CN113836642B - Low-rotation-speed characteristic expansion method for aero-engine component - Google Patents
Low-rotation-speed characteristic expansion method for aero-engine component Download PDFInfo
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- G—PHYSICS
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Abstract
The application belongs to the field of aeroengine starting simulation, and particularly relates to a low-rotation-speed characteristic expansion method of an aeroengine component.
Description
Technical Field
The application belongs to the field of aeroengine starting simulation, and particularly relates to an aeroengine component low-rotation-speed characteristic expansion method.
Background
The component characteristics of an aeroengine are the basis for studying engine steady state and transition state performance. Component characteristic data above the slow vehicle speed is usually obtained through experiments, but the component characteristics in the low-speed working range are generally difficult to obtain through experimental methods due to the complex structure of the turbofan engine. Whereas for the start-up simulation model, the low rotational speed characteristics of the component are key to the start-up simulation. Thus, obtaining the low rotation speed characteristic of the component is a first step of starting simulation, and the current common method is to extrapolate the characteristic of the component in the starting state range according to the known characteristic that the compressor and the turbine are higher than the rotation speed of the slow vehicle, and the characteristic can also be obtained by approximate calculation according to the aerodynamic thermodynamic principle followed by the working of the component. Currently, there are many existing property extrapolation methods, such as exponential extrapolation based on the flow similarity principle, parabolic extrapolation, nie Qiaye f method using converted torque, extrapolation of properties based on loss and ridge line theory, construction of component properties using inter-stage calculation, and the like.
The exponential extrapolation principle is simple, easy to program and achieve, and has enough engineering precision. In addition, the characteristics of the exponential extrapolation expansion are flow, pressure ratio and efficiency, which are consistent with the characteristics required for calculation in the starting simulation program, and the calculation formula in the program is not required to be modified. Based on the effects of incompressible flow or neglecting fluid compressibility, the index in the similarity relationship is a constant, and the indices of flow relationship, work relationship and power relationship are 1, 2 and 3, respectively. However, for the compressor and turbine of an aeroengine, the incompressible fluid assumption is not satisfied in the low rotational speed state, and therefore, the influence of the fluid compressibility is considered by taking the exponential relationship as a variable, and further, since all extrapolation characteristics are related to the selected reference rotational speed, correction is required for the extrapolation characteristics. From the published literature, the correlation index and the correction coefficient are given according to empirical values.
Disclosure of Invention
In order to solve the above problems, the present application provides a low rotation speed characteristic expansion method of an aeroengine component, where the aeroengine component has an exponential overall relation equation when considering compressibility:
wherein w is cor，a 、w cor，b The point a and the point b of the aeroengine component are converted flow, n cor，a ,n cor,b The converted rotation speed of the a point and the b point of the aeroengine component is L i,a ,L i,b Isentropic work for points a and b of the aeroengine component, P w,a ,P w,b For the actual power of the a point and the b point of the aeroengine component, m, n and r are respectively corrected index variables, and k m 、k n 、k r The low-rotation-speed characteristic expansion method of the aero-engine component is characterized by comprising the following steps of:
step S1: according to the characteristics of the components of the aero-engine, drawing a characteristic curve of the aero-engine at a speed higher than a target speed C, wherein the characteristic curve is an initial curve, selecting an initial curve with a lower speed as a lower speed line C1, and selecting a curve with a high speedThe initial curve is marked as a higher rotation speed line C2, and the k is set according to the similar working points of the low rotation speed line C1 and the higher rotation speed line C2 m 、k n 、k r Respectively obtaining values of m, n and r as preset values, and calculating the reference values of m, n and r through the exponential relation equation corresponding to the aero-engine component;
step S2: expanding the higher rotation speed line C2 to a low rotation speed through an algorithm based on the reference values of m, n and r calculated in the step S1 and the exponential relation equation corresponding to the aeroengine component, and expanding to obtain a new rotation speed line C new ；
Step S3: adjusting the reference values of m, n and r and the k through an algorithm model m 、k n 、k r To make the new rotation speed line C new Fitting with the lower rotating speed line C1 according to preset conditions;
step S4: making the initial lower rotating speed line C1 be the new higher rotating speed line C2, making the lower rotating speed line be the new lower rotating speed line C1, and regulating the obtained m, n and r values and k through an algorithm model m 、k n 、k r The step S2-S4 is returned to when the lower rotation speed line C1 is the target rotation speed line Ctarget, the m, n and r values and the k are output m 、k n 、k r Is a value of (2).
