CN114676530B - Method for designing transition state working line of gas turbine engine - Google Patents
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Abstract
The application belongs to the field of aero-engine design, and relates to a method for designing a transition state working line of a gas turbine engine, wherein after each section flow is continuous and each part is in an instantaneous stable working state in the set transition state working line, the corresponding relation between the conversion rotating speed of a gas generator and the pneumatic parameters of the working point of the gas turbine is determined; determining the corresponding relation between the fuel flow w f and the pneumatic parameters of the working point of the gas turbine; obtaining different transition state working lines composed of different working points at each rotating speed; when the gas turbine transition state working line is designed, N ghs、wf is used as a variable, delta N and delta w f are used as step sizes, so that the working point design meeting the constraint conditions of the transition state working line can be achieved, the transition state working line meeting the constraint conditions and the time corresponding to each rotating speed can be obtained, the optimal transition process working line design scheme can be directly obtained without repeated test and compact, the design is efficient, the time consumption is short, and the quantitative analysis is efficient and stable.
Description
Technical Field
The application belongs to the field of aero-engine design, and particularly relates to a method for designing a transition state working line of a gas turbine engine.
Background
The process of rapidly transitioning a gas turbine from one steady state operating condition to another steady state operating condition is referred to as a transition state process, and the transition state includes a start-up process, an acceleration process, a deceleration process, a sudden load increase, a sudden load dump, and the like. The gas turbine common working line (short for working line) is a representation of a gas turbine aerodynamic thermodynamic mathematical model on a compressor characteristic diagram. The general transition state operating line design is constrained by a plurality of conditions, such as the acceleration process of the gas turbine, the surge margin of the compressed gas turbine, the acceleration time, the heat load of the gas turbine, the mechanical strength of the rotor and the like, and the transition state design is one of important parts of the design of the gas turbine.
The prior art method (hereinafter referred to as "prior art scheme") for designing the transition state working line of the gas turbine is to discretize a continuous function of the transition state with time as a variable, then simulate and calculate the change of each performance parameter of the transition process under different given control schemes (such as the control law of the fuel W f) with time by adopting a part-level transition state pneumatic thermodynamic model, and continuously adjust the control scheme according to the simulation result so as to find the transition state working line which better meets the constraint condition.
The prior art scheme replaces a physical gas turbine by a gas turbine simulation model, and continuously performs 'trial and error' on a control scheme, which is equivalent to reverse design, so as to obtain a near-optimal transition state working line scheme as far as possible, and has the following defects:
1) Quantitative analysis of the control parameter variation of each discrete point is very difficult to influence the transition state performance rule, and quantitative analysis of the control parameter variation of each discrete point is very important to the transition state performance rule and the transition state working line design.
2) The optimal transition state working line generally requires that each discrete point reach the optimal working point, and the optimal transition state working line scheme is very difficult to design by adopting the prior art scheme;
Therefore, how to quantitatively analyze the transition state operating curve of a gas turbine is a problem to be solved.
Disclosure of Invention
The application aims to provide a design method of a transition state working line of a gas turbine engine, which aims to solve the problems that in the prior art, quantitative analysis of the transition state working line of the gas turbine is difficult and finding out the optimal working point of each discrete point is difficult.
The technical scheme of the application is as follows: a gas turbine engine transition state operating line design method comprising: setting continuous flow of each section in a transition state working line, setting the rotating speed n of the gas generator and the fuel flow w f when each part is in an instantaneous stable working state; determining the balance relation between the compressor and the gas turbine flow in the transition state, and acquiring a compressor characteristic diagram when the gas turbine guide is in a critical or supercritical state and the gas turbine front gas temperature similar parameter T t4/Tt2 is a constant; determining the pneumatic parameters of the working point of the gas turbine; acquiring a compressor characteristic diagram when the gas turbine is in a low-rotation-speed area and the gas turbine guide is in a subcritical state; determining the corresponding relation between the gas flow w f and the gas turbine front gas temperature similar parameter T t4/Tt2; controlling the fuel flow w f of each fuel gas generator under the conversion rotating speed N ghs to obtain the corresponding relation between the fuel flow w f and the pneumatic parameters of the working points of the gas turbine, and determining the positions of the working points on the characteristic lines of the same rotating speed in the transition process; according to the positions of the working points on the characteristic lines of the equal rotation speed in the transition process, establishing a transition state aerodynamic thermodynamic mathematical calculation model of the gas turbine; and designing a transition state working line of the gas turbine according to the positions of working points on the characteristic lines of each equal rotating speed in the transition state aerodynamic heating power mathematical calculation model of the gas turbine.
