Gas turbine vibration modeling for the supervision of their dynamic

The 2sd International Conference on Applied Automation and Industrial Diagnostics, Djelfa on 16-17 September 2017, Algeria

Gas turbine vibration modeling for the supervision of their dynamic behavior in an accident situation: Case of Solar TITAN 130 1

1*,

Merouane Alaoui , Ahmed Hafaifa

2

Mouloud Guemana and Ahmed Chaibet

3

Applied Automation and Industrial Diagnostics Laboratory, Faculty of Science and Technology, University of Djelfa 17000 DZ, Algeria Emails : [email protected], [email protected], [email protected] Emails: [email protected], [email protected] 2 Faculty of Science and Technology, University of Medea 26000 DZ, Algeria Emails: [email protected] 3 Aeronautical Aerospace Automotive Railway Engineering School, ESTACA Paris, France. Email: [email protected] Abstract This work deals with the phenomena of vibration of turbines in accidental situations, the appearance and propagation of a crack or hole in a blade of a wheel of the rotating machine is a phenomenon that must also be taken into account Both by the manufacturers and by the operators of these machines. In order to ensure that their installations are not damaged, the latter have a few tools in which online vibration monitoring is one of the most commonly used. Based on a vibration measurement at bearings, it allows continuous monitoring of the mechanical condition of the equipment and an early diagnosis of the main defects. Firstly, we study the system of vibration monitoring of the turbine. From the regularly collected vibrations, it is possible to detect any malfunctions and to follow their evolution in order to plan or postpone a mechanical intervention. This continuous monitoring is carried out during operation of the machine. Keywords: Gas turbine vibration, monitoring system, vibration predictions. 1 Introduction The vibration monitoring system in the gas turbine proposed in this article adopts the fundamental strategy known from the industrial diagnostic literature [16] [19], it is carried out in three fundamental steps, in a first step, Is to determine whether the process in question behaves or operates correctly in relation to the specifications which the engineer has set himself during the design of the system in question, and then a second step, the object of which is to investigate certain characteristics of the defect Its moment of appearance, its amplitude, its gravity and finally the last step which follows from the two preceding steps, makes it possible to decide the action to be taken on the system, it may be necessary to maintain the system in the same operating mode , To correct its operation or to stop it completely. The feedback on the solar turbine TITAN 130 of the compressor station SC3 moudjbara Algeria showed the presence of the holes in the blades of the fixed and mobile HP wheels of the turbine following the shearing of a screw in the diaphragm. The first objective of this work is the modeling of


an accidental slowdown without contact. The initial conditions correspond to the normal conditions of operation of a turbine at nominal speed under own weight. At any given moment, a blade stands out at the most unfavorable position. The shaft line is disconnected and slows down until the machine is completely stopped. However, near critical speeds, design play between shaft and diaphragm is consumed by large unbalance. The large unbalance corresponding to the loss of a blade causes strong vibrations of the turbine, notably in the vicinity of certain speeds of rotation for which the vibratory response is maximum. It is therefore necessary to represent the dynamic behavior of the stator and to couple its response with that of the rotor by means of the contact forces, which represents the second objective of this work. 2. Gas turbine The large unbalance corresponding to the loss of metal or fin terminates strong vibrations of the turbine, notably in the vicinity of certain speeds of rotation for which the vibratory response of the turbine is maximum: these speeds of rotation are called critical speeds and they can not be avoided during the accidental stopping of the rotor which changes from its nominal speed to a zero speed. Simulations carried out show that when the critical velocities change, the excitation force, and consequently the vibration level, is such that contacts can occur between the rotor and the stator at several points along the shaft line. Particularly with regard to the seals provided on the diaphragms, shown in Figure 1, shows the geometry of a diaphragm of the turbine TC01 TITAN 130 of the compression station SC3-Moudjbara willaya of DJELFA -ALGERIE disassembled during a maintenance operation, the contact being able to take place between the inner ring and the Periphery of the shaft. In this article we aim at the following objectives: 1.

