This study is to predict the flutter of the first rotor blade of the two-stage axial turbine of a rocket engine turbopump, where the turbine was designed by the Japan Aerospace Exploration Agency (JAXA) in the project of Dynamic Design Team (DDT). The number of blade counts of the first rotor of the turbine is 36. A pre-stressed modal analysis has been carried out using ANSYS Mechanical 18.1 on a single rotor blade using fixed support at the hub and rotational velocity boundary conditions, for getting natural frequencies and mode shapes (eigenvectors). The first four modes of Inconel 718 and Titanium 64 blade have been taken for the CFD calculation. However, ANSYS CFX 18.1 has been taken as the solver for the CFD calculation of the simulations. Reynolds Average Navier Stoke’s equations have been used as the governing equation. H2 ideal gas has been considered as a working fluid. Shear Stress Transport (SST) model has been used as the turbulence model. At the inlet, total pressure and total temperatures are 7.55 MPa and 500 K respectively. At the outlet, static pressure is 1.71 MPa. The blade wall has been considered as a no-slip, whereas the slip wall has been considered for the hub and casing. The rotational speed of the rotor blade has taken as 60600 rpm where the rotational axis is Z-axis. A transient blade row model has been used for the unsteady calculations. Results of this study have been presented by graphical and contour representations. Aerodynamic damping coefficient and blade’s wall work per cycle have been taken as the parameters for the analysis. However, the stability of Inconel and Titanium blades is predicted for -90 ≤ IBPA ≤ +90 degrees, whereas instability or flutter of the blades may occur when -180 ≤ IBPA < -90 degrees or +90 < IBPA ≤ +180 degrees.
Abstract
This study is to predict the flutter of the first rotor blade of the two-stage axial turbine of a rocket engine turbopump, where the turbine was designed by the Japan Aerospace Exploration Agency (JAXA) in the project of Dynamic Design Team (DDT). The number of blade counts of the first rotor of the turbine is 36. A pre-stressed modal analysis has been carried out using ANSYS Mechanical 18.1 on a single rotor blade using fixed support at the hub and rotational velocity boundary conditions, for getting natural frequencies and mode shapes (eigenvectors). The first four modes of Inconel 718 and Titanium 64 blade have been taken for the CFD calculation. However, ANSYS CFX 18.1 has been taken as the solver for the CFD calculation of the simulations. Reynolds Average Navier Stoke’s equations have been used as the governing equation. H2 ideal gas has been considered as a working fluid. Shear Stress Transport (SST) model has been used as the turbulence model. At the inlet, total pressure and total temperatures are 7.55 MPa and 500 K respectively. At the outlet, static pressure is 1.71 MPa. The blade wall has been considered as a no-slip, whereas the slip wall has been considered for the hub and casing. The rotational speed of the rotor blade has taken as 60600 rpm where the rotational axis is Z-axis. A transient blade row model has been used for the unsteady calculations. Results of this study have been presented by graphical and contour representations. Aerodynamic damping coefficient and blade’s wall work per cycle have been taken as the parameters for the analysis. However, the stability of Inconel and Titanium blades is predicted for -90 < IBPA < +90 degrees, whereas instability or flutter of the blades may occur when -180 < IBPA < -90 degrees or +90 < IBPA < +180 degrees.
Keywords: Rocket Engine Turbopump, Modal analysis, Flutter analysis, Aerodynamic Damping Coefficient.
Nomenclature
SST Shear Stress Transport
RANS Reynolds Average Navier Stoke
IBPA Interblade Phase Angle
ND Nodal Diameter magnitude
NB Number of blade
DDT Dynamic Design Team
JAXA Japan Aerospace Exploration Agency
CFD Computational Fluid Dynamics
Wcyc Wall Work per cycle
Emax Maximum kinetic Energy
δ Damping coefficient
p Fluid Pressure
v Blade’s velocity
A Blade’s surface area
n Unit vector
ω natural frequency
A max Maximum displacement amplitude
m Mass of the blade
T Time period of vibration cycle
t time
1. Introduction:
In a turbomachine, the energy in a fluid is transformed into mechanical energy by rotating a turbine. The machine includes a compressor and turbine for power generation. The compressor and turbine consist of several rotating and stationary disks with blades arranged circumferentially in a periodic manner that allow the fluid to compress and expand as it moves throughout the engine. The engine must create very high power to deliver liquid fuel to the thrust chamber by turbo-pumps, where the turbo-pump consists of inducer, impeller, shaft, turbine etc.
