulation.
Based on the assumption of axial symmetry, a three-dimensional steady flow field is obtained, and circumferential density weighted average is carried out on the three-dimensional steady flow field according to a formula (1), so that a two-dimensional steady background flow field on a meridian plane can be obtained.
Wherein q represents a constant background flow physical quantity, p represents density,
represents the background flow physical quantity after circumferential averaging,
indicating the fluid average density, theta the circumferential coordinate, and subscripts s and p the suction and pressure surfaces of the blade, respectively.
In step S2, based on the immersion boundary theory, the distributed blade force is used to replace the action of the blade geometry on the flow field, and the main control equation of the flow field inside the compressor is converted into a Navier-Stokes equation with a force source term, thereby implementing the construction of the Navier-Stokes equation with the force source term.
Wherein the Navier-Stokes equation comprises:
the continuous equation:
the momentum equation:
energy equation:
where p represents the fluid density, t represents time,
representing the velocity vector in an absolute coordinate system, pi representing the surface stress tensor of the fluid micelle,
representing the blade force vector and e representing the internal energy.
Wherein, the fluid micelle surface stress tensor can be expressed as: Π ═ Τ -p δ;
where, γ is the viscous stress, p is the fluid micelle surface pressure, and neglecting the viscous force, the fluid micelle surface stress tensor can be expressed as:
Π＝-pδ (5)
wherein p represents the surface pressure of the fluid micelle, and delta is a 3-order unit matrix;
specifically, δ may be
Since the steady background flow is derived from viscosity calculations, the method theoretically includes viscosity effects. In addition, the blade force is divided into a turning force for turning the flow direction of the fluid and a loss force causing flow loss according to the action of the blade on the flow field during blade force modeling, and the loss force actually includes the influence of viscosity. The blade force model has been developed, and reference can be made to the existing blade force model, which is not described herein.
In step S3, for the internal flow field of the compressor, influence of heat conduction and heat radiation is ignored, the internal energy e is expressed by pressure and density, and the vector control equation (Navier-Stokes equation) is expanded in the flow line coordinate system (S, θ, n), so that the main control equation satisfied by the fluid on each flow line can be obtained, where S is the flow direction, θ is the circumferential direction, and n is the normal direction.
In step S4, the transient physical quantity in the master control equation is expressed as a linear superposition of the background flow and the small disturbance, and the master control equation is linearized based on the linear superposition of the background flow and the small disturbance.
Since the method focuses on the stall starting point, the transient physical quantity in the master control equation can be expressed as the linear superposition of the background flow and the small disturbance according to the linear stability analysis, namely q is q + q', and the symbol
Representing background flow and q' small disturbance. From this expression, the master control equation can be linearized.
In step S5, based on the assumption of axial symmetry, a small disturbance quantity expression for expressing the relationship between the small disturbance quantity and the disturbance quantity amplitude, the eigenvalue, and the disturbance circumferential wave number is obtained;
based on the assumption of axial symmetry, the small perturbation quantity satisfies:
in the formula (6)
Representing the disturbance amount amplitude (the amplitude of the disturbance amount), ω and m are a characteristic value (a system characteristic value) and a disturbance circumferential wave number (a circumferential wave number of the disturbance), respectively, r represents a radial coordinate, and z represents an axial coordinate.
In step S6, substituting the small-disturbance-quantity expression into the linearized main control equation to obtain a first characteristic value equation;
substituting the small-disturbance-quantity expression into the linearized main control equation to obtain a first characteristic value equation comprises the following steps:
substituting the expression (6) into the linearized control equation for sorting to obtain a first characteristic value equation in the following form:
wherein X (omega) is a coefficient matrix with a variable omega,
is a column vector formed by the disturbance quantity amplitudes.
Step S7, obtaining a characteristic value imaginary part based on a first characteristic value equation and a two-dimensional steady background flow field in the compressor;
attention is paid to: the first eigenvalue equation is a partial differential equation and therefore requires numerical discretization, and the present disclosure may use a spectral approach. The first eigenvalue equation can be solved in combination with appropriate boundary conditions. The boundary conditions give zero inlet disturbance and zero outlet pressure disturbance. In addition, the existence of the blade force in the blade area is different from a main control equation of a blade-free area, so that the whole area is subjected to partition processing, and the information transmission between adjacent sub-areas is continuously realized through the disturbance quantity continuity and the first-order partial derivative of the disturbance quantity along the streamline.
