Advanced Nonlinear Modeling of Gas Turbine Dynamics DOI: http://dx.doi.org/10.5772/intechopen.82015

a constant speed value 8100 rpm during the first 175 s, than a linear change to 12,400 rpm during 12 s, and the same constant value up to the transient end.

Figure 11 illustrates the dynamics of the HPT radial clearance simulated by ENDM in comparison with the steady-state clearance simulation (completely warmed-up turbine parts). One can state that ENDM correctly reflects the physics of real warming-up. From the beginning of the engine acceleration, the clearance descends in 15 s because the blade is rapidly warmed up. Next, the clearance grows due to the casing warming up. Finally, the clearance descends once more as the disk begins to warm up.

Figures 12 and 13 present the results of the comparison of the initial and enhanced dynamic models between each other and with experimental data for the same test-case transient. The plots of a fuel consumption variable in Figure 12 clearly show that the ENDM and experimental curves practically coincide. Both show the same fuel consumption overshoot after the control parameter change, and this overshoot gradually decreases during 150 s for both curves. This elevated fuel

Figure 11.

displacements are computed by similar algorithms. All these algorithms correspond

To verify the simplified dynamic clearance model (see Section 2), the following

• during the time interval τ ¼ 0:::120 s, the turbofan engine operates at idle conditions (k<sup>α</sup> =0.2031, kt =0.4125, kn ¼ 0:5929) to warm up turbine parts;

• during the time interval τ ¼ 120:::500 s, engine operates under the reference

Total HPT disk displacements (mechanical and temperature-induced) were computed for this test case in ANSYS and by the proposed SDCM (see Section 2). As shown in Figure 10, the simulation curves practically coincide. The maximum difference observed at the mode change moment is about 0.05 mm and then it lessens. Thus, the simplified model can be considered accurate enough and can be

As mentioned in the beginning of Section 2, the enhanced nonlinear dynamic model (ENDM) has been developed for a turbofan engine of a maneuverable aircraft. The main objective was to help with the synthesis and adjustment of the algorithms of an engine automatic control system. The developed ENDM is based on the original nonlinear dynamic model (NDM) and the simplified dynamic clearance models (SDCMs) created for a high-pressure turbine (HPT) and a low-

To verify the accuracy of the ENDM, it was compared with original NDM and with experimental data. A test-case transient was set by a low-pressure rotor speed nLP (control variable) profile and constant ambient conditions. The profile presents

to Blocks 1.4 and 2.4 of the engine ENDM presented in Figure 1.

7. Verification of the enhanced nonlinear dynamic model

7.1 Verification of the simplified dynamic clearance model

mode conditions (k<sup>α</sup> = 1.0, kt = 1.0, kn = 1.0).

used within ENDM of the turbofan engine under analysis.

Total disk displacement simulation (dashed line—ANSYS; solid line—SDCM).

7.2 Accuracy of the simulation of engine dynamic performance

engine dynamics test case was prepared:

Aerospace Engineering

pressure turbine.

Figure 10.

168

Dynamics of the HPT radial clearance (1—steady-state operating modes; 2—ENDM).

Figure 12. Fuel consumption dynamics (1—experimental data; 2—ENDM; 3—NDM).

begins to decrease with a maximal 7% thrust dip at the 12th second. Finally, the thrust gradually increases up to a steady-state value. Such behavior of the thrust simulated by ENDM completely corresponds to the known empirical information

In this way, all the comparison results show that, first, the dynamic clearance

nonlinear dynamic model accurately simulates this effect and in general provides by

This chapter describes a novel method to enhance a detailed physics-based nonlinear gas turbine model widely used for the aims of aircraft engine control and diagnostics. The method allows us to solve the issue of the impact of varying turbine tip clearances on the dynamic engine performance. This issue is especially impor-

Using the proposed method, an enhanced nonlinear dynamic model of a turbofan engine for a maneuverable aircraft has been developed on the basis of an initial nonlinear dynamic model and a simplified dynamic clearance model created with the results of the finite element simulation of turbine parts. The comparison with the initial model and experimental data confirmed a drastic improvement of the

This work has been carried out with the support of the National Polytechnic

influence is significant and cannot be neglected, and, second, the enhanced

far more realistic simulation than the initial dynamic model does.

tant for the engines of maneuverable aircrafts.

Advanced Nonlinear Modeling of Gas Turbine Dynamics

DOI: http://dx.doi.org/10.5772/intechopen.82015

accuracy of dynamic gas turbine simulation.

Institute of Mexico (research project 20181152).

t time, s; temperature of a heated part, K

U radial displacement of a heated part, mm

δ radial clearance between rotor and stator parts, mm

T temperature of air or gas, K T~ characteristic temperature, K

α heat transfer coefficient Δδ clearance change, mm

ε strain; relative error, %

Θ~ temperature coefficient

° reference engine operating mode

η efficiency σ stress

st static

Superscripts

171

about the clearance influence.

8. Conclusion

Acknowledgements

A surface k coefficient n rotation speed P pressure

Nomenclature

#### Figure 13.

High-pressure rotor speed dynamics (1—experimental data; 2—ENDM; 3—NDM).

consumption is explained by increased turbine clearances due to the delay in disk warming-up. In contrast, the NDM curve does not manifest a visible overshoot, and the transient process is by far shorter. One can make the same conclusion analyzing the plots of a high-pressure rotor speed in Figure 13: the ENDM curve better fits experimental data, in particular, better reflects the effect of increased clearances.

The thrust is the principal parameter of a turbofan. However, under the control law nLP = const used in the experiments, it is constant as well, and the increased clearances are compensated by the additional fuel consumption observed in Figure 12.

To show the impact of the clearances dynamically changed on the thrust, the simulation of the turbofan under the control law of a constant low pressure turbine temperature was performed. Figure 14 shows the thrust simulated by both models. It can be seen that, during the first 5 s of intensive engine dynamics, both models are equal. Then, the NDM thrust remains constant, whereas the ENDM thrust

Figure 14. Thrust dynamics (1—ENDM; 2—NDM).

Advanced Nonlinear Modeling of Gas Turbine Dynamics DOI: http://dx.doi.org/10.5772/intechopen.82015

begins to decrease with a maximal 7% thrust dip at the 12th second. Finally, the thrust gradually increases up to a steady-state value. Such behavior of the thrust simulated by ENDM completely corresponds to the known empirical information about the clearance influence.

In this way, all the comparison results show that, first, the dynamic clearance influence is significant and cannot be neglected, and, second, the enhanced nonlinear dynamic model accurately simulates this effect and in general provides by far more realistic simulation than the initial dynamic model does.