Thus, turbines are used for driving turbo-pump too. However, the turbine blades are exposed to a fluid moving at high speeds in some cases higher than the speed of sound. In this scenario, the aerodynamic forces can reach a level where the aero-elastic stability of the system must be carefully evaluated to avoid flutter. However, Flutter is a self-initiated and self-maintained aero-elastic instability phenomenon that arises when the unsteady pressure fields in the flow resulting from the vibration of a structure start feeding energy back to the structure. This results in an exponential increase in the oscillation amplitude if there is not enough damping in the system to dissipate the energy from the flow. It will significantly affect the whole engine function and safety of the aircraft if a problem arises in the turbine section.
In a system corresponding to a structure exposed to a fluid, the aerodynamic forces due to the fluid movement are balanced by the inertial and elastic forces in the structure. However, when this balance is disrupted, the system becomes unstable and flutter occurs. The mutual interaction between the aerodynamic, inertial and elastic forces involved in the flutter phenomenon is studied by the engineering science of dynamic aero-elasticity in the collar’s triangle of forces. For example, an aircraft moves through the air, loads act on the structure and cause deformations of the flexible structure. These deformations will change the geometry of the structure which leads to a change in the flow and aerodynamic loads, resulting in a loop of loads and deformations. In most cases the aerodynamic loads and the internal elastic loads in the structure will converge to equilibrium. However, there are cases when the loop becomes unstable, causing increasing deformations leading to structural failure of the aircraft.
Anyway, failures of any high-speed rotating components can be dangerous to passengers and personnel. The failure in aircrafts occur during development of engine testing and in-service especially in rotors, stators blades, according to Antony et al. [1]. To understand the behavior of the turbine blade and to minimize the chances of failure, Efe-Ononeme et al. [2] used the composite material in place of titanium alloy. Witek and Stachowicz [3] used two different material for turbine blade IN 738 and U500 have to determine the natural frequency of vibration of turbine blade. Kumar et al. [4] utilized FEM technique to analyze the effect of the rotational speed of the engine and the heat field on the natural frequencies and the vibration of the blade. Zinovieva et al. [5] used AL 2024 material to determine the mode shapes and natural frequencies of vibration of turbine blade.
The problem of turbine failure was the subject of several investigations [6-8]. The results of stress, fracture and modal analysis of the turbine and compressor blades were described in [9]. Witek [10] shows that the vibration have a negative influence on the fatigue life of the aircraft engine blades. The fatigue process of aircraft components can be also accelerated with corrosion [11]. The investigations of vibration analysis of the blades are described in [12]. Witek and Stachowicz [13] studied for determining the resonant frequencies and free vibration modes of the turbine blade subjected to complex thermomechanical loads. They analyzed the effect of the rotational turbine speed on the natural frequencies of the aircraft engine blade. Max Louyot at el. [14], presented the development of both an analytical modal analysis based on the assumed mode approach and potential flow theory, and a modal force CFD approach for rotating disks in dense fluid. Eduard Egusquiza at el. [15] investigated the influence of the rotor and supporting structures on the impeller response such as the natural frequencies and mode shapes but suspended. Experimental and numerical simulation were used for the investigation. Ming Zhang et al. [16] studied the influence of cracked blade stiffness on the natural frequency values and mode-shapes. Ashwani Kumar et al. [17] introduced a new material for wind turbine blades. They selected Al 2024 as the new material for the turbine blades. Haresh Pal Singh et al. [18] analyzed for vibrational and stress conditions considering four different materials. Habib Ullah et al. [19] conducted a numerical investigation of modal and fatigue performance of a horizontal axial tidal current turbine using fluid structure interaction.
The Campbell diagram is of great assistance to predict potential occurrences of resonant vibration; this can be accomplished by maintaining the dangerous crossings between the natural frequencies of the bladed disk and the engine order lines away from the operational speed of the rotor. On the other hand, flutter cannot be predicted with a Campbell diagram by itself. The flutter of blades within compressors and turbines has been a serious cause of machine failure which has been difficult to predict and expensive to correct. Flutter prediction has challenged the design engineers for decades. However, nowadays, the increase in the computational power has allowed the use of Computational Fluid Dynamics (CFD) methods to estimate the aerodynamic loads on the blades as well as Finite Element Methods (FEM) to predict the vibratory characteristics of the bladed disks. Both of these tools can be used to calculate the flutter margins.