Since the disturbance magnitude is not all zero, i.e.
In equation (7)
The condition for a non-zero solution is that the determinant of the coefficient matrix X (ω) is zero, i.e.:
|X(ω)|＝0 (8)
and solving the equation (8) to obtain the characteristic value omega. The solving method is not unique, and the patent suggests that a Singular Value Decomposition (SVD) method is adopted. The characteristic value is a complex number, which can be expressed as ω ═ ωr+iωi. According to
It can be seen that when the imaginary part ω of the feature value isiWhen the disturbance quantity amplitude is less than zero, the disturbance quantity amplitude is reduced along with the time, and the streamline system is stable; when the imaginary part ω of the feature valueiWhen the disturbance quantity amplitude is larger than zero, the disturbance quantity amplitude is increased along with the time, and the streamline system is unstable. Imaginary part omegaiThe larger, representing a faster increase in disturbance magnitude over time, the more unstable the flow. According to the characteristic, the stability of each streamline system of the compressor can be quantitatively evaluated.
Experiments show that the circumferential propagation speed of the stall premonitory wave and the rotor rotation speed are the same order, so that two dimensionless quantities can be obtained by respectively carrying out dimensionless treatment on the real part and the imaginary part of the characteristic value by utilizing the rotor rotation speed omega: relative velocity RS (relative speed) and attenuation factor DF (damping factor), namely:
and the flow stability of the streamline system can be judged according to the positive and negative values and the magnitude of the attenuation factor DF.
According to the process, the quantitative distribution of the flow stability conditions on a plurality of flow lines along the radial direction can be obtained, and then the weak link of the flow stability in the compressor can be analyzed, so that the method can be used for guiding the design.
As an alternative of the above embodiment, based on the disturbance quantity continuity and the disturbance quantity continuity along the first-order partial derivative of the streamline as the matching conditions, the first eigenvalue equations of the compressors at different stages are integrated into a complete second eigenvalue equation, and the second eigenvalue is obtained based on the second eigenvalue equation and the steady background flow field inside the compressor. The "second" of the second feature values herein is calculated based on the second feature value equation only for the purpose of surface, and is still a feature value for determining the stability of the fluid in nature; because the eigenvalue matrix integrated by the main control equation set satisfied by the fluid on the grid point of the single streamline is fast in calculation when the eigenvalue of the eigenvalue matrix is solved, the alternative scheme is applied to the multistage compressor as shown in fig. 2 (in the figure, A represents a blade tip streamline, B represents a blade root streamline, C represents an inlet airflow, and D represents a blade root streamline D, E represents an outlet airflow). The difficulty is that when eigenvalue matrixes of different stages of compressors are combined together, matching conditions need to be established and expressed in a coefficient matrix of a first eigenvalue equation. In order to ensure information transfer from stage to stage, the disturbance variable is continuously matched with the first partial derivative of the disturbance variable along the streamline at the interface. The influence of the blades on the flow field is still characterized by volume force modeling for the blade area, so that the first eigenvalue equation is still processed in a partitioning mode (the blade area and the non-blade area) when being established, and finally the first eigenvalue equation sets of all the areas are integrated into a complete second eigenvalue equation through matching conditions, so that the flow stability of the whole streamline system is judged according to the eigenvalue of the equation coefficient matrix. Therefore, the streamline-based axial flow compressor flow stability prediction method is popularized to multi-stage and even multi-shaft compressors. As the streamlines at different radial positions have a stability prediction result, the radial distribution condition of the flow stability of the multistage compressor can be finally given, and the radial quantitative analysis of the flow stability can be given.
As an alternative to the above embodiment, the method further comprises:
extracting the amplitude of the disturbance quantity of the streamline on the interface between the stages from the second characteristic value;
obtaining the disturbance quantity on the interface between the stages based on the amplitude of the disturbance quantity on the interface between the stages and the corresponding second characteristic value;
taking the disturbance quantity on the interstage interface as the boundary condition of the inlet and the outlet of each stage of the gas compressor to independently analyze the stability of each stage of the multi-stage gas compressor, and obtaining the quantitative distribution of the radial flow stability of each streamline of each stage of the gas compressor;
and comparing and judging to obtain the most unstable radial streamline of the compressor according to the quantitative distribution of the stability between the stages.
