1.3 Tip clearance dynamic effect

There is also an important indirect dynamic effect of the warming-up of engine parts, and this effect has not been taken into consideration in the NDMs yet. The point is that during engine transients, the dynamics of the warming-up is different for a rotor and a stator. The rotor parts, especially massive disks, change slowly their temperature while relatively thin stator parts are warmed up faster. Consequently, the radial displacements of rotor blade tips delay from those of the corresponding casing surfaces, and tip clearances dynamically increase during engine acceleration and decrease during the deceleration.

a simplified dynamic clearance model (SDCM) was formed. Forth, SDCM was integrated into a nonlinear dynamic model of the turbofan resulting in an enhanced nonlinear dynamic model (ENDM). The rest of this chapter is devoted to the results of the mentioned finite element method calculations, description of the SDCM and its integration into NDM, and the results of simulation by the enhanced model. A high-pressure turbine and its disk are mostly used to exemplify the proposed

The structure and operation of the above-mentioned ENDM are illustrated by Figure 1. Modules 1–4 constitute SDCM of an engine component, compressor or turbine. Module 5 presents an initial engine model, which, in conjunction with SDCM, presents the enhanced nonlinear model. Only one component is presented on this scheme for simplicity. The software of ENDM includes SDCMs for all the components where the dynamic clearance effect is significant. The enhanced model has been developed for a low-bypass two-spool turbofan engine of a maneuverable aircraft. All simplified relations for the clearance model were obtained through exhaustive calculations in ANSYS with the solid models of engine stator and rotor hot parts, namely disk, blade, and casing. The below description of the clearance model is given for a high-pressure turbine (HPT) of this engine as a component

The initial nonlinear dynamic model includes the dynamics of two engine rotors. The corresponding differential equations are solved through their integration by an iterative procedure. In each step, the corrections to state variables (rotation speeds) are obtained and all engine variables are renewed. The enhanced engine model

methodology.

example.

Figure 1.

157

Structure of the enhanced nonlinear dynamic model.

2. Enhanced nonlinear dynamic model

Advanced Nonlinear Modeling of Gas Turbine Dynamics

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

As the result of increased tip clearance losses, the efficiency of compressor and turbine components lowers and overall engine performance significantly degrades. Sobey and Suggs 1963 demonstrate in book [15] that the 1% turbine tip clearance increase results in the 1% reduction of turbine efficiency and the 1.5–2% increase of engine-specific fuel consumption. The impact of a compressor clearance is even greater: the 1% clearance increase causes the 1.5–3% specific fuel consumption growth. As shown in [16] for the acceleration from the idle to the take-off regime, the increase rate of aircraft engine thrust can reduce twice due to the dynamic clearance increase. The maintenance results show that the corresponding thrust loss can reach from 3 to 15% and takes place from 20th to 60th second after the engine regime change. Thus, significant thrust reduction can happen during the aircraft take-off putting the flight at risk.

Since modern aircraft gas turbine engines need effective control and monitoring systems, accurate detailed nonlinear dynamic models are in increasing demand. In this way, the modeling of the above-described dynamic clearance effect must be implemented in NDMs. So far, such dynamic models use fixed component performance maps obtained at steady states for warmed-up components. The difficulty to introduce the effect of dynamic clearances consists in the fact that they depend on stress-strain state of the stator and rotor parts, and the stresses and strains have irregular distribution that varies in time. Thus, it becomes clear that accurate modeling of the dynamic clearance effect needs the application of finite element methods to the heated parts. The problem is that such calculations are very timeconsuming and cannot be directly implemented in NDMs.

As mentioned above, the clearance effect can be modeled only by the analysis of stress-strain state of both stator and rotor HPs with a known initial temperature distribution and a heating rate. The clearance model that meets such conditions was considered in [17]. Unfortunately, this model does not take into account a real shape of HPs and therefore cannot ensure a high accuracy of dynamic engine simulation. The model presented by Archipov et al. in [18] already accounts for the shape but takes other strong limitation that the material properties are independent on material. The authors also make a disputable statement that aerodynamic and pressure gas forces have significant influence on the clearances only for high-power lowspeed turbines of industrial power plants. Kurzke proposed NDM with the dynamic clearance model integrated [19]. However, this model does not take into account a radial disk extension and the aerodynamic action of gases on the blade and the casing. Paper [20] compares three variations of the dynamic clearance model. It was found that impulse response model is the most accurate but also time- and memoryconsuming. Thus, this model cannot be directly integrated into NDM.