The simulation of the dynamics of a turbine must be separated into two main fields. The first is the simulation of fluid flow. The second is the simulation of the structure mechanical response. In this latter case, accurate simulation of the Eigen-frequencies of the turbine structure is important, including effects from the rotorstator interaction. During the design process, the coincidence between the excitation frequencies and an Eigenfrequency of the structure must be prevented. Otherwise, large vibrations are produced, resulting in fatigue cracks as described in one example by Ohashi [20]. The use of computational methods based on FEM is increasing rapidly to solve the real problems in few years [21]. Actually, FEM is an approximation technique used for numerical solution of acoustic problems, electromagnetic problems, heat transfer, fluid problems and static and dynamic structural analysis. Computational fluid dynamic (CFD) is largely used as a tool for simulating the fluid flows over turbine blades [22, 23]. The use of large Eddy simulation (LES) is also increasing for simulating the real problems [24]. For structural analysis, FSI modeling is one of the methods which uses the coupled CFD and FEA methods [25]. Both CFD numerical [25] and experimental methods [26] are suitable for the validation of results. The experimental test method is performed to obtain highly accurate and reliable results but it requires a great deal of time, experience and cost [27]. Therefore, nowadays the numerical method has become more popular for the optimization of turbine blade performance [28].
However, present study is to predict stability and instability of the first rotor blade of two stage axial turbine of a rocket engine turbopump by analysing the graphical and contour representations of aerodynamics damping coefficients and wall work per cycle on the blade surface with interblade phase angle. Besides, the present work documents a validation of the aerodynamic damping distribution on the surface of the rotor blade of the Nasa Rotor 67 obtained via CFD simulation by comparing them with the benchmarking result.
2. Computational methods:
The durable and reliable compressors or turbines engineering needs an accurate and efficient prediction of blade damping. However, a variety of methods have been developed and served well over the years. Recently, CFD analysis of aerodynamic damping of the blade has been enabled by the development of unsteady CFD methods combined with the available and affordable computing power. Unsteady CFD methods are used for predicting the fluid flow in a turbine rotor. Mechanical pre-stressed modal analysis determines the deformations of the blade. In this investigation, blade motion for the first several moments is prescribed in the CFD code, for a range of nodal diameters. Aerodynamic damping coefficients are calculated based on the predicted blade forces and the specified blade motion after obtaining the periodic unsteady solutions.
However, the simulation of many blades in a given row depending on the nodal diameter is required in traditional unsteady CFD methods. Nowadays, computational methods have been developed which is able to do a simulation with 1 or 2 blades per row and can give the full sector solution. Thus, these methods can save computing time and machine resources. Thus, two-blade passages of the first rotor of the turbine have been taken for the full section solution in this study, shown in figure 1. Moreover, the Fourier Transformation method has a property that is suitable for the aerodynamic damping prediction. Besides, aerodynamic damping prediction by the Fourier Transformation methods matches very closely with the reference full sector solutions. The Fourier transformation methods also provide solutions faster than average periodic reference cases. Therefore, in this present study, Fourier Transformation methods have been used to predict the damping coefficients for a range of nodal diameters.
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Figure 1: Two blade passages of the first rotor showing inlet, outlet and periodic boundary region.
3. Geometry and meshing:
The geometry has been chosen here for flutter prediction is the first rotor blade of two stages liquid hydrogen turbo-pump turbine designed by JAXA (Japan Aerospace Exploration Agency) in the project called Dynamic Design Team (DDT). The geometry of the nozzle and the rotor blades is given in Reference [29]. The specification values of the blade row are shown in Table 1. The geometry has been shown in the fig. 2.
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Figure 2: Three dimensional view of meshing of the 1st rotor of the reference turbine [29].
Table 1 Design values of the 1st rotor of the reference turbine [29].
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Meshing of the geometry has been done by using ANYS TurboGrid 18.1. The figure 2 also depicts the meshing of the geometry. The meshing details has been presented in the table 2.