Preferably, the algorithm model in steps S3 and S4 includes a genetic algorithm, and a gradient descent method.
Preferably, the preset condition in step S3 is that the relative error Δ is minimum, and generally, the Δ is calculated as follows:
wherein y is 1,i And y new,i The lower rotation speed line C1 and the new rotation speed line C are respectively set new And the ordinate corresponding to the same abscissa is obtained, and when the ordinate corresponding to the same abscissa is not available, the same ordinate can be interpolated by a proper interpolation method.
If the slope of the curve is large, to reduce the effect of the slope, the relative error Δ can be calculated using the following equation:
wherein y is 1,i And C new I is the lower rotation speed line C1 and the new rotation speed line C, respectively new When the same abscissa has no corresponding ordinate, the same ordinate can be interpolated by a proper interpolation method; k (k) 1,i For the slope of the corresponding point on the curve C1, j is an adjustment coefficient greater than 0, and j=5 is generally taken.
Preferably, the aeroengine component comprises a compressor, and the specific characteristic equation corresponding to the compressor is as follows:
wherein W is c,new -a scaled flow of said compressor expansion speed point, W c,ref -a scaled flow of said compressor reference speed point, n cor,new -a converted speed of the compressor expansion speed point; n is n cor,ref -a converted speed, pi, of said compressor reference speed point c,new -said compressor expansion speed point-to-pressure ratio, pi c,ref -said compressor expansion speed point-to-pressure ratio, η c,new -efficiency, η of said compressor expansion speed point c,ref -efficiency of said compressor reference rotation speed point, gamma-gas constant, q=m+n-r, k q ＝k m ·k n /k r 。
Preferably, the aeroengine component comprises a turbine, and the turbine corresponds to a specific characteristic equation:
wherein the method comprises the steps of，W T,new -a scaled flow of said turbine expansion speed point, W T,ref -a scaled flow of said turbine reference speed point, n cor,new -converted speed of rotation of the turbine expansion speed point, n cor,ref -a converted rotational speed of the turbine reference rotational speed point, pi T,new -said turbine expansion speed-to-pressure ratio, pi T,ref -said turbine expansion speed-to-pressure ratio, η T,new -efficiency, η of said turbine expansion speed point T,ref -efficiency of the turbine reference speed point, gamma-gas constant, q=r- (m+n), k q ＝k r /(k m k n )。
Preferably, the number of characteristic curves above the target rotation speed in step S1 is not less than 2.
Preferably, said k m 、k n 、k r Is 1.
Preferably, the characteristic curves of the aero-engine component include a flow rate versus pressure curve, a flow rate versus efficiency curve, and a pressure versus efficiency curve.
Preferably, the compressibility of the aeroengine component is taken into account when plotting the characteristics of the aeroengine component and is based on flow similarity theory.
Preferably, in step S1, the most efficient point is generally selected according to the similar operating point.
The advantages of the present application include: aiming at the problem that the low-rotation-speed characteristics of the components in the aeroengine starting simulation are difficult to obtain, the method for expanding the low-rotation-speed characteristics of the components based on the flow similarity theory is researched, and a method for giving the extrapolated correlation coefficient of the low-rotation-speed characteristics of the rotating components of different types is provided, so that the low-rotation-speed characteristics of the components which are more accurate and close to the actual effect are obtained, and accurate input conditions are provided for the starting simulation.
