SCIENCE CHINA Technological Sciences • Article •
doi: 10.1007/s11431-016-9010-y
Effects of axial gap on aerodynamic force and response of shrouded and unshrouded blade JIANG JinPeng1, LI JiaWen1, CAI GuoBiao1 & WANG Jue1,2* 2
1 School of Astronautics, Beihang University, Beijing 100191, China; System Engineering Division, China Academy of Launch Vehicle Technology, Beijing 100076, China
Received November 4, 2016; accepted February 6, 2017; published online March 14, 2017
Forced response analysis of a rocket engine turbine blade was conducted by a decoupled fluid-structure interaction procedure. Aerodynamic forces on the rotor blade were obtained using 3D unsteady flow simulations. The resulting aerodynamic forces were interpolated to the finite element (FE) model through surface effect elements prior to conducting forced response calculations. Effects of axial gap on aerodynamic forces were studied. In addition, influence of axial gap on the response of the shrouded blade was compared with that on the response of the unshrouded blade. Results demonstrated that as the axial gap increases, time-averaged pressure on the blade surface changes very little, while the pressure fluctuations decrease significantly. Pressure and aerodynamic forces on the blade surface display periodic variation, and the vane passing frequency component is dominant. Amplitudes of aerodynamic forces decrease with increasing axial gap. Restricted by the shroud, deformation and response of shrouded blade are much lower than those of the unshrouded blade. The response of unshrouded blade shows obvious beat vibration phenomenon, while the response of the shrouded blade does not have this characteristic because the shroud restrains multiple harmonics. Blade response in time domain was converted to frequency domain using fast Fourier transformation (FFT). Results revealed that the axial gap mainly affects the forced harmonic at the vane passing frequency, while the other two harmonics at natural frequency are hardly affected. Amplitudes of the unshrouded blade response decrease as the axial gap increases, while amplitudes of the shrouded blade response change very little in comparison. axial gap, forced response, shrouded blade, unshrouded blade, aerodynamic forces Citation:
Jiang J P, Li J W, Cai G B, et al. Effects of axial gap on aerodynamic force and response of shrouded and unshrouded blade. Sci China Tech Sci, 2017, 60, doi: 10.1007/s11431-016-9010-y
Introduction 1 Axial turbines are widely used in aircraft and rocket engines. The flow in turbines is highly unsteady and turbulent because of the aerodynamic interaction between adjacent rows, owing to the effect of wakes and potential flow field [1]. The unsteady interaction between blade rows can affect turbine performance. Moreover, the strong periodic flow can cause high amplitudes of blade vibration. High cycle fatigue fail*Corresponding author (email:
[email protected]) © Science China Press and Springer-Verlag Berlin Heidelberg 2017
ure owing to vibration stresses is a serious concern in gas turbines where it has been known to cause catastrophic engine failure [2]. The axial gap between vanes and blades is known to be one of the crucial design parameters, for impacting addressing the unsteady interaction and, thus, affect the turbine performance and blade loading. The rotor-stator interaction has been thoroughly studied by many researchers [3–6], and many of those investigations have focused on the effect of the axial gap on unsteady flow interaction. Korakianitis [7] showed that the mechanisms of generation of unsteady pressure distributions owing to potential flow and wake are different. Effects of the axial gap on the tech.scichina.com link.springer.com
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rotor-stator interaction are related to the stator-to-rotor pitch ratio owing to the potential flow and wake. The unsteady effects do not always decrease monotonically with increasing rotor-stator gap. Total pressure loss was