The design of a system for supervision and monitoring of vibrations in gas turbines,

2.

to study the dynamic behavior coupled rotor-stator during an accidental slowdown,

3.

Exploration by experimental and analytical numerical models of the vibratory response of a

rotor of rotating machine affected by cracks in order to exhibit the parameters likely to favor the detection of the cracks in the framework of a monitoring procedure. The interpretation of the data from the vibration monitoring system in the turbine N ° 01, Solar TITAN 130 of the SC3-Moudjbara-Willaya compression station of DJELFA-ALGERIA.

2


Fig 1. Arrangement of the diaphragm in the HP Solar TITAN 130 turbine assembly A gas turbine is a continuous flowing rotating engine, equipped with an axial compressor and combustion chambers; It is able to itself produce a fluid under pressure and at a very high temperature which, by undergoing its expansion phase in the deferent stages of the turbine, supplies mechanical energy to the outside, A self-sufficient unit that is sufficient for itself. The solar turbine turbine TITAN 130 (FIG. 2) is a two-shaft, axial-flow turbine comprising the following main assemblies and components: An air inlet assembly, A turbine compressor assembly A compressor / combustion chamber diffuser assembly A turbine assembly An exhaust manifold One output drive shaft. The main components of the turbine remain precisely aligned via counter flanges having pilot surfaces and are bolted together to form a rigid assembly. The turbine develops its output power by transforming the energy of the gas expansion into mechanical rotational power. The energy of expansion of the gases drives the stages of the turbine which turn the compressor section of the turbo machine. The gases then pass through the free turbine which, taking up their energy, transmits the latter to the output drive shaft which drives the driven equipment. Refer to Table 1 for the specifications of the Titan 130-19802 Gas Turbine, shown in Figure 2.

3


Fig 2. Turbine Solar TITAN 130 Table 1: Characteristics of the Solar TITAN 130 gas turbine Quantity

Value

Output Power

14 500 kW (19800 hp)

Heat Rate

9940 kJ/kW-hr (7025Btu /hp-hr)

Exhaust Flow

180050 kg/hr (396,940 lb/hr)

Exhaust Temperature

505°C (940°F)

Max Speed NGP

11222 rpm

Max Speed NGP

8856 rpm

3. Supervision and monitoring of vibration defects The monitoring of the defects of the vibrations proposed in this work for the supervision of a gas turbine Solar TITAN 130 consists of the subsystems associated with the control system of the turbine, has for object to make the detection, the localization And the identification of axial, radial and velocity vibration defects in the critical locations of the turbine. This helps the operator to monitor and make a decision to resume an order. The proposed approach is based on the FDI (Fault detection and isolation) [1] [2] [3] [16] [19] method, illustrated in Figure 3, to detect any deviation by generation of residues that are The fault detector of the normal vibration behavior of the turbine examined, the location makes it possible to trace the fault and locate the faulty component (s) and the identification determines the moment of occurrence of the fault, Duration and its amplitude and alerts the operators of the presence of a defect.

4


The vibration control adopted in this work is based on a vibration monitoring system using proximity probes, accelerometers and transducers to measure displacements and acceleration. Measurements of the radial and axial vibration data are made by the various activated probes and measure the gap DC voltage between the probe and a moving surface of the turbine under test to measure the high frequency displacement. The vibration monitoring system uses seismic sensors to measure speed or acceleration, which seismic devices, also known as accelerometers, measure the movements at lower frequencies. Indeed, the seismic measurements are based on the elastic deformation of a piezoelectric element mounted on a relatively high mass of inertia. Where, the system checks for errors and the status is correct. The vibration monitoring system, shown in Figure 3, communicates status and vibration data to the turbine control adaptation system via a communication adapter module and with location monitoring and identification modules also referred to as module monitors. Also, proximity detection or transducer input modules, named according to the vibration data they transmit, such as the radial or seismic inputs of the vibration sensors, are used in the system for monitoring the vibration defects of the tested gas turbine.