Drawings
FIG. 1 is a graph of aero-engine fan flow-to-pressure ratio;
FIG. 2 is an aero-engine fan flow-efficiency graph;
FIG. 3 is a high pressure turbine pressure ratio-flow graph of an aircraft engine;
FIG. 4 is a pressure ratio-flow graph of an aircraft engine high pressure turbine.
Detailed Description
For the purposes, technical solutions and advantages of the present application, the following describes the technical solutions in the embodiments of the present application in more detail with reference to the drawings in the embodiments of the present application. In the drawings, the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The described embodiments are some, but not all, of the embodiments of the present application. The embodiments described below by referring to the drawings are exemplary and intended for the purpose of explaining the present application and are not to be construed as limiting the present application. All other embodiments, based on the embodiments herein, which would be apparent to one of ordinary skill in the art without undue burden are within the scope of the present application. Embodiments of the present application will be described in detail below with reference to the accompanying drawings.
Exponential extrapolation is based on the effect of incompressible flow or neglecting fluid compressibility, with flow, work and power similarities as follows:
wherein a and b are different working points, w cor To convert flow, n cor To convert the rotation speed L i For isentropic work, pw is the actual power.
When considering compressibility, two lower rotation speed lines are generally adopted to calculate a new exponential relationship, and a correction coefficient is added to correct the new exponential relationship, wherein the new exponential relationship equation is as follows:
wherein m, n and r are respectively the modified exponential variables, k m 、k n 、k r Respectively are provided withIs the corresponding correction coefficient.
The key to the expansion of the low rotational speed characteristics of the component is to obtain a correlation coefficient adapted to a rotating component, including m, n, r, k m 、k n 、k r At present, according to the published literature, numerical values are directly given, but specific given step methods of the numerical values are not mentioned, and in addition, the corresponding values of the components with different models are different, so that the given values in the literature cannot be directly applied.
The compressor characteristic relation equation of the exponential extrapolation method based on the flow similarity principle is as follows:
wherein q=m+n-r, k q ＝k m k n /k r 。
The high-pressure turbine characteristic relation equation of the exponential extrapolation method based on the flow similarity principle is as follows:
wherein q=r- (m+n), k q ＝k r /(k m k n )。
Step S1: according to the characteristics of the fan and the high-pressure turbine of the aero-engine, a characteristic curve of the aero-engine, which is higher than a target rotating speed by 0.1, is drawn, and the rotating speeds are tested by 0.2, 0.3 and 0.4 in the diagrams of fig. 1 and 2 (corresponding to fan components) and the diagrams of fig. 3 and 4 (corresponding to high-pressure turbine components); selecting two curves C1 and C2 with lower rotating speed and rotating speed, wherein the characteristic curve with the test rotating speed of 0.3 is a lower rotating speed line C1, the characteristic curve with the test rotating speed of 0.4 is a higher rotating speed line C2, and the k is made according to similar working points (generally selecting the point with highest efficiency) m 、k n 、k r The values of m, n and r are calculated according to the exponential relation equation corresponding to the aeroengine component, wherein the value is 1;
step S2: let said k m 、k n 、k r The value of (2) is 1, the higher rotation speed line C2 is expanded by an algorithm based on the reference values of m, n and r calculated in the step 1 and the exponential relation equation corresponding to the aeroengine component, and a new rotation speed line C is obtained by expansion new The expansion means obtaining coefficients according to two corresponding points on the two test rotating speeds, calculating corresponding points according to the coefficients and a reference rotating speed line, and drawing a corresponding graph.
Step S3: adjusting the m, n, r values and the k by an algorithm model m 、k n 、k r To make the new rotation speed line C new Fitting the lower rotating speed line C1 with the reference values of m, n and r according to preset conditions to automatically optimize the rotating speed line C new The low rotation speed characteristic expansion correlation coefficient of the self-adaptive part is given as close as possible to a lower rotation speed line C1 in the 2 rotation speed lines. The optimization problem is described as follows:
inputting the condition: c (C) new And data points on the C1 characteristic line;
optimizing variables: m, n, r, k m 、k n 、k r Genetic algorithm and gradient descent method
Optimization target: the relative error delta is minimal and delta is calculated as follows:
wherein: y1, i and y new I is curves C1 and C, respectively new If the same abscissa is not available, the corresponding ordinate of the same point on the upper abscissa can be interpolated to the same abscissa by a proper interpolation method.
