METHODOLOGY FOR A MODELING STARTING PROCESS OF A MICRO GAS TURBINE ENGINE

Abstract

The present invention belongs to the technical field of engine modeling, and provides a methodology for modeling a starting process of a micro gas turbine engine, comprising the following steps: modeling micro gas turbine engine speed; modeling a relationship between micro gas turbine engine performance parameters and speed; and performing error analysis. Since most existing micro gas turbine engine modeling methodologies are methodologies using pure mechanism or machine learning, it is difficult to accurately describe the starting process of a micro gas turbine engine, and machine learning requires a lot of test data. In engineering practice, pure mechanisms commonly used at present are complicated in operation, low in efficiency, and low in modeling accuracy. The invention provides a methodology for modeling a starting process of a micro gas turbine engine based on a combination of a mechanism and an identification method, which makes up for the deficiencies of the prior art. The present invention is simple in operation and high in accuracy, and can implement modeling of the whole micro gas turbine engine. The methodology has certain extensibility and can be extended to other fields.

Claims

1. A methodology for modeling a starting process of a micro gas turbine engine, characterized by comprising the following steps: step 1: dividing the starting process of the micro gas turbine engine into three stages: first stage, the engine speed is from zero speed to the speed at which the turbine begins to produce power, at which the engine is completely driven to accelerate by a starter; second stage, the engine speed is from the speed at which the turbine begins to produce power to starter disengagement speed; and third stage, the engine speed is from the starter disengagement speed to idle speed; modeling the starting process in accordance with each stage of the starting process of the engine; first stage, the engine speed is from zero speed to the speed at which the turbine begins to produce power, i.e. from zero speed to ignition speed, at which the engine is completely driven to accelerate by a starter, satisfying the engine rotor motion equation, i.e. satisfying formula (1): $\begin{array}{cc}J.Math.\frac{d.Math..Math.}{\mathrm{dt}}=M_{\mathrm{st}}& \left(1\right)\end{array}$ in the formula, M.sub.st=K.sub.stI.sub.st, where I.sub.st represents the current value of the starter, and K.sub.st represents the torque constant of the starter; represents the angular velocity of the micro gas turbine engine, and J represents the moment of inertia reduced to the shaft of the micro gas turbine engine, i.e. equivalent moment of inertia, which is reduced by using conservation of mechanical energy for different micro gas turbine engine structures; specific reduction formula (2) is as follows:
J.sup.2=J.sub.1.sub.1.sup.2+J.sub.2.sub.2.sup.2+ . . . +J.sub.n.sub.n.sup.2(2) in the formula, J.sub.1 represents the moment of inertia of a load 1 driven by the shaft of the micro gas turbine engine, and .sub.1 represents the angular velocity of the load 1 driven by the shaft of the micro gas turbine engine; J.sub.2 represents the moment of inertia of a load 2 driven by the shaft of the micro gas turbine engine, and .sub.2 represents the angular velocity of the load 2 driven by the shaft of the micro gas turbine engine; J.sub.n represents the moment of inertia of a load n driven by the shaft of the micro gas turbine engine, and .sub.n represents the angular velocity of the load n driven by the shaft of the micro gas turbine engine; second stage, the engine speed is from ignition speed to starter disengagement speed, at which the engine is driven to accelerate by the starter and the turbine together, satisfying the engine rotor motion equation, i.e. satisfying formula (3): $\begin{array}{cc}J.Math.\frac{d.Math..Math.}{\mathrm{dt}}=M_{\mathrm{st}}+M_{\mathrm{gas}}& \left(3\right)\end{array}$ in the formula, M.sub.gas represents the residual torque M.sub.gas of the micro gas turbine engine after ignition, and M.sub.T represents the torque generated by the turbine; M.sub.C represents the torque consumed by the compressor, which is in direct proportion to the square of the compressor speed; M.sub.f represents the torque consumption caused by friction, which is in direct proportion to the square of the speed; M.sub.st represents the torque supplied by the electric starter, which is identical to that in formula (1); J is identical to that in formula (1), and is identical to that in formula (1); third stage, the engine speed is from starter disengagement speed to idle speed when the micro gas turbine engine is under the action of the residual speed, satisfying formula (4): $\begin{array}{cc}J.Math.\frac{d.Math..Math.}{\mathrm{dt}}=M_{\mathrm{gas}}& \left(4\right)\end{array}$ in the formula, J is identical to that in formula (1), is identical to that in formula (1); and M.sub.gas is identical to that in formula (3); step 2: modeling micro gas turbine engine speed at the first stage first, obtaining equivalent moment of inertia of the engine through calculation, see formula (2); obtaining a torque value added to the shaft of the micro gas turbine engine by the starter by using the rotor motion equation in combination with the current value of the starter according to M.sub.st=K.sub.stI.sub.st through calculation, performing integration on same by using the first-order Runge-Kutta method, to obtain the micro gas turbine engine speed of the model, and guarantee that the error between the micro gas turbine engine speed and the gas turbine engine speed in the test data is within 5%; step 3: modeling micro gas turbine engine speed at the second stage step 3.1: obtaining equivalent moment of inertia of the engine through calculation, see formula (2); obtaining the residual torque of the gas turbine engine by using the rotor motion equation in combination with the current value of the starter, wherein the residual torque of the gas turbine engine=torque generated by the turbinetorque consumed by the compressortorque caused by friction, screening all points where the absolute value of the residual torque of the gas turbine engine is zero, and according to the screened points where the absolute value of the residual torque of the gas turbine engine is zero, confirming the fuel amount corresponding to each point by using the linear interpolation method, i.e. steady-state fuel amount corresponding to a point; step 3.2: on the basis of step 3.1, performing polynomial fitting, to obtain a relational expression between the gas turbine engine speed and the steady-state fuel amount, wherein the relational expression is a ternary polynomial, expression (5) is as follows:
W.sub.fss=1.69310.sup.16N.sub.g.sup.37.63710.sup.12N.sub.g.sup.2+2.84210.sup.7N.sub.g0.0004557 (5) step 3.3: since the function relationship between the residual torque of the micro gas turbine engine and the fuel amount difference is very complicated and is highly non-linear, simplifying the function relationship, thus describing the complicated relationship by using piecewise linear functions, provided that the relationship between the residual torque of the gas turbine engine and the fuel amount difference is a piecewise linear function relationship, i.e. simplifying using formula (6):
M.sub.gas=k(n)(W.sub.fW.sub.fss)+b(n)(3) in the formula, k(n) and b(n) represent coefficients, for different gas turbine engine speeds, the values thereof are different, that is, the values of k(n) and b(n) represent functions of the gas turbine engine speed n, (W.sub.fW.sub.fss) represents the difference between the dynamic fuel amount and the steady-state fuel amount obtained by the polynomial, for different gas turbine engine speeds, the values thereof are different; step 3.4: summing the residual torque of the micro gas turbine engine and the torque acted on the shaft of the gas turbine engine by the starter, performing integration on same by using the first-order Runge-Kutta method, to obtain the calculated micro gas turbine engine speed of the model, and guarantee that the error between the micro gas turbine engine speed and the gas turbine engine speed in the test data is within 5%; step 3.5: in order to guarantee the error between the micro gas turbine engine speed and the gas turbine engine speed in the test data is within 5% mentioned in step 3.4, adjusting k(n) and b(n) in formula (6) in real time according to the micro gas turbine engine speed, so that the speed of the constructed micro gas turbine engine starting model is close to the actual test speed to a maximum extent; step 4: modeling micro gas turbine engine speed at the third stage first, obtaining the equivalent moment of inertia of the engine through calculation, see formula (2); obtaining the torque value added to the shaft of the micro gas turbine engine by the starter by using the rotor motion equation in combination with the fuel amount according to formula (6) through calculation, performing integration on same by using the first-order Runge-Kutta method to obtain the micro gas turbine engine speed of the model, and guarantee that the error between the micro gas turbine engine speed and the gas turbine engine speed in the test data is within 5%; adjusting k(n) and b(n) in formula (6) in real time according to the micro gas turbine engine speed, so that the speed of the constructed micro gas turbine engine starting model is close to the actual test speed to a maximum extent; step 5: since the relationship between the micro gas turbine engine performance parameters (including compressor outlet temperature, compressor outlet pressure, combustion chamber outlet pressure, turbine outlet temperature and turbine outlet pressure) and the gas turbine engine speed is very close, fitting the function expression between the gas turbine engine performance parameters and the gas turbine engine speed, that is:
T.sub.2=K.sub.TN.sub.g.sup.2(7) in formula (7), T.sub.2 represents compressor outlet temperature, K.sub.T represents compressor outlet temperature coefficient, for different starting processes, the parameters thereof are different, and N.sub.g represents micro gas turbine engine speed;
P.sub.2=K.sub.pN.sub.g.sup.2(8) in formula (8), P.sub.2 represents compressor outlet pressure, K.sub.P represents compressor outlet pressure coefficient, for different starting processes, the parameters thereof are different, and N.sub.g represents micro gas turbine engine speed;
P.sub.3C=K.sub.cN.sub.g.sup.2(9) in formula (9), P.sub.3C represents combustion chamber outlet pressure, K.sub.c represents combustion chamber outlet pressure coefficient, for different starting processes, the parameters thereof are different, and N.sub.g represents micro gas turbine engine speed;
P.sub.4=constant+k.sub.wpN.sub.g(10) in formula (10), the turbine outlet pressure P.sub.4 is modeled into constant value+k.sub.wpN.sub.g, the constant value is 1.03 times as much as the standard atmospheric pressure, k.sub.wpN.sub.g is related to micro turbine engine speed during operation, and k.sub.wp varies with the micro turbine engine speed;
T.sub.4=K.sub.tN.sub.g N.sub.g[0,0.4N.sub.gt]
T.sub.4=constant N.sub.g[0.4N.sub.gt,N.sub.idle](11) in formula (11), T.sub.4 represents turbine outlet temperature, K.sub.1 represents turbine outlet temperature coefficient, for different starting processes, the parameters thereof are different, N.sub.g represents speed of the micro gas turbine engine, N.sub.gt represents rated speed of the micro gas turbine engine, and N.sub.idle represents idle speed of the micro gas turbine engine; step 6: linearly discretizing the obtained polynomial function relationship between the micro gas turbine engine performance parameters and speed, that is, linearly discretizing formulas (7), (8), (9), (10) and (11), wherein in order to guarantee the discretization accuracy, the step length value of the micro gas turbine engine speed is taken as 0.2%N.sub.gt, and putting the discretized data in a corresponding one-dimensional linear interpolation table.