Combustor

Ambient Conditions

Exhaust Temperature

Axial compressor

Load

Turbin e

Model identification

Actuators

Control laws adaptation

Residuals generation

Sensors

Detection

Localization

Identification

Fig 3. Vibration Diagnostics and Monitoring

5


4. Linear modeling and accidental computation The development of a one-dimensional rotor model is adopted where the variables to be calculated are the displacements of a beam in a three-dimensional space and the rotor angular position [ [20]. For the shaft line model, the rotating part of the turbo-generator group is composed of shafts on which are mounted bladed wheels. The various bodies of the shaft line are supported by bearings, the turbine is sufficiently slender to represent it by timoshenko beams in rotation. in facto, considering a straight section of the rigid rotor. Figure 4, illustrates an example of a shaft comprising each of the elements: the simple supports can be seen as infinitely rigid bearings and can obviously be replaced by more realistic bearing elements. After introducing the necessary marks for describing the kinematics of the shaft line, the methodology used to model the turbine can be summarized as follows: Write the kinetic and deformation energies for each of the rotor components; Spatially discrete the different elements by the finite element method; Derive the energies calculated according to the Lagrange equations; Assemble the equations of the motion obtained for each element to represent the dynamics of the structures.

Fig 4. Example of a turbine model and its associated mesh In general, and in order to describe the dynamics of a mechanical system, the preliminary and necessary step of the modeling consists in defining the parameters and the marks associated with the movement of the structure. Thus the marks corresponding to a beam in the three-dimensional space are shown in Figure 5 where:

is the neutral axis of the rotor in its initial configuration;

and

are

the main axes of inertia of the rotor under consideration; U, V and W are respectively the displacements along the X, Y and Z axes of the point of intersection between the cross section and the neutral axis of the shaft line;

( , ,

) is the absolute coordinate system linked to a cross-

6


section of the beam (initial configuration);

( , ,

) is an intermediate rotation mark; R (

)

is the reference point linked to the cross-section of the beam (deformed configuration).

The transition from the reference

to the reference R is done by three successive rotations

corresponding to the angles of Euler with

are precession.

Fig 5. Notations for a disc

Rotation around

(nutation);

Rotation around

(clean rotation).

The proper rotation of the beam and of the torsion angle

is then composed of the rotation of the rigid body of the shaft

(FIG. 6).

Fig 6. Transition from Rg to R

7


For the calculation of the instantaneous vector of rotation of the reference R with respect to the reference frame

. By definition, the rotation speed of the solid is written:

(1)

(2)

(3) Consider an infinitely rigid circular disc subjected to a variable speed of rotation. The disc being in deformable, this results in a zero deformation energy. Using the notations introduced in Figure 5, the displacement field associated with the disk is:

(4)

(5) Where the different quantities are: -

the mass of the disc;

-

: The instantaneous velocity vector with O fixed in; The disk inertia operator.

Since the principal axes of the disk are x, y and z, and given the symmetries, the inertia operator is written:

(6) All calculations made, the exact expression of the kinetic energy is:

8


(7) It is classical to work with linearized equations of motion, obtained from the energies developed to order 2. In the present case, such an approximation would result in the forgetting of terms resulting from the gyroscopic effect

as well as coupling between the different vibrations of the turbine

. This is why we develop this energy by keeping the terms of order 3. Therefore, we obtain:

(8) The tree is modeled by a rotating timoshenko beam. The general formulation of the kinetic energy of the tree is obtained by extending the case of the disk: the energy of a beam slice, of infinitesimal length dz, is that of a disk of the same dimension (equation (8) ). Thus, by integrating this formula along the length of the tree, it comes:

(9) The deformation energy of a rotating Timoshenko beam is equal to:

(10) Where k is the correction factor for shear stiffness. For the unbalance phenomenon, it is chosen to represent the loss of a fin (Fig. 7), or a residual imbalance resulting from the imperfect balancing of the rotor (Figure 8), the Solar Turbine turbine TITAN 130 No. 01 of The SC3-Moudjbara compressor station during a maintenance operation.