Our previous papers [21, 22] generally follow the ideas of the impulse response model. First, solid models of hot parts of a turbofan had been created. Second, multiple calculations were conducted using the finite element method to understand how the displacements of the hot part surfaces depend on the external temperatures and the loads applied. Third, on the basis of these numerical experiments, 1.3 Tip clearance dynamic effect

Aerospace Engineering

take-off putting the flight at risk.

156

engine acceleration and decrease during the deceleration.

consuming and cannot be directly implemented in NDMs.

consuming. Thus, this model cannot be directly integrated into NDM.

Our previous papers [21, 22] generally follow the ideas of the impulse response model. First, solid models of hot parts of a turbofan had been created. Second, multiple calculations were conducted using the finite element method to understand how the displacements of the hot part surfaces depend on the external temperatures and the loads applied. Third, on the basis of these numerical experiments,

There is also an important indirect dynamic effect of the warming-up of engine parts, and this effect has not been taken into consideration in the NDMs yet. The point is that during engine transients, the dynamics of the warming-up is different for a rotor and a stator. The rotor parts, especially massive disks, change slowly their temperature while relatively thin stator parts are warmed up faster. Consequently, the radial displacements of rotor blade tips delay from those of the corresponding casing surfaces, and tip clearances dynamically increase during

As the result of increased tip clearance losses, the efficiency of compressor and turbine components lowers and overall engine performance significantly degrades. Sobey and Suggs 1963 demonstrate in book [15] that the 1% turbine tip clearance increase results in the 1% reduction of turbine efficiency and the 1.5–2% increase of engine-specific fuel consumption. The impact of a compressor clearance is even greater: the 1% clearance increase causes the 1.5–3% specific fuel consumption growth. As shown in [16] for the acceleration from the idle to the take-off regime, the increase rate of aircraft engine thrust can reduce twice due to the dynamic clearance increase. The maintenance results show that the corresponding thrust loss can reach from 3 to 15% and takes place from 20th to 60th second after the engine regime change. Thus, significant thrust reduction can happen during the aircraft

Since modern aircraft gas turbine engines need effective control and monitoring systems, accurate detailed nonlinear dynamic models are in increasing demand. In this way, the modeling of the above-described dynamic clearance effect must be implemented in NDMs. So far, such dynamic models use fixed component performance maps obtained at steady states for warmed-up components. The difficulty to introduce the effect of dynamic clearances consists in the fact that they depend on stress-strain state of the stator and rotor parts, and the stresses and strains have irregular distribution that varies in time. Thus, it becomes clear that accurate modeling of the dynamic clearance effect needs the application of finite element methods to the heated parts. The problem is that such calculations are very time-

As mentioned above, the clearance effect can be modeled only by the analysis of stress-strain state of both stator and rotor HPs with a known initial temperature distribution and a heating rate. The clearance model that meets such conditions was considered in [17]. Unfortunately, this model does not take into account a real shape of HPs and therefore cannot ensure a high accuracy of dynamic engine simulation. The model presented by Archipov et al. in [18] already accounts for the shape but takes other strong limitation that the material properties are independent on material. The authors also make a disputable statement that aerodynamic and pressure gas forces have significant influence on the clearances only for high-power lowspeed turbines of industrial power plants. Kurzke proposed NDM with the dynamic clearance model integrated [19]. However, this model does not take into account a radial disk extension and the aerodynamic action of gases on the blade and the casing. Paper [20] compares three variations of the dynamic clearance model. It was found that impulse response model is the most accurate but also time- and memorya simplified dynamic clearance model (SDCM) was formed. Forth, SDCM was integrated into a nonlinear dynamic model of the turbofan resulting in an enhanced nonlinear dynamic model (ENDM). The rest of this chapter is devoted to the results of the mentioned finite element method calculations, description of the SDCM and its integration into NDM, and the results of simulation by the enhanced model. A high-pressure turbine and its disk are mostly used to exemplify the proposed methodology.