Preferably, the specific design method of the transition state working line of the gas turbine comprises the following steps: the method comprises the steps of adopting a gas turbine transition state pneumatic thermodynamic mathematical calculation model, changing time t into a rotating speed N ghs, and discretizing the rotating speed N ghs by a step delta N; at each discrete rotation speed node n k, taking the fuel flow w f as a variable, discretizing the fuel flow w f by a step length Deltaw f, and calculating the corresponding working point position and performance of each fuel flow; selecting working points meeting the constraint conditions of the transition state working line according to the performance of each working point on each equal-rotation-speed characteristic line; obtaining a transition state working line meeting constraint conditions according to the working points at each discrete rotating speed node; and integrating the rising and falling rotation speed rate at each discrete rotation speed node n k on the transition state working line to obtain the time corresponding to each rotation speed.
Preferably, the calculation method of the working point position and the performance thereof corresponding to the fuel flow comprises the following steps: and calculating the corresponding working point position and performance of each fuel flow by adopting a transition state model.
Preferably, the calculation method of the working point position and the performance thereof corresponding to the fuel flow comprises the following steps: and a steady-state aerodynamic thermal model is adopted, the back pressure of the gas turbine and the rotor power extraction quantity of the gas generator in the state of equal rotation speed n k are changed according to a rotor dynamics equation, and the similar parameter T t4/Tt2 of the gas temperature before the gas turbine or the fuel flow w f are changed to calculate the performance of each working point on the equal rotation speed characteristic.
Preferably, the calculation method of the working point position and the performance thereof corresponding to the fuel flow comprises the following steps: and constructing a single-rotor gas generator into a single-rotor gas turbine model, and calculating the performance of each working point corresponding to a similar parameter T t4/Tt2 or a fuel flow w f of the gas turbine before different gas turbines on the equal rotation speed characteristics according to a rotor dynamics equation.
Preferably, the equilibrium relationship between compressor and gas turbine flow at transition is:
Wherein, T t2 -total inlet temperature of the gas compressor; p t2 -total pressure at the compressor inlet; t t4 -total combustor outlet temperature.
Preferably, the calculation formula of the pneumatic parameters of the working point of the gas turbine is as follows:
Wherein N ghs is the conversion rotating speed of the gas generator, Pi is the compressor pressure ratio; wa is the compressor inlet air flow; SM is the compressor surge margin.
Preferably, the relationship between the gas flow w f and the gas turbine pre-gas temperature similarity parameter T t4/Tt2 is:
Tt4/Tt2＝f(wf)
the relationship between the obtained fuel flow and the gas turbine working point aerodynamic parameters is as follows:
According to the design method of the transition state working line of the gas turbine engine, after the flow of each section in the transition state working line is continuous and each part is in an instantaneous stable working state, the conversion rotating speed N ghs of the gas generator can be obtained through the rotating speed N of the gas generator, and the corresponding relation between the conversion rotating speed of the gas generator and the pneumatic parameters of the working point of the gas turbine is determined; obtaining a corresponding relation between the fuel oil flow w f and the pneumatic parameters of the working point of the gas turbine through a conversion relation between the fuel oil flow w f and the gas temperature similar parameter T t4/Tt2 before the gas turbine; the working point positions of all working points on the characteristic lines of all the same rotating speeds in the transition process can be directly obtained through the conversion rotating speed N ghs of the gas generator and the similar parameter T t4/Tt2 of the gas temperature before the gas turbine, and different transition state working lines formed by different working points at all the rotating speeds are determined; when the gas turbine transition state working line is designed, N ghs、wf is used as a variable, delta N and delta w f are used as step sizes, so that the working point design meeting the constraint conditions of the transition state working line can be achieved, the transition state working line meeting the constraint conditions and the time corresponding to each rotating speed can be obtained, the optimal transition process working line design scheme can be directly obtained without repeated test and compact, the design is efficient, the time consumption is short, and the quantitative analysis is efficient and stable.