Table 2: Meshing details of the 1st rotor of the turbine.
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4. Modal analysis:
A pre-stressed modal analysis was carried out using ANSYS Mechanical 18.1 on a single rotor blade using fixed support at the hub and rotational velocity boundary conditions, for getting natural frequencies and mode shapes (eigenvectors). The computed first mode shape is shown in Figure 3. The first four modes for the materials Inconel718 and Titanium Alloy were used in this study. The frequencies of the first four modes for the materials Inconel718 and Titanium Alloy were presented in table 4, where the properties of the materials were presented in table 3. The mode shape, consisting of nodal coordinates and normalized modal displacements, was extracted into an ASCII file which was then imported into ANSYS CFX to map it onto the CFD mesh as discussed in the computational methods section.
Table 3: material properties of Inconel718 and Titanium Alloy.
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Table 4: natural frequencies of first four modes for the materials Inconel718 and Titanium Alloy.
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Figure 3: contour of the first mode shape (natural frequency 49900 Hz) for Inconel718.
5. CFD details and boundary conditions:
In this study, ANSYS CFX 18.1 has been taken as the solver for the calculation of the simulations. Reynolds Average Navier Stoke’s equations have been used as the governing equation. H2 ideal gas has been considered as a working fluid. Shear Stress Transport (SST) model has been used as the turbulence model. At the inlet, total pressure and total temperatures are 7.55 MPa and 500 K respectively. At the outlet, static pressure is 1.71 MPa. The blade wall has been considered as a no-slip, whereas the slip wall has been considered for the hub and casing. The rotational speed of the rotor blade has taken as 60600 rpm where the rotational axis is Z-axis. A transient blade row model has been used for the unsteady calculations. The time period of the unsteady analysis is equal to 1 / (frequency of the blade) where the frequency of the blade has been taken from frequencies of the modes, shown in table 4. 72-time steps have been taken for each time period where 200 iterations have been taken for each time step.
6. Mesh independency checking
A grid dependency study is the first preference of any numerical simulation. For this purpose, an extensive test is carried out with different number of mesh elements such as mesh 1 (1018536 elements), mesh 2 (1303821 elements), and mesh 3 (1534287 elements) respectively. Figure 4 shows the area integrated wall power density of the first mode of Inconel blade with time-steps for the IBPA of 90 degrees with mentioned mesh sizes. In all cases, the wall power density distributions are the same. It implies that the solution is grid independent.
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Figure 4: Area integrated wall power density with time-steps for IBPA of 90 degrees for different mesh sizes.
6. Solver Validation:
Before starting of present investigation the numerical solver is required to be validated. For the validation, the study of Robin Elder et al. [30] is considered. For this case, Nasa Rotor 67 has been taken as geometry for the analysis, where the number of blades is 22 and Tip Clearance is 0.61 mm. The rotational speed of the blade is 16043 rpm. Blade and fluid material are Titanium alloy, Air Ideal Gas respectively. Reynolds Average Navier Stoke’s equations have been used as the governing equation. Shear Stress Transport (SST) model has been used as the turbulence model. At the inlet, total pressure and total temperature are 1 atm and 288 K respectively. At the outlet, Mass Flow Rate is 33.25 kg/s. A transient blade row model has been used for the unsteady calculations. The time period of the unsteady analysis is equal to 1 / (frequency of the blade) where frequency has been taken from the modal analysis of this case. 88-time steps have been taken for each time period where 200 iterations have been taken for each time step. Current results of damping coefficient with respect to Inter blade phase angle has been compared with the results of reference study which has been presented in figure 5. Although there are some little discrepancies, both results are in good agreement. Discrepancies may occur due to various numerical setup differences which are not mentioned in the reference study.
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Figure 5: Variation of damping coefficient with respect to Inter blade phase angle.