Extracting the amplitude of the disturbance quantity of the streamline on the interface between the stages from the second characteristic value, and combining the corresponding second characteristic value to obtain the disturbance quantity on the interface between the stages
And performing stability analysis on each stage of the multistage gas compressor by using the obtained disturbance quantity on the interstage interface as the inlet and outlet boundary condition of each stage of the gas compressor, and finally obtaining the quantitative distribution of the radial flow stability of a plurality of flow lines of each stage of the gas compressor, thereby finally obtaining the conclusion that the flow of the stage is firstly unstable according to the quantitative comparison of the stability between the stages.
In engineering, the distribution condition of the radial flow stability of the multistage compressor, namely the blade tip, the blade leaf or the blade root is firstly instable, and the distribution condition of the axial flow stability, namely which stage is firstly instable and which stage is the worst in flow stability, are concerned. In order to solve the problem, according to the technical scheme disclosed by the disclosure, after the flow stability of the whole multi-stage compressor system is predicted, not only can the system characteristic value corresponding to each radial streamline be obtained, but also the corresponding characteristic vector can be obtained. The eigenvector is effectively the magnitude of the perturbation at the solved grid point on the single streamline. For each streamline, extracting the amplitude of the disturbance quantity of the streamline on the interface between the stages from the system characteristic vector obtained by analyzing the integral stability of the multistage compressor, and combining the corresponding system characteristic value to obtain the specific form of the disturbance quantity on the interface between the stages
The obtained disturbance quantity on the interstage interface is used as the boundary condition of the inlet and the outlet of each stage of the compressor to independently perform stability analysis on each stage of the multi-stage compressor, and finally the quantitative distribution of the flow stability of a plurality of radial flow lines of each stage of the compressor can be obtained, so that the conclusion that the flow of the stage is the most unstable is finally obtained according to the quantitative comparison of the stability between the stages, and the method has very important significance for guiding engineering application and the design of the compressor.
The radial and axial non-uniformity of the flow field in the compressor is fully considered on the basis of the global stability analysis idea, and more flow details are included.
The stability analysis method can be used for carrying out stability analysis on the multistage or even multi-shaft compressor, and the calculated amount and the calculated time can be completely accepted by engineering. For a multi-stage compressor, the method can quantitatively give the flow stability condition on each radial streamline, namely the flow stability in the radial quantitative distribution, and can quantitatively compare the flow stability condition of each stage. The method can judge the weak link of the radial flow stability of the whole compressor, namely the blade root, the blade leaf or the blade root flow is least stable or the first instable, and can indicate which stage of the multistage compressor has the worst flow stability and which stage is the first instable. The method has very important significance for the stability design of the axial flow compressor in the design stage and problem analysis in specific engineering practice.
The stability of the compressor is quickly and reliably predicted under the condition of considering the geometric and flow non-uniformity of blades in the compressor, the stability prediction method is applicable to a multistage or even multi-shaft compressor, the flow stability of the compressor under the condition of non-uniform air intake, namely distorted air intake, can be predicted, the weak position of the flow stability of the compressor can be given, the blade tip, the blade root or the blade root is most unstable in flow, and the stage of the multistage compressor is most unstable in flow, so that the design of the compressor is guided, and the directional guidance is provided for a designer to perfect the design scheme of the compressor. The method for predicting the flow stability of the axial flow compressor, which is developed by the disclosure, needs to calculate time consumption and can be accepted by engineering application, so that the method can be used for analyzing and solving problems in engineering practice.
In order to more clearly illustrate the advantages and effects of the technical scheme of the disclosure, the method is applied to the flow stability prediction of the single-Rotor transonic axial flow compressor NASA Rotor37 at 100% of the design rotating speed.
FIG. 3 is a graph of the distribution of the attenuation factor DF along each streamline in the radial direction at each flow point by the NASA Rotor 37. It should be noted that 31 streamlines are radially arranged, and are sequentially named from 1 to 31 from the hub to the casing in the blade height direction, namely the horizontal axis streamline coordinate in fig. 2. The vertical axis in fig. 3 is the dimensionless parametric attenuation factor DF characterizing the flow stability. The larger the DF, the faster the small perturbation increases with time, i.e. the worse the flow stability. The graph in fig. 3 is the flow rate. As can be seen in FIG. 3, at each flow point, the streamline flow stability at the tip location is the worst, i.e., the tip location is the weak link in the NASA Rotor37 flow stability. In addition, it can be clearly seen that as the flow rate gradually decreases, i.e., the throttling process proceeds, the streamline flow stability at the tip position is continuously deteriorated, which is consistent with the conclusion that the compressor is closer to the stall boundary as the flow rate decreases in the experiment.