Drawings
In order to more clearly illustrate the technical solution provided by the present application, the following description will briefly refer to the accompanying drawings. It will be apparent that the figures described below are merely some embodiments of the application.
FIG. 1 is a schematic diagram of the overall flow of the present application;
FIG. 2 is a schematic diagram of the effect of T t4/Tt2 of the present application on the steady state operating point of a combustion engine;
FIG. 3 is a schematic diagram of different operating points and operating lines corresponding to different fuel flow control laws of the present application;
FIG. 4 is a schematic diagram of a transition state operating line design for a gas turbine according to the present application.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application become more apparent, the technical solutions in the embodiments of the present application will be described in more detail below with reference to the accompanying drawings in the embodiments of the present application.
The design method of the transition state working line of the gas turbine engine utilizes the rotation speed n of the gas generator and the fuel flow w f to quantitatively analyze the influence law of the control parameter change of each discrete point on the transition state performance, and carries out forward design according to the quantitative analysis result of the influence law of the control parameter change of each discrete point on the transition state performance, so as to design the optimal transition state working line.
The steady-state aerodynamic thermodynamic process of the gas turbine follows a component level model of the same physical laws of mass flow balance, pressure balance, power balance of the compressor and the turbine, and the same physical rotational speed of the compressor and the turbine, and the mathematical model is generally solved by adopting numerical solutions such as Newton-Raphson method (N-R), N+1 point residual method, broyden method and the like, so that the data are relatively large, and are not further described here.
As shown in fig. 1, the specific method includes:
Step S100, setting the continuous flow of each section in a transition state working line, and setting the rotation speed n of the gas generator and the flow w f of the fuel oil when each component is in an instantaneous stable working state;
When the gas turbine is in transition state operation, aerodynamic thermal parameters describing the operation state of the gas turbine change with time, energy and mass may be accumulated and released between sections, the flow of each section is no longer continuous, and unsteady heat exchange exists between the high-temperature air flow and the wall surfaces of the blades and the casing. For a gas turbine, when the gas turbine works in a transition state, the volumes of all parts are smaller, the aerodynamic thermal parameters change much faster than the rotation speed, for example, about 10ms when an air micro-cluster passes through the gas turbine, and 70s-100s when the gas turbine is started, so that the heat accumulation and the heat accumulation effect caused by the volume effect of the parts and the heat exchange (namely heat insulation) between the air flow and the blades and the casing wall surface can be ignored, the flow of all the sections is approximately considered to be continuous at any moment, and all the parts are in instantaneous stable state working, namely the steady state assumption is made. The transition state thus satisfies the other equations in the steady-state model in addition to the compressor and turbine power balance equations in the steady-state model (see equation (1)).
Nt+Nq＝Nc (1)
The constraint relation between the transition state compressor and the turbine power satisfies the rotor dynamics equation, see formula 2, when the rotation speed of the gas turbine is stable,Equation (2) is converted to equation (1) and thus the steady state can be considered a special case in the transition state.
In the formula (1) and the formula (2):
n-gas generator rotational speed;
t-time;
-a gas generator rotational speed rate of change;
N t -gas turbine output;
n c -the power consumption of the compressor;
N q -power supplied by the starter motor during the start-up process, other transitions nq=0;
J-gas generator rotor moment of inertia.
Step S200, determining the balance relation between the compressor and the gas turbine flow in the transition state, and obtaining a compressor characteristic diagram when the gas turbine guide is in a critical or supercritical state and the gas turbine front gas temperature similar parameter T t4/Tt2 is a constant; determining the corresponding relation between the pneumatic parameters of the working point of the gas turbine and the similar parameters T t4/Tt2 of the gas temperature before the gas turbine;
When the gas turbine is in a transition state, the flow of the compressor and the gas turbine is balanced, and the flow balance formula is as follows:
wherein:
T t2 -total inlet temperature of the gas compressor;
P t2 -total pressure at the compressor inlet;
t t4 -total combustor outlet temperature.