7. Results and discussion:
The aerodynamic damping coefficient is a very important parameter in the design of turbines, compressors, and fans to predict the failures due to blade flutter and to estimate blade life cycles. Actually, for the case of sufficiently stiff blades, the influence of the fluid flow on the blade’s natural frequencies and eigenvectors is negligible. As a result, the airflow can result only in small additional damping for the stability case or additional energy inflow for the flutter case without a change of natural frequencies and eigenvectors [30]. Therefore, only aerodynamic damping has been considered in this study, though Mechanical and aerodynamic damping can be evaluated in separate ways. At the beginning of the simulation, the periodic displacement of the blade and natural frequency of interest is extracted by modal analysis. In the next step, unsteady CFD is carried out taking into consideration the periodic displacement and natural frequency of the blade. Unsteady calculations were performed using the Fourier Transformation method with two blade passages and the reference periodic method which requires simulation of half the wheel for even nodal diameter cases and the full wheel for odd (and zero) nodal diameter cases. Finally, aerodynamic work per cycle Wcyc and aerodynamic damping acting on the blade can be calculated by the equations 1, 2 and 3, where Emax is the maximum kinetic energy of the vibration mode and S is the damping coefficient [31].
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In equation (1), (2) and (3), p is the fluid pressure, v is the velocity of the blade due to imposed vibrational displacements, A is the blade surface area, n is the surface normal unit vector, ω is the natural frequency of the given mode, A max is the maximum displacement amplitude, m is the mass of the blade, and T is the time period Illustrations are not included in the reading sample of the vibration cycle. The numerator of equation (2) represents the work per vibration cycle, and the term in the denominator is used to non-dimensionalize the work and represents the blade’s maximum kinetic energy of the vibration mode. However, it is important to consider the aerodynamic effects of adjacent blades for the calculations of blade flutter. There is a finite number of disc nodal diameters for a rotor disc assembly consisting of a number of blades. Where the nodal diameters are lines of zero displacements during the vibration of the disk; they go across it passing through its centre. A forward and backward travelling wave mode exists for each nodal diameter. At Nodal Diameter (ND) of zero, all the blades vibrate in phase with an Interblade Phase Angle (IBPA) of zero. However, each blade will be out of phase with respect to the others by a finite Interblade phase angle
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Where 0 < ND < NB / 2 for an even number of blades and 0 < ND < (NB-1) / 2 for an odd number of blades. Thus, for this study, the possible interblade phase angles are from -180 to +180 degrees, as the number of blades is 36.
Actually, the positive values of the aerodynamic damping coefficient indicate a stable system and the negative values indicate an unstable system for blade vibrations, so it is investigated whether the aerodynamic damping value on the Inconel blade is positive or negative with respect to the interblade phase angles. Aerodynamic damping calculations were performed for the 1st, 2nd, 3rd, and 4th modes with a range of interblade phase angle (IBPA). Interblade phase angles in a range with an increment of 20 degree were investigated. Figures 6 (a, b) show the aerodynamic damping coefficient of (a) Inconel and (b) Titanium blades with the variation of interblade phase angles. Symmetric curves of aerodynamic damping on the blades for the positive and negative IBPA are noticed in the figures. The figures show the results for the first four modes for both materials. The first two modes and the last two modes create big differences in the magnitude of the aerodynamic damping coefficient. However, the 1st mode closely follows the 2nd mode in results, whereas the 3rd and 4th modes also create curves that are very near to the horizontal line of the graphs. Moreover, maximum aerodynamic damping addition to the blade surfaces are for the interblade phase angle of zero. Then, the magnitude of the damping coefficient on the blades are gradually decreasing by the increase of interblade phase angle magnitude, and finally damping coefficients become negative for IBPA < -90 degrees or IBPA > +90 degrees. It is also noticed that the aerodynamic damping coefficients on the blades of all modes are positive for -90 < IBPA < +90 degrees, whereas aerodynamic damping coefficients are negative when IBPA < -90 degrees or IBPA > +90 degrees. Thus, the stabilities of the Inconel and Titanium blades are predicted for -90 < IBPA < +90 degrees, while instability or flutter of the blades may occur when IBPA < -90 degrees or IBPA > +90 degrees.
Figure 6: Variation of damping coefficient with the variation of IBPA for (a) Inconel 718 and (b) Titanium 64.
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Figure 7: Variation of work per cycle with the variation of IBPA for (a) Inconel 718 and (b) Titanium 64.