Description

DESCRIPTION OF DRAWINGS

[0023] FIG. 1 is a flow chart of modeling of a micro gas turbine engine.

[0024] FIG. 2 is a diagram showing a relationship between residual torque and fuel amount.

[0025] FIG. 3 is a diagram showing a relationship between fuel amount difference and residual torque.

[0026] FIGS. 4(a)-4(f) are comparison diagrams of modeling errors of a starting process, where (a) error of compressor outlet temperature; (b) error of compressor outlet pressure; (c) error of combustion chamber outlet pressure; (d) error of turbine outlet pressure; (e) error of turbine outlet temperature; (f) error of gas turbine engine speed.

DETAILED DESCRIPTION

[0027] To make the purpose, the technical solution and the advantages of the present invention more clear, the present invention will be further described below in detail in combination with the drawings and the examples.

[0028] A methodology for modeling a starting process of a micro gas turbine engine, comprising the following steps:

[0029] Step 1: dividing the starting process of the micro gas turbine engine into three stages: first stage, the engine speed is from zero speed to the speed at which the turbine begins to produce power, at which the engine is completely driven to accelerate by a starter; second stage, the engine speed is from the speed at which the turbine begins to produce power to starter disengagement speed; third stage, the engine speed is from the starter disengagement speed to idle speed;

[0030] modeling the starting process in accordance with each stage of the starting process of the engine;

[0031] first stage, the engine speed is from zero speed to the speed at which the turbine begins to produce power (i.e. from zero speed to ignition speed), at which the engine is completely driven to accelerate by a starter, satisfying the engine rotor motion equation, i.e. satisfying formula (1):

[00001]$\begin{array}{cc}J.Math.\frac{d.Math..Math.}{\mathrm{dt}}=M_{\mathrm{st}}& \left(1\right)\end{array}$

[0032] in the formula, M.sub.st=K.sub.stI.sub.st, where I.sub.st represents the current value of starter, K.sub.st represents the torque constant of the starter, for different types of starters, the values thereof are different. The starter referred here is an electric starter. represents the angular velocity of the micro gas turbine engine, J represents moment of the inertia reduced to the shaft of the micro gas turbine engine, i.e. equivalent moment of inertia, which is reduced by using conservation of mechanical energy for different micro gas turbine engine structures. Specific reduction formula (2) is as follows:

J.sup.2=J.sub.1.sub.1.sup.2+J.sub.2.sub.2.sup.2+ . . . +J.sub.n.sub.n.sup.2(2)

[0033] in the formula, J.sub.1 represents the moment of inertia of a load 1 driven by the shaft of the micro gas turbine engine, and .sub.1 represents the angular velocity of the load 1 driven by the shaft of the micro gas turbine engine; J.sub.2 represents the moment of inertia of a load 2 driven by the shaft of the micro gas turbine engine, and .sub.2 represents the angular velocity of the load 2 driven by the shaft of the micro gas turbine engine; J.sub.n represents the moment of inertia of a load n driven by the shaft of the micro gas turbine engine, and .sub.n represents the angular velocity of the load n driven by the shaft of the micro gas turbine engine.