As can be seen from equation (3):
as shown in fig. 2, when the gas turbine guide is in a critical or supercritical state, q (λ t) =1, the k value can be regarded approximately as a constant, in which case, when the gas turbine pre-gas temperature similarity parameter T t4/Tt2 is a constant, the air flow rate through the gas turbine is a similar parameter Proportional to the compressor boost ratio pi. Slope can be made on the compressor mapIs a straight line of (a). By taking a series of values of the temperature-similar parameter T t4/Tt2, a series of straight lines can be obtained on the compressor characteristic diagram.
Step S300, obtaining a compressor characteristic diagram when the gas turbine is in a low rotation speed area and the gas turbine guide is in a subcritical state;
when the gas turbine is in a low rotation speed area, the compressor pressure ratio pi is lower, the gas turbine guide is in a subcritical state, q (lambda t) <1, the K value in the formula (1) is not kept to be constant any more, and the compressor pressure ratio pi is similar to the flow rate parameter The relationship is not proportional but a curve relationship passing through pi=1 point on the ordinate axis.
Step S400, determining the relation between the gas flow w f and the gas temperature similar parameter T t4/Tt2 before the gas turbine; controlling the fuel flow w f of each fuel gas generator under the conversion rotating speed N ghs to obtain the corresponding relation between the fuel flow w f and the pneumatic parameters of the working points of the gas turbine, and determining the positions of the working points on the characteristic lines of the same rotating speed in the transition process;
as shown in fig. 3, the equivalent gas generator converts the rotational speed at each time On the characteristic line, the larger the value of the gas temperature similarity parameter T t4/Tt2 before the gas turbine is, the closer the working points on the characteristic line of equal rotation speed are to the surge boundary (see figure 1), and from another angle, each characteristic line of equal rotation speed can be considered to be composed of a series of working points, each working point has a unique T t4/Tt2 value which corresponds to each working point one by one, namely, the corresponding relation between the pneumatic parameters of the working points of the gas turbine and the conversion rotation speed N ghs of the gas generator is obtained, and the equation set (4) is obtained:
wherein:
N ghs -the conversion rotating speed of the gas generator,
Pi-compressor pressure ratio;
Wa-compressor inlet air flow;
SM-compressor surge margin.
Step S500, establishing a gas turbine transition state aerodynamic thermodynamic mathematical calculation model according to the positions of working points on the characteristic lines of the same rotating speed in the transition process;
The fuel flow w f has a functional relationship with the gas turbine pre-gas temperature similarity parameter T t4/Tt2: t t4/Tt2＝f(wf), so equation set (4) can be converted into equation set (5), and thus the value of T t4/Tt2 can be controlled by controlling the fuel flow w f at each rotation speed N ghs, so as to control the working point positions of the transition process on each equal rotation speed characteristic line, such as the working point C and the working point D corresponding to different fuel flows at the same rotation speed in fig. 2, and the working point E and the working point F corresponding to different fuel flows at another rotation speed. The transition operating line can be considered to be composed of operating points at each rotational speed, and different operating points at each rotational speed constitute different transition operating lines, such as transition operating line 1 and transition operating line 2 in fig. 3.
Equation set (5) is:
And S600, designing a transition state working line of the gas turbine according to the positions of working points on the characteristic lines of each equal rotating speed in the transition state aerodynamic heating power mathematical calculation model of the gas turbine.
As shown in fig. 4, the specific design method of the transition state working line of the gas turbine is as follows:
Step S610, a gas turbine transition state aerodynamic thermodynamic mathematical calculation model is adopted, the time t is used as a variable and is changed into the rotating speed N ghs, the rotating speed N ghs is discretized by the step delta N, and the value of a transition state starting point N 0、Wf0 is given;
Step S620, at each discrete rotation speed node n k, taking the fuel flow w f as a variable, discretizing the fuel flow w f by a step length Deltaw f, namely Wf i+1＝Wfi +DeltaWf, and calculating the corresponding working point position and performance of each fuel flow;
the calculation methods of the working point positions corresponding to the fuel flow and the performance of the working point positions are common in a plurality of methods.