FIG. 4 shows the variation of the decay factor DF with flow for each streamline in the radial direction by the NASA Rotor 37. In fig. 4, the attenuation factor DF is plotted on the vertical axis, the flow is plotted on the horizontal axis, and the radial streamline is plotted. As can be seen from the figure, the streamline near the blade tip position has obviously poor flow stability as the flow rate is reduced, namely, the throttling process is carried out. The flow lines at other positions, especially near the blade root, have little change in flow stability with the throttling process. This also indicates that the flow near the tip is a weak link in the flow stability of the compressor, and that the flow at the tip is sensitive to the throttling process. The optimum design of the tip portion is critical if the flow stability of the compressor is to be improved.
The calculation illustrates that the method not only can quantitatively analyze the flow stability condition of the axial flow compressor, but also has quick calculation and reliable result, and can be applied to engineering practice to guide the design of the compressor.
Example 2:
as shown in fig. 5, the prediction apparatus for streamline flow stability of an axial flow compressor includes:
the acquisition module 1 is used for acquiring a two-dimensional steady background flow field in the compressor;
the Navier-Stokes equation building module 2 is used for building a Navier-Stokes equation with a force source item;
the master control equation acquisition module 3 is used for developing the Navier-Stokes equation under a streamline coordinate system to obtain a master control equation;
the master control equation linearization module 4 is used for expressing the transient physical quantity in the master control equation into linear superposition of background flow and small disturbance, and linearizing the master control equation based on the linear superposition of the background flow and the small disturbance;
the small disturbance quantity expression obtaining module 5 is used for obtaining a small disturbance quantity expression for expressing the relationship between the small disturbance quantity and the disturbance quantity amplitude, the characteristic value and the disturbance circumferential wave number based on the axial symmetry assumption;
the first characteristic value equation obtaining module 6 is used for substituting the small disturbance quantity expression into the linearized main control equation to obtain a first characteristic value equation;
the characteristic value calculation module 7 is used for obtaining a characteristic value imaginary part based on a first characteristic value equation and a two-dimensional steady background flow field in the gas compressor;
and the stability judging module 8 is used for judging whether the imaginary part of the characteristic value is greater than zero, judging that the streamline flow of the compressor is unstable if the imaginary part of the characteristic value is greater than zero, and otherwise, judging that the streamline flow of the compressor is stable.
As an alternative embodiment, the obtaining of the two-dimensional steady background flow field inside the compressor includes: obtaining a three-dimensional steady flow field, and performing circumferential density weighted average on the three-dimensional steady flow field according to the following formula to obtain a secondary steady background flow field in the compressor;
wherein q represents a steady background flow physical quantity, ρ represents a fluid density,
represents the background flow physical quantity after circumferential averaging,
indicating the fluid average density, theta the circumferential coordinate, and subscripts s and p the suction and pressure surfaces of the blade, respectively.
As an alternative embodiment, the Navier-Stokes equation comprises:
the continuous equation:
the momentum equation:
energy equation:
where p represents the fluid density, t represents time,
representing the velocity vector in an absolute coordinate system, pi representing the surface stress tensor of the fluid micelle,
representing the blade force vector and e representing the internal energy. The fluid micelle surface stress tensor is expressed by the following formula;
Π＝-pδ
wherein p represents the surface pressure of the fluid micro-cluster, and delta is a 3-order unit matrix.
As an alternative embodiment, based on the assumption of axial symmetry, obtaining a small disturbance quantity expression for expressing a relationship between the small disturbance quantity and the disturbance quantity amplitude, the eigenvalue, and the disturbance circumferential wave number includes:
based on the assumption of axial symmetry, a small perturbation expression is obtained,
wherein q' represents a small disturbance amount,
representing the disturbance magnitude, omega representing a characteristic value, m representing the disturbance circumferential wave number, theta representing a circumferential coordinate, and t representing time.
As an alternative embodiment, substituting the small-perturbation expression into the linearized master control equation to obtain the first eigenvalue equation includes:
substituting the small-disturbance-quantity expression into the linearized control equation to obtain a first characteristic value equation as follows:
wherein X (omega) is a coefficient matrix with a variable omega,
is a column vector formed by the disturbance quantity amplitudes.