9


Fig 7. Damaged fins (Solar turbine TITAN130)

Fig 8. HP Wheel Rotor (Solar TITAN130 turbine) By introducing an unbalance as a point mass, located at a distance from the axis of rotation. Considering the notations introduced in Figure 9, the displacement field associated with the unbalance is determined by:

(11) Thus the velocity of the unbalance is:

10


Fig 9. Notation for unbalance

(12)

(13)

(14) Equation (14) shows that the unbalance excites the rotor in torsion and shows a strong coupling between the torsion angle and the angular position of the shaft. The torsion angle β could be neglected before the angular position φ, ie φ + β ≃ φ in equation (14), but it has been chosen not to use this approximation. The various external forces that apply to the rotor are presented in this section. One considers the force of the bearings which support the line of trees, the gravity and the torques that are exerted on the shaft. For the bearing model in a turbine the shaft line is supported by fluid bearings. Accidental studies have shown that certain fluid bearings, in which the amplitudes of the vibrations become excessive, adopt a non-linear behavior, particularly when passing critical speeds where the oil film is crushed. Taking into account the contact with the stator, the deflection of the shaft is reduced. Thus, in the first approach, a behavior of the linear bearings of bearings can be retained, this behavior being a function of the speed of rotation. In particular, with the hypothesis of small displacements, the coefficients of stiffness and damping can be calculated by linearizing the REYNOLDS equations around the equilibrium position []. Then by calculating the virtual work

W bearing of the external forces acting on the shaft, it

comes:

11


(15)

With

and

the components of the generalized force acting on the bearings. After linearization,

these forces are rewritten in matrix form:

(16) With the terms stiffness and damping matrices described by piecewise linear functions of the rotation speed. 5. Application results Figure 10; Represents the arrangement of the vibration sensors in a Solar Turbine TITAN 130 gas turbine. The results obtained by the turbine vibration monitoring system show an imbalance caused by damage to the turbine rotor blades when it is put into operation Step dated 22/09/2014. Figure 11; Represents the detection of an unbalance by the system for monitoring the vibrations of the turbine at the bearing B1-in the x-axis. Figure 12 shows the temporal variation of the speed of the turbine during its operation from the rise in speed until its slowing down and total shutdown. The operators of the SC3 compression station carried out a maintenance operation for the dismantling of the turbine and the replacement of the damaged fins, Figure 7 shows the damaged and damaged fins of the turbine.

Fig 10. Vibration Sensor Layout (Solar Turbine TITAN 130 Supervisory System)

12


Fig. 11. Vibratory response of turbine subject to unbalance - Solar turbine TITAN 130

Fig. 12. Variation of turbine speed in% 6. Conclusion This work deals with the phenomena of vibration of turbines in accidental situations, the appearance and propagation of a crack or hole in a fin of the rotor of the rotating machine is a phenomenon which must be taken into account both by Manufacturers and by the operators of these machines. In order to ensure that their installations are not damaged, the latter have a few tools whose on-line vibration monitoring is one of the most commonly used. Based on measurements of the vibrations at the bearings, it allows a continuous monitoring of the mechanical state of the materials and an early diagnosis of the main defects. The vibratory supervision system of the turbine makes it possible to detect any malfunctions and