Preferably, the calculation method of the working point position corresponding to the fuel flow and the performance thereof is as follows: and calculating the corresponding working point position and performance of each fuel flow by adopting a transition state model.
Preferably, the calculation method of the working point position corresponding to the fuel flow and the performance thereof is as follows: by adopting a steady-state aerodynamic thermal model, according to a rotor dynamics equation, the performance calculation of each working point on the equal rotation speed characteristic is carried out by changing the pressure after the gas turbine in the equal rotation speed N k state, the rotor power extraction quantity of the gas generator (the power extraction value is N t+Nq-Nc in the formula (2)) and the like, and changing the gas temperature similar parameter T t4/Tt2 or the fuel flow w f before the gas turbine.
Preferably, the calculation method of the working point position corresponding to the fuel flow and the performance thereof is as follows: the single-rotor gas generator is built into a single-rotor gas turbine model (the output power of the gas turbine is N t+Nq-Nc in a formula (2)), and performance calculation of each working point corresponding to a similar parameter T t4/Tt2 of the gas temperature or a fuel flow w f before the gas turbine on the equal rotation speed characteristic is performed according to a rotor dynamics equation.
Step S630, selecting working points meeting the constraint condition of the transition state working line according to the performance of each working point on each equal-rotation-speed characteristic line;
Step S640, obtaining a transition state working line meeting constraint conditions according to the working points at each discrete rotating speed node;
Step S650, integrating the rotational speed increasing and decreasing rates at each discrete rotational speed node n k on the transition state working line to obtain the time corresponding to each rotational speed.
The time t is:
After the flow of each section in the set transition state working line is continuous and each component is in the instantaneous stable working state, the conversion rotating speed N ghs of the gas generator can be obtained through the rotating speed N of the gas generator, and the corresponding relation between the conversion rotating speed of the gas generator and the pneumatic parameters of the working point of the gas turbine is determined through the step S200; and obtaining the corresponding relation between the fuel oil flow w f and the pneumatic parameters of the working point of the gas turbine through the conversion relation between the fuel oil flow w f and the gas temperature similar parameter T t4/Tt2 before the gas turbine, namely the step S400.
The working point positions of all working points on the characteristic lines of all the same rotating speeds in the transition process can be directly obtained through the conversion rotating speed N ghs of the gas generator and the similar parameter T t4/Tt2 of the gas temperature before the gas turbine, and different transition state working lines formed by different working points at all the rotating speeds are determined.
When the gas turbine transition state working line is designed, N ghs、wf is used as a variable, delta N and delta w f are used as step sizes, so that the working point design meeting the constraint conditions of the transition state working line can be achieved, the transition state working line meeting the constraint conditions and the time corresponding to each rotating speed can be obtained, the optimal transition process working line design scheme can be directly obtained without repeated test and compact, the design is efficient, the time consumption is short, and the quantitative analysis is efficient and stable.
The foregoing is merely illustrative of the present application, and the present application is not limited thereto, and any changes or substitutions easily contemplated by those skilled in the art within the scope of the present application should be included in the present application. Therefore, the protection scope of the present application shall be subject to the protection scope of the claims.