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Actually, negative work done per cycle represents an energy extraction from the blade (stable motion), while the positive value represents an energy addition to the blade (unstable motion, Flutter), where the work done per cycle of the blade means the area and time-integrated wall work density. Figures 7 (a, b) shows wall work done per cycle on the (a) Inconel and (b) Titanium blades with interblade phase angles. The figures depict symmetric curves of wall work per cycle on the blades for the positive and negative IBPA. The figures show the comparison of the results of the first four modes of the blades. The first two modes and the last two modes create big differences in the magnitude of work done per cycle. The 1st mode closely follows the 2nd mode in results, whereas the 3rd and 4th modes also create curves that are very near to the horizontal line of the graphs. The maximum energy extraction from the blade surfaces are for the interblade phase angle of zero, and then energy extractions are gradually decreasing by the increase of interblade phase angle magnitude, and finally, the energies are added to the blade surfaces for IBPA > +90 degrees or IBPA < -90 degrees. The works per cycle on the blade surfaces of all modes are negative for -90 < IBPA < +90 degrees, whereas works per cycle are positive when IBPA < -90 degrees or IBPA > +90 degrees. Thus, the stabilities of the Inconel and Titanium blades are predicted for -90 < IBPA < +90 degrees, while instability or flutter of the blades may occur for IBPA < -90 degrees or IBPA > +90 degrees.
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Figure 8: comparison of (a) damping ratio, (b) work per cycle with IBPA of Inconel 718 and Titanium 64.
Figures 8 (a, b) compare the results of (a) damping coefficient and (b) work per cycle with the variation of IBPA of the first two modes of Inconel and Titanium blades. It is noticed from figure 8 (a) that the aerodynamic damping coefficient of the Inconel blade is higher than that of the Titanium blade for all modes. On the other hand, 8 (b) shows that the energy extraction from the Inconel blade surface is higher than that from the Titanium blade surface for all modes. Therefore, it is clear that the Inconel blade can extract more energy from the blade surface as well as experience more stable motion by the aerodynamic damping than the Titanium blade.
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Figure 9: Variation of (a) damping ratio, (b) work per cycle of the first mode of Inconel blade with the IBPA.
Figures 9 (a, b) show the (a) damping ratio and (b) work done for the first mode of Inconel 718 with IBPA from 0 to +180 degrees. The results for IBPA > 100 degrees are specially checked, as the calculations for IBPA > 100 degrees in other results were skipped due to save computational time and resources. When IBPA > +90 degrees, the damping coefficients on the blade are negative and gradually decreasing, whereas work done on the blade are positive and gradually increasing. From the previous figures, other modes have given the same signs of the damping ratio and work done like the first mode. Thus, it can be guessed that other modes will also give the same sign of damping ratio and work done for IBPA > +100 degrees as well as will experience instability for IBPA > + 100 degrees.
The figure 10 shows the time-averaged wall work density (J/m2) of the first mode on the Inconel blade surface for IBPA of 0 and 180 degrees. However, Time average wall work density represents the average value of wall work density over the period of the cycle. It is clear from the figure that the negative wall work region for IBPA of 0 degrees is significantly more than that of 180 degrees. Moreover, the red contour region or maximum positive wall work region for IBPA of 180 degrees is more than that of 0 degrees. More specially, most of the contour regions of wall work density for IBPA of 0 degrees are blue (or negative valued), but some red (positive valued) contour regions are noticed near the tip area of the pressure side of the outlet edge of the blade. On the other hand, for IBPA of 180 degrees, some blue (negative valued) contour regions are found in the middle of the pressure side of the blade, and other contour regions are from sky-blue to red ( or positive valued wall work) regions. Therefore, it is again interpreted for the first mode that stability can be predicted for IBPA of 0 degrees, whereas instability can be found in the case of IBPA of 180 degrees.
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Figure 10: Distribution of time averaged wall work density (J/m[2]) of the first mode on the Inconel blade surface for IBPA of (a) 0 and (b) 180 degrees.
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Figure 11: Area integrated wall power density of first mode of Inconel blade with time-steps for IBPA of 0, 100 and 180 degrees.
Figure 11 shows the variation of area integrated wall power density of the first mode of Inconel blade for IBPA of 0, 100 and 180 degrees with the variation of time steps. The results are taken for 5 periods and 360time steps. The wall power density varies approximately between 660 W and -660 W. Other than the phase angle of the curves, all curves are the same. Moreover, it is also noticed from the figure that the phase angle of the curves varies with the variation of the interblade phase angle of the blade. For instance, the curve’s phase angles are 0, 100 and 180 degrees for the interblade phase angle of 0, 100 and 180 degrees respectively.