[0034] Second stage, the engine speed is from ignition speed to starter disengagement speed, at which the engine is driven to accelerate by the starter and the turbine together, satisfying the engine rotor motion equation, i.e. satisfying formula (3):

[00002]$\begin{array}{cc}J.Math.\frac{d.Math..Math.}{\mathrm{dt}}=M_{\mathrm{st}}+M_{\mathrm{gas}}& \left(3\right)\end{array}$

[0035] in the formula, M.sub.gas represents the residual torque M.sub.gas=M.sub.TM.sub.CM.sub.f of the micro gas turbine engine after ignition, M.sub.T represents the torque generated by the turbine, M.sub.C represents the torque consumed by the compressor, which is in direct proportion to the square of the compressor speed in general, and M.sub.f represents the torque consumption caused by friction, which is in direct proportion to the square of the speed in general; M.sub.st represents the torque supplied by the electric starter, which is identical to that in formula (1). The calculation process of J is identical to that in formula (1), and is identical to that in formula (1).

[0036] Third stage, the engine speed is from starter disengagement speed to idle speed when the micro gas turbine engine is under the action of the residual speed, satisfying formula (4):

[00003]$\begin{array}{cc}J.Math.\frac{d.Math..Math.}{\mathrm{dt}}=M_{\mathrm{gas}}& \left(4\right)\end{array}$

[0037] in the formula, J is identical to that in formula (1), and co is identical to that in formula (1). The calculation process of M.sub.gas is identical to that in formula (3).

[0038] Step 2: modeling micro gas turbine engine speed at the first stage

[0039] First, obtaining equivalent moment of inertia of the engine through calculation (see formula (2) for details); obtaining a torque value added to the shaft of the micro gas turbine engine by the starter by using the rotor motion equation in combination with the current value of the starter according to M.sub.st=K.sub.stI.sub.st through calculation, performing integration on same by using the first-order Runge-Kutta method (Euler method), to obtain the micro gas turbine engine speed of the model, and guarantee that the error between the micro gas turbine engine speed and the gas turbine engine speed in the test data is within 5%.

[0040] Step 3: modeling micro gas turbine engine speed at the second stage

[0041] Step 3.1: obtaining equivalent moment of inertia of the engine through calculation (see formula (2) for details); obtaining the residual torque of the gas turbine engine by using the rotor motion equation in combination with the current value of the starter, wherein the residual torque of the gas turbine engine=torque generated by the turbinetorque consumed by the compressortorque caused by friction, screening all points where the absolute value of the residual torque of the gas turbine engine is zero, and according to the screened points where the absolute value of the residual torque of the gas turbine engine is zero, confirming the fuel amount corresponding to each point by using the linear interpolation method, i.e. steady-state fuel amount corresponding to a point;

[0042] Step 3.2: on the basis of step 3.1, performing polynomial fitting, to obtain a relational expression between the gas turbine engine speed and the steady-state fuel amount, wherein the relational expression is a ternary polynomial, specific polynomial coefficients are somewhat different since fuel types are different, the fuel adopted here is natural gas, see formula (5) for specific expression thereof:

W.sub.fss=1.69310.sup.16N.sub.g.sup.37.63710.sup.12N.sub.g.sup.2+2.84210.sup.7N.sub.g0.0004557(5)

[0043] Step 3.3: since the function relationship between the residual torque of the micro gas turbine engine and the fuel amount difference is very complicated and is highly non-linear, simplifying the function relationship, describing the complicated relationship by using piecewise linear functions, provided that the relationship between the residual torque of the gas turbine engine and the fuel amount difference is a piecewise linear function relationship, i.e. describing using formula (6):

M.sub.gas=k(n)(W.sub.fW.sub.fss)+b(n) (6)

[0044] in the formula, k(n) and b(n) represent coefficients, for different gas turbine engine speeds, the values thereof are different, that is, the values of k(n) and b(n) represent functions of the gas turbine engine speed n, (W.sub.fW.sub.fss) represents the difference between the dynamic fuel amount and the steady-state fuel amount obtained by the polynomial, for different gas turbine engine speeds, the values thereof are different;