Claims (4)
1. A method of designing a transition state operating line for a gas turbine engine, comprising:
Setting continuous flow of each section in a transition state working line, setting the rotating speed n of the gas generator and the fuel flow w f when each part is in an instantaneous stable working state;
Determining the balance relation between the compressor and the gas turbine flow in the transition state, and acquiring a compressor characteristic diagram when the gas turbine guide is in a critical or supercritical state and the gas turbine front gas temperature similar parameter T t4/Tt2 is a constant; determining the corresponding relation between the pneumatic parameters of the working point of the gas turbine and the similar parameters T t4/Tt2 of the gas temperature before the gas turbine;
Acquiring a compressor characteristic diagram when the gas turbine is in a low-rotation-speed area and the gas turbine guide is in a subcritical state;
Determining a relationship between the gas flow w f and a gas turbine pre-gas temperature similarity parameter T t4/Tt2; controlling the fuel flow w f of each fuel gas generator under the conversion rotating speed N ghs to obtain the corresponding relation between the fuel flow w f and the pneumatic parameters of the working points of the gas turbine, and determining the positions of the working points on the characteristic lines of the same rotating speed in the transition process;
According to the positions of the working points on the characteristic lines of the equal rotation speed in the transition process, establishing a transition state aerodynamic thermodynamic mathematical calculation model of the gas turbine;
According to the working point positions on the characteristic lines of each equal rotating speed in the gas turbine transition state aerodynamic heating power mathematical calculation model, designing a gas turbine transition state working line;
The specific design method of the transition state working line of the gas turbine comprises the following steps:
The method comprises the steps of adopting a gas turbine transition state pneumatic thermodynamic mathematical calculation model, changing time t into a rotating speed N ghs, and discretizing the rotating speed N ghs by a step delta N;
At each discrete rotation speed node n k, taking the fuel flow w f as a variable, discretizing the fuel flow w f by a step length Deltaw f, and calculating the corresponding working point position and performance of each fuel flow;
selecting working points meeting the constraint conditions of the transition state working line according to the performance of each working point on each equal-rotation-speed characteristic line;
obtaining a transition state working line meeting constraint conditions according to the working points at each discrete rotating speed node;
Integrating the rising and falling rotation speed rate at each discrete rotation speed node n k on the transition state working line to obtain the time corresponding to each rotation speed;
The equilibrium relationship between compressor and gas turbine flow at transition state is:
Wherein, T t2 -total inlet temperature of the gas compressor; p t2 -total pressure at the compressor inlet; t t4 -total combustor outlet temperature;
the calculation formula of the pneumatic parameters of the working point of the gas turbine is as follows:
Wherein N ghs is the conversion rotating speed of the gas generator, Pi is the compressor pressure ratio; wa is the compressor inlet air flow; SM is the compressor surge margin;
The relation between the gas flow w f and the gas turbine front gas temperature similar parameter T t4/Tt2 is as follows:
Tt4/Tt2＝f(wf)
the relationship between the obtained fuel flow and the gas turbine working point aerodynamic parameters is as follows:
2. The method for designing a transition state operating line of a gas turbine engine according to claim 1, wherein the operating point position corresponding to the fuel flow and the performance thereof are calculated by: and calculating the corresponding working point position and performance of each fuel flow by adopting a transition state model.
3. The method for designing a transition state operating line of a gas turbine engine according to claim 1, wherein the operating point position corresponding to the fuel flow and the performance thereof are calculated by: and a steady-state aerodynamic thermal model is adopted, the back pressure of the gas turbine and the rotor power extraction quantity of the gas generator in the state of equal rotation speed n k are changed according to a rotor dynamics equation, and the similar parameter T t4/Tt2 of the gas temperature before the gas turbine or the fuel flow w f are changed to calculate the performance of each working point on the equal rotation speed characteristic.
4. The method for designing a transition state operating line of a gas turbine engine according to claim 1, wherein the operating point position corresponding to the fuel flow and the performance thereof are calculated by: and constructing a single-rotor gas generator into a single-rotor gas turbine model, and calculating the performance of each working point corresponding to a similar parameter T t4/Tt2 or a fuel flow w f of the gas turbine before different gas turbines on the equal rotation speed characteristics according to a rotor dynamics equation.
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| DE2715300B2 (en) * | 1977-04-05 | 1979-04-26 | Motoren- Und Turbinen-Union Muenchen Gmbh, 8000 Muenchen | Device for the optimal regulation or control of turbine jet engines for aircraft |
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| CN103267644A (en) * | 2012-06-28 | 2013-08-28 | 沈阳黎明航空发动机(集团)有限责任公司 | Engine performance simulation method |
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