If the slope of the curve is large (fig. 2 and 3), to reduce the effect of the slope, the relative error Δ can be calculated using the following formula:
wherein: y1, i and y new I is curves C1 and C, respectively new If the upper abscissa is the ordinate corresponding to the same point, if the upper abscissa is not the same abscissa, the upper abscissa can be interpolated to the same abscissa by a proper interpolation method; k1, i is the slope of the corresponding point on the curve C1, j is the adjustment coefficient greater than 0, and j=5 is generally taken.
Step S4: making the old lower rotation speed line C1 as the test rotation speed 0.3 be the new higher rotation speed line C2, making the rotation speed line which is lower than the old lower rotation speed line C1 as the test rotation speed 0.2 be the new lower rotation speed line C1, and making the m, n, r values and k obtained by regulating the gradient descent method m 、k n 、k r The step S2-S4 is returned to when the lower rotation speed line C1 is the target rotation speed line Ctarget, the m, n and r values and the k are output m 、k n 、k r Is a value of (2).
As described above, taking a certain fan and a high-pressure turbine as examples, the comparison of the low-rotation speed characteristics obtained by the invention and actual test data is shown in figures 1-4, and the maximum errors of the fan pressure ratio, the efficiency, the high-pressure turbine flow and the efficiency are respectively 1.3%, 1.8%, 0.6% and 3.4%, so that the engineering precision requirements are met.
Claims (10)
1. An aircraft engine component low rotation speed characteristic expansion method, wherein the aircraft engine component has an exponential relation equation:
wherein w is cor，a 、w cor，b Converted flow rate of a point a and b point n of the aeroengine component cor，a ,n cor,b The converted rotation speed of the a point and the b point of the aeroengine component is L i,a ,L i,b Isentropic work for points a and b of the aeroengine component, P w,a ,P w,b For the actual power of the a point and the b point of the aeroengine component, m, n and r are respectively corrected index variables, and k m 、k n 、k r Correction coefficients corresponding to the m, n, and r, respectively, and an aeroengine unitThe low-rotation-speed characteristic expanding method is characterized by comprising the following steps of:
step S1: according to the characteristics of the components of the aero-engine, drawing a characteristic curve of the aero-engine at a speed higher than a target speed C, wherein the characteristic curve is an initial curve, selecting an initial curve with a lower speed as a lower speed line C1, selecting an initial curve with a high speed as a higher speed line C2, and enabling the k to be the same working point as the lower speed line C1 and the higher speed line C2 m 、k n 、k r Respectively obtaining values of m, n and r as preset values, and calculating the reference values of m, n and r through the exponential relation equation corresponding to the aero-engine component;
step S2: expanding the higher rotation speed line C2 to a low rotation speed through an algorithm based on the reference values of m, n and r calculated in the step S1 and the exponential relation equation corresponding to the aeroengine component, and expanding to obtain a new rotation speed line C new ；
Step S3: adjusting the reference values of m, n and r and the k through an algorithm model m 、k n 、k r To make the new rotation speed line C new Fitting with the lower rotating speed line C1 according to preset conditions;
step S4: making the initial lower rotating speed line C1 be the new higher rotating speed line C2, making the rest lower rotating speed lines be the new lower rotating speed line C1, and regulating the obtained m, n and r values and k through an algorithm model m 、k n 、k r The step S2-S4 is returned to when the lower rotation speed line C1 is the target rotation speed line Ctarget, the m, n and r values and the k are output m 、k n 、k r Is a value of (2).