13


monitor their evolution from the regularly collected vibrations in order to plan or postpone a mechanical intervention. This continuous monitoring is carried out during operation of the machine. This avoids frequent stops leading to a drop in production, on the one hand, and repeated passages at the resonant frequencies favoring the phenomenon of cracking, on the other hand. The feedback from the supervision system on the Solar TITAN 130 turbine of the SC3 Moudjbara Algeria compressor station dated 22/09/2014 showed an imbalance in the vibratory behavior at bearing 1B in the x axis, The presence of holes in the wings of the mobile and stationary HP wheels of the turbine following a shear of a screw in the diaphragm, a corrective maintenance operation was undertaken to disassemble the turbine and replace the damaged fins in the period of 05 / 11/2016 to 21/11/2016. The objective of this work was the modeling of the accidental vibration behavior of the contactless turbine. The initial conditions correspond to the normal conditions of operation of a turbine at nominal speed under own weight. At a given moment, a wing is detached at the most unfavorable position. The shaft line is disconnected and slows down until the machine is completely stopped. However, near critical speeds, design play between shaft and diaphragm is consumed by large unbalance. The large unbalance corresponding to the loss of a fin causes strong vibrations of the turbine, notably in the vicinity of certain speeds of rotation for which the vibratory response is maximum. References [1].

Ahmed Hafaifa, Mouloud Guemana and Attia Daoudi, Vibration supervision in gas turbine based on parity space approach to increasing efficiency. Journal of Vibration and Control, June 2015, vol. 21, pp.1622-1632.

[2].

Ahmed Hafaifa, Mouloud Guemana and Saadat Boulanouar, Monitoring system based on real data acquisition for vibrations control in gas turbine system. Revue de Nature & Technologie: A- Sciences fondamentales et Engineering, Janvier 2016, n° 14, pp. 13 – 18.

[3].

Ahmed Hafaifa, Rachid Belhadef and Mouloud Guemana, Modelling of surge phenomena in a centrifugal compressor: experimental analysis for control. Systems Science & Control Engineering: An Open Access Journal, Taylor & Francis, 2014, vol. 2 no.1, pp.632-641.

[4].

Sébastien Roques. Modélisation du comportement dynamique couple rotor-stator d'une turbine en

situation

accidentelle.

Mécanique

[physics.med-ph].

Ecole

Centrale

de

Nantes,

2007.Français [5].

Philippe MUZARD, Etude du comportement dynamique linéaire et non linéaire d’un rotor d’hélicoptère application au couplage rotor-fuselage mémoire de thèse de Doctorat, décembre 1994 Ecole centrale de Lyon- France.

[6].

Jean-marc Pugnet, Dynamique des machines tournantes pour la conception des turbines à vapeur et des compresseurs centrifuges de la Theorie à la pratique, memoire de these de Doctorat, Décembre 2010, Institut National des Sciences Appliquées de Lyon-France

[7].

Saber El Arem. Vibrations non-linéaires des structures fissurées : Application aux rotors de turbines. Matériaux. Ecole des Ponts Paris Tech, 2006. France.

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[8].

Ashwani Kumar, Arpit Dwivedi, Vipul Paliwal and Pravin P. Patil, Free vibration analysis of Al 2024 wind turbine blade designed for uttarakhand region based on FEA. Procedia Technology, 2014, vol. 14, pp. 336-347.

[9].

Beskletnyi M.E. and Igumentsev E.A., Vibration diagnostics for gas turbine installation blades according to the critical level of rotor torsional vibrations. Strength of Materials, 1981, vol. 13, no. 2, pp. 252-255.

[10]. Boulanouar Saadat, Ahmed Hafaifa and Mouloud Guemana, Vibration analysis and measurement based on defect signal evaluation: Gas turbine investigation. Journal of Advanced Research in Science and Technology, 2016, vol. 3, no 1, pp.271-280. [11]. Christoph Pilger and Lars Ceranna, The influence of periodic wind turbine noise on infrasound array measurements. Journal of Sound and Vibration, 2017, vol. 388, pp. 188-200. [12]. De Silva B.M.E., Negus B. and Worster J., Mathematical programming methods for the optimal design of turbine blade shapes. Journal of Sound and Vibration, 1976, vol. 46, no. 4, pp. 501514

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Gas turbine vibration modeling for the supervision of their dynamic

Gas turbine vibration modeling for the supervision of their dynamic

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