As an optional implementation manner, the device further comprises a second eigenvalue calculation module, which is used for integrating the first eigenvalue equations of the compressors in different stages into a complete second eigenvalue equation based on the disturbance quantity continuity and the disturbance quantity continuity along the first-order partial derivative of the streamline as matching conditions, and obtaining a second eigenvalue based on the second eigenvalue equation and the internal steady background flow field of the compressor.
As an optional implementation manner, the apparatus further includes a compressor radial flow line stability determination module, configured to:
extracting the amplitude of the disturbance quantity of the streamline on the interface between the stages from the second characteristic value;
obtaining the disturbance quantity on the interface between the stages based on the amplitude of the disturbance quantity on the interface between the stages and the corresponding second characteristic value;
taking the disturbance quantity on the interstage interface as the boundary condition of the inlet and the outlet of each stage of the gas compressor to independently analyze the stability of each stage of the multi-stage gas compressor, and obtaining the quantitative distribution of the radial flow stability of each streamline of each stage of the gas compressor;
and comparing and judging to obtain the most unstable radial streamline of the compressor according to the quantitative distribution of the stability between the stages.
Carrying out non-dimensionalization on the imaginary part of the characteristic value through the rotor rotating speed by the following formula to obtain a non-dimensionalized attenuation factor:
wherein DF is a dimensionless attenuation factor, omega is the rotor speediIs the imaginary part of the eigenvalue.
The principle and effect of this embodiment are consistent with those of embodiment 1, and the description of this embodiment is not repeated.
In the description herein, reference to the description of the terms "one embodiment/mode," "some embodiments/modes," "example," "specific example," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment/mode or example is included in at least one embodiment/mode or example of the application. In this specification, the schematic representations of the terms used above are not necessarily intended to be the same embodiment/mode or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments/modes or examples. Furthermore, the various embodiments/aspects or examples and features of the various embodiments/aspects or examples described in this specification can be combined and combined by one skilled in the art without conflicting therewith.
Furthermore, the terms "first", "second" and "first" are used for descriptive purposes only and are not to be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one such feature. In the description of the present application, "plurality" means at least two, e.g., two, three, etc., unless specifically limited otherwise.
It will be understood by those skilled in the art that the foregoing embodiments are merely for clarity of illustration of the disclosure and are not intended to limit the scope of the disclosure. Other variations or modifications may occur to those skilled in the art, based on the foregoing disclosure, and are still within the scope of the present disclosure.
Claims (8)
1. The method for predicting the streamline flow stability of the axial flow compressor is characterized by comprising the following steps:
acquiring a two-dimensional steady background flow field inside the compressor;
constructing a Navier-Stokes equation with a force source item;
developing a Navier-Stokes equation under a streamline coordinate system to obtain a master control equation;
expressing transient physical quantity in a main control equation into linear superposition of background flow and small disturbance, and linearizing the main control equation based on the linear superposition of the background flow and the small disturbance;
based on the assumption of axial symmetry, obtaining a small disturbance quantity expression for expressing the relationship between the small disturbance quantity and the disturbance quantity amplitude, the characteristic value and the disturbance circumferential wave number;
substituting the small perturbation expression into the linearized main control equation to obtain a first characteristic value equation;
obtaining a characteristic value imaginary part based on a first characteristic value equation and a two-dimensional steady background flow field in the compressor;
judging whether the imaginary part of the characteristic value is greater than zero, if so, judging that the streamline flow of the compressor is unstable, otherwise, judging that the streamline flow of the compressor is stable;
the Navier-Stokes equation comprises:
the continuous equation:
the momentum equation:
energy equation:
where p represents the fluid density, t represents time,
representing the velocity vector in an absolute coordinate system, pi representing the surface stress tensor of the fluid micelle,
representing blade force vectors, e representing internal energy;
the fluid micelle surface stress tensor is expressed by the following formula;
Π＝-pδ
wherein p represents the surface pressure of the fluid micro-cluster, and delta is a 3-order unit matrix.