2. The method for expanding low rotational speed characteristics of an aircraft engine component according to claim 1, wherein the algorithm model of steps S3 and S4 comprises a genetic algorithm, a gradient descent method.
3. The method for expanding low rotational speed characteristics of an aeroengine component as defined in claim 1, wherein the preset condition in step S3 is that the relative error Δ is minimum, and the Δ is calculated as follows:
wherein y is 1,i And y new,i The lower rotation speed line C1 and the new rotation speed line C are respectively set new When the same abscissa has no corresponding ordinate, the same ordinate can be interpolated by a proper interpolation method;
if the slope of the curve is large, to reduce the effect of the slope, the relative error Δ can be calculated using the following equation:
wherein y is 1,i And C new I is the lower rotation speed line C1 and the new rotation speed line C, respectively new When the same abscissa has no corresponding ordinate, the same ordinate can be interpolated by a proper interpolation method; k (k) 1,i The slope of the corresponding point on the curve C1 is shown, and j is an adjustment coefficient greater than 0.
4. The method for expanding low rotational speed characteristics of an aircraft engine component according to claim 1, wherein the aircraft engine component comprises a compressor, and the specific characteristic equation corresponding to the compressor is as follows:
wherein W is c,new -a scaled flow of said compressor expansion speed point, W c,ref -a scaled flow of said compressor reference speed point, n cor,new -a converted speed of the compressor expansion speed point; n is n cor,ref -a converted speed, pi, of said compressor reference speed point c,new -said compressor expansion speed point-to-pressure ratio, pi c,ref -said compressor expansion speed point-to-pressure ratio, η c,new -efficiency, η of said compressor expansion speed point c,ref -efficiency of said compressor reference rotation speed point, gamma-gas constant, q=m+n-r, k q ＝k m ·k n /k r 。
5. The aircraft engine component low rotational speed characteristic extension method according to claim 1, wherein the aircraft engine component comprises a turbine, and the turbine corresponds to a specific characteristic equation:
wherein W is T,new -a scaled flow of said turbine expansion speed point, W T,ref -a scaled flow of said turbine reference speed point, n cor,new -converted speed of rotation of the turbine expansion speed point, n cor,ref -a converted rotational speed of the turbine reference rotational speed point, pi T,new -said turbine expansion speed-to-pressure ratio, pi T,ref -said turbine expansion speed-to-pressure ratio, η T,new -efficiency, η of said turbine expansion speed point T,ref -efficiency of the turbine reference speed point, gamma-gas constant, q=r- (m+n), k q ＝k r /(k m k n )。
6. The method for expanding low rotational speed characteristics of an aircraft engine component according to claim 1, wherein the number of characteristic curves at the above-target rotational speed in step S1 is not less than 2.
7. The aircraft engine component low rotational speed characteristic extension method according to claim 1, wherein k is m 、k n 、k r Is 1.
8. The method of expanding low rotational speed characteristics of an aircraft engine component according to claim 1, wherein the characteristic curves of the aircraft engine component include a flow to pressure ratio curve, a flow to efficiency curve, and a pressure ratio to efficiency curve.
9. The method for expanding low rotational speed characteristics of an aircraft engine component according to claim 1, wherein compressibility of the aircraft engine component is considered when plotting the characteristic curve of the aircraft engine component and is based on a flow similarity theory.
10. The method for expanding low rotational speed characteristics of an aircraft engine component according to claim 1, wherein the highest efficiency point is selected according to similar operating points in step S1.
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| CN109753695A (en) * | 2018-12-13 | 2019-05-14 | 西北工业大学 | A kind of engine components characteristic expanding method |
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| CN106569977A (en) * | 2016-09-26 | 2017-04-19 | 南京航空航天大学 | Method for modeling starting process of turboshaft engine |
| CN107882636A (en) * | 2017-10-26 | 2018-04-06 | 中国航发湖南动力机械研究所 | Aero-engine compressor slow-speed of revolution characteristics of components extended method and device |
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