8. Conclusion:
From the above study, it can be concluded that aerodynamic damping and wall work per cycle on the blade create symmetric curves for positive and negative IBPA. However, the magnitude of aerodynamic damping and wall work per cycle on the blade changes with the variation of the modes of the blade, but their signs (notation of positive and negative) are independent of the mode variation. The magnitude of aerodynamic damping and wall work per cycle on the blade of the first and second modes of each material is always larger than that of the third and fourth modes. On the other hand, the magnitude of aerodynamic damping and wall work per cycle on the Inconel blade of all modes is always larger than that of the Titanium blade. Aerodynamic damping of all cases is negative for IBPA < -90 degrees or IBPA > +90 degrees. Alternatively, wall work per cycle of all cases are positive for IBPA < -90 degrees or IBPA > +90 degrees. Therefore, instability or flutter of the blades may occur when -180 < IBPA < -90 degrees or +90 < IBPA < +180 degrees, whereas the stability of Inconel and Titanium blades is predicted for -90 < IBPA < +90 degrees.
Acknowledgment
All the members of Funazaki Laboratory (specially Mr. ODAJIMA Tatsuya) of the Mechanical Engineering Department of Iwate University, Morioka, Japan are gratefully acknowledged for their supports and cooperation.
References:
[1] A.D. Antony, M. Gopalsamy, C.B. Viswanadh, and R. Krishnaraj, Structural dynamic analysis of turbine blade, 247(1) 2017 IOP Publishing.
[2] O.E. Efe-Ononeme, A. Ikpe, G.O. Ariavie, Modal analysis of conventional gas turbine blade materials (Udimet 500 and IN738) for industrial applications, J. Eng. Technol. Appl. Sci. 3 (2) (2018) 119-133.
[3] L. Witek and F. Stachowicz, Modal analysis of the turbine blade at complex thermomechanical loads, Strength Mater. 48 (4) (2016) 474-480.
[4] A. Kumar, A. Dwivedi, V. Paliwal, and P.P. Patil, Free vibration analysis of Al 2024 wind turbine blade designed for Uttarakhand region based on FEA, Procedia Technol. 14 (2014) 336-347.
[5] Zinovieva, Tatiana V., and Artem A. Moskalets. ‘‘Modal Analysis of Turbine Blade as One-and ThreeDimensional Body.”Advances in Mechanical Engineering. Springer, Cham, 2018. 195-204.
[6] W. Maktouf and K. Sai, “An investigation of premature fatigue failures of gas turbine blade,” Eng. Fail. Anal., 47, 89-101 (2015).
[7] 3. K. S. Song, S. G Kim, D. Jung, and Y. H. Hwang, “Analysis of the fracture of a turbine blade on a
turbojet engine,” Eng. Fail. Anal., 14, 877-883 (2007).
[8] L. Witek, “Fatigue investigations of the compressor blades with mechanical defects,” Key Eng. Mater., 598, 269-274 (2014).
[9] Akash Shukla and S. P. Harsha, “An experimental and FEM modal analysis of cracked and normal steam turbine blade,” Materials Today: Proceedings, 2, 2056- 2063 (2015).
[10] L. Witek, “Crack growth simulation in the compressor blade subjected to vibration using boundary element method,” Key Eng. Mater., 598, 261-268 (2014).
[11] L. Witek, “Failure analysis of the wing-fuselage connector of an agricultural aircraft,” Eng. Fail. Anal., 13, 572-581 (2006).
[12] R. P. Pridorozhnyi, A. V. Sheremet’ev, and A. P. Zinkovskii, “On the rational choice of the azimuthal crystallographic orientation of single-crystal cooled rotor blades in aircraft gas turbine engines,” Strength Mater., 47, No. 3, 415-421 (2015).
[13] L. Witek1 and F. Stachowicz; Modal analysis of the turbine blade at complex thermomechanical loads; Strength of Materials, Vol. 48, No. 4, July, 2016; DOI 10.1007/s11223-016-9788-6.