[0045] Step 3.4: summing the residual torque of the micro gas turbine and the torque acted on the shaft of the gas turbine engine by the starter, performing integration on same by using the first-order Runge-Kutta method (Euler method), to obtain the calculated micro gas turbine engine speed of the model, and guarantee that the error between the micro gas turbine engine speed and the gas turbine engine speed in the test data is within 5%;

[0046] Step 3.5: in order to guarantee the error between the micro gas turbine engine speed and the gas turbine engine speed in the test data is within 5% mentioned in step 3.4, adjusting k(n) and b(n) in formula (6) in real time according to the micro gas turbine engine speed, so that the speed of the constructed micro gas turbine engine starting model is close to the test speed to a maximum extent.

[0047] Step 4: modeling micro gas turbine engine speed at the third stage

[0048] First, obtaining equivalent moment of inertia of the engine through calculation (see formula (2) for details); obtaining the torque value added to the shaft of the micro gas turbine engine by the starter by using the rotor motion equation in combination the fuel amount according to formula (6) through calculation, performing integration on same by using the first-order Runge-Kutta method (Euler method) to obtain the micro gas turbine engine speed of the model, and guarantee that the error between the micro gas turbine engine speed and the gas turbine engine speed in the test data is within 5%; adjusting k(n) and b(n) in formula (6) in real time according to the micro gas turbine engine speed, so that the speed of the constructed micro gas turbine engine starting model is close to the test speed to a maximum extent.

[0049] Step 5: since the relationship between the micro gas turbine engine performance parameters (mainly including compressor outlet temperature, compressor outlet pressure, combustion chamber outlet pressure, turbine outlet temperature and turbine outlet pressure) and the gas turbine engine speed is very close, fitting the function expression between the gas turbine engine performance parameters and the gas turbine engine speed by using a data fitting tool coming with MATLAB, that is:

T.sub.2=K.sub.TN.sub.g.sup.2(7)

[0050] in formula (7), T.sub.2 represents compressor outlet temperature, K.sub.T represents compressor outlet temperature coefficient, for different starting processes, the parameters thereof are different, and N.sub.g represents micro gas turbine engine speed;

P.sub.2=K.sub.PN.sub.g.sup.2(8)

[0051] in formula (8), P.sub.2 represents compressor outlet pressure, K.sub.P represents compressor outlet pressure coefficient, for different starting processes, the parameters thereof are different, and N.sub.g represents micro gas turbine engine speed;

P.sub.3C=K.sub.cN.sub.g.sup.2(9)

[0052] in formula (9), P.sub.3C represents combustion chamber outlet pressure, K.sub.c represents combustion chamber outlet pressure coefficient, for different starting processes, the parameters thereof are different, and N.sub.g represents micro gas turbine engine speed;

P.sub.4=constant+k.sub.wpN.sub.g(10)

[0053] in formula (10), the turbine outlet pressure P.sub.4 is modeled into constant value+k.sub.wpN.sub.g, the constant value is 1.03 times as much as the standard atmospheric pressure, k.sub.wpN.sub.g is related to the micro turbine engine speed during operation, and k.sub.wp varies with the micro turbine engine speed;

T.sub.4=K.sub.tN.sub.g N.sub.g[0,0.4N.sub.gt]

T.sub.4=constant N.sub.g[0.4N.sub.gt,N.sub.idle](11)

[0054] in formula (11), T.sub.4 represents turbine outlet temperature, K.sub.t represents turbine outlet temperature coefficient, for different starting processes, the parameters thereof are different, N.sub.g represents speed of the micro gas turbine engine, N.sub.gt represents rated speed of the micro gas turbine, and N.sub.idle represents idle speed of the micro gas turbine.

[0055] Step 6: linearly discretizing the obtained polynomial function relationship between the micro gas turbine engine performance parameters and speed, that is, linearly discretizing formulas (7), (8), (9), (10) and (11), wherein in order to guarantee the discretization accuracy, the step length value of the micro gas turbine engine speed is taken as 0.2%N.sub.gt, and putting the discretized data in a corresponding one-dimensional linear interpolation table.

[0056] Error analysis: according to the test data of the gas turbine engine, it is obtained that the difference between each of compressor outlet pressure, compressor outlet temperature, combustion chamber outlet pressure, turbine outlet pressure, turbine outlet temperature, micro gas turbine engine speed and the gas turbine engine starting model is within 5%, indicating that the methodology for modeling a starting process of a micro gas turbine engine proposed by the present invention is effective and feasible.