2. The method of claim 1, wherein the obtaining a two-dimensional steady background flow field inside the compressor comprises: obtaining a three-dimensional steady flow field, and performing circumferential density weighted average on the three-dimensional steady flow field according to the following formula to obtain a two-dimensional steady background flow field inside the compressor;
wherein q represents a steady background flow physical quantity, ρ represents a fluid density,
represents the background flow physical quantity after circumferential averaging,
indicating the fluid average density, theta the circumferential coordinate, the subscript s the suction side of the blade and the subscript p the pressure side of the blade.
3. The method of claim 1, wherein obtaining a small disturbance quantity expression for expressing a relation of a small disturbance quantity with respect to a disturbance quantity amplitude value, a characteristic value, and a disturbance circumferential wave number based on an axial symmetry assumption comprises:
based on the assumption of axial symmetry, a small perturbation expression is obtained,
wherein q' represents a small disturbance amount,
representing the disturbance magnitude, ω representing a characteristic value, m representing the disturbance circumferential wave number, θ representing a circumferential coordinate, t representing time, r representing a radial coordinate, and z representing an axial coordinate.
4. The method of claim 3, wherein substituting the low-perturbation expression into the linearized master control equation to obtain the first eigenvalue equation comprises:
substituting the small-disturbance-quantity expression into the linearized control equation to obtain a first characteristic value equation as follows:
wherein X (omega) is a coefficient matrix with a variable omega,
is a column vector formed by the disturbance quantity amplitudes.
5. The method as claimed in claim 1, wherein the first eigenvalue equations of the compressors of different stages are integrated into a complete second eigenvalue equation based on the disturbance quantity continuity and the disturbance quantity continuity along the first-order partial derivative of the streamline, and the second eigenvalue is obtained based on the second eigenvalue equation and the compressor internal steady background flow field.
6. The method of claim 5, wherein the method further comprises:
extracting the amplitude of the disturbance quantity of the streamline on the interface between the stages from the second characteristic value;
obtaining the disturbance quantity on the interface between the stages based on the amplitude of the disturbance quantity on the interface between the stages and the corresponding second characteristic value;
taking the disturbance quantity on the interface between the stages as the boundary condition of the inlet and the outlet of each stage of the compressor to independently analyze the stability of each stage of the multi-stage compressor, and obtaining the quantitative distribution of the flow stability of each radial streamline of each stage of the compressor;
and comparing and judging to obtain the most unstable radial streamline of the compressor according to the quantitative distribution of the stability between the stages.
7. The method of claim 1, wherein the method further comprises: carrying out non-dimensionalization on the imaginary part of the characteristic value through the rotor rotating speed by the following formula to obtain a non-dimensional attenuation factor, and judging the streamline stability of the compressor according to the non-dimensional attenuation factor;
wherein DF is a dimensionless attenuation factor, omega is the rotor speediFor the imaginary part of the eigenvalues, m represents the perturbation circumferential wave number.
8. Axial compressor streamline flow stability prediction device, its characterized in that includes:
the acquisition module is used for acquiring a two-dimensional steady background flow field in the compressor;
the Navier-Stokes equation building module is used for building a Navier-Stokes equation with a force source item;
the master control equation acquisition module is used for developing the Navier-Stokes equation under a streamline coordinate system to obtain a master control equation;
the master control equation linearization module is used for expressing the transient physical quantity in the master control equation into linear superposition of background flow and small disturbance, and linearizing the master control equation based on the linear superposition of the background flow and the small disturbance;
the small disturbance quantity expression acquisition module is used for acquiring a small disturbance quantity expression for expressing the relation between the small disturbance quantity and the disturbance quantity amplitude, the characteristic value and the disturbance circumferential wave number based on the axial symmetry hypothesis;
the first characteristic value equation obtaining module is used for substituting the small disturbance quantity expression into the linearized main control equation to obtain a first characteristic value equation;
the characteristic value calculation module is used for obtaining a characteristic value imaginary part based on a first characteristic value equation and a two-dimensional steady background flow field in the gas compressor;
the stability judging module is used for judging whether the imaginary part of the characteristic value is greater than zero, if the imaginary part of the characteristic value is greater than zero, judging that the streamline flow of the compressor is unstable, and otherwise, judging that the streamline flow of the compressor is stable;
the Navier-Stokes equation comprises:
the continuous equation:
the momentum equation:
energy equation:
where p represents the fluid density, t represents time,
representing the velocity vector in an absolute coordinate system, pi representing the surface stress tensor of the fluid micelle,
representing the blade force vector and e representing the internal energy.
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