[14] Max Louyot, Bernd Nennemann, Christine Monette, and Frederick P. Gosselin; Modal analysis of a spinning disk in a dense fluid as a model for high head hydraulic turbines; Journal of Fluids and Structures 94 (2020) 102965; doi.org/10.1016/j.jfluidstructs.2020.102965
[15] Eduard Egusquiza, Carme Valero, Alex Presas, Xingxing Huang, Alfredo Guardo, and Ulrich Seidel; Analysis of the dynamic response of pump-turbine impellers. Influence of the rotor; Mechanical Systems and Signal Processing 68-69 (2016) 330-341; dx.doi.org/10.1016/j.ymssp.2015.05.034
[16] Ming Zhang, David Valentin, Carme Valero, Alexandre Presas, Monica Egusquiza, Eduard Egusquiza; Experimental and numerical investigation on the influence of a T large crack on the modal behaviour of a Kaplan turbine blade; Engineering Failure Analysis 109 (2020) 104389; doi.org/10.1016/j.engfailanal.2020.104389.
[17] Ashwani Kumar, Arpit Dwivedi, Vipul Paliwal, Pravin P Patil; Free Vibration Analysis of Al 2024 Wind Turbine Blade Designed for Uttarakhand Region Based on FEA; 2nd International Conference on Innovations in Automation and Mechatronics Engineering, ICIAME 2014, Procedia Technology 14 (2014) 336 - 347.
[18] Haresh Pal Singh, Ashish Rawat, Avi Raj Manral, and Pushpendra Kumar; Computational analysis of a gas turbine blade with different materials; Materials Today: Proceedings, in press, doi.org/10.1016/j.matpr.2020.06.486.
[19] Habib Ullah, Muzamil Hussain, Naseem Abbas, Hassaan Ahmad, Mohammed Amer, and Muhammad Noman; Numerical investigation of modal and fatigue performance of a horizontal axis tidal current turbine using fluid-structure interaction; Journal of Ocean Engineering and Science 4 (2019) 328-337, doi.org/10.1016/j.joes.2019.05.008
[20] Ohashi, H. Case Study of Pump Failure Due to Rotor-Stator Interaction. Inter- national Journal of Rotating Machinery 1, 1 (1994), 53-60.
[21] M. Hussain, R. Khan, N. Abbas, J. King Saud Univ. - Sci. 31 (2019) 222-229.
[22] B.S. Kim, S.Y. Bae, W.J. Kim, S.L. Lee, M.K. Kim, in: Proceeding of the IOP Conference Series on Earth and Environmental Science, 15, 2012.
[23] K.-P. Kim, M.R. Ahmed, Y.-H. Lee, Renew. Energy 48 (2012) 557-564.
[24] Q. Hu, Y. Li, Y. Di, J. Chen, J. Renew. Sustain. Energy 9 (2017) 064501.
[25] R.F. Nicholls-Lee, S.R. Turnock, S.W. Boyd, in: Proceeding of the Ninth European Wave Tidal Energy Conference, 2011, pp. 1-8.
[26] F. Jing, W. Ma, L. Zhang, S. Wang, X. Wang, J. Hydrodyn. Ser. B 29 (2017) 109-117.
[27] A. Olczak, T. Stallard, T. Feng, P.K. Stansby, J. Fluids Struct. 64 (2016) 87-106.
[28] M. Edmunds, R. Malki, A.J. Williams, I. Masters, T.N. Croft, Int. J. Mar. Energy 7 (2014) 20-42.
[29] k. Namba, K. Funazaki, S. Kawasaki and K. Yada, A Study on Blade Profile Optimization for Turbine Stages in a Rocket Engine Turbopump, Research on blade shape optimization of turbine stage for rocket engine turbo pump, Volume: 48, Issue: 1, Page: 53-60, Publication year: Jan. 10, 2020
[30] V. V. Vedeneev, M. Kolotnikov and P. Makarov, Experimental Validation of Numerical Blade Flutter Prediction, Journal of Propulsion and Power, vol. 31, No 5, September-October 2015.
[31] T. Miura, N. Sakai, N. Kanazawa, and K. Nakayama, FORCED RESPONSE EXCITATION OF A COMPRESSOR STATOR OWING TO SHOCK WAVE INDUCED BY ADJACENT ROTOR BLADE, Proceedings of ASME Turbo Expo 2021, Turbomachinery Technical Conference and Exposition, GT2021, June 7-11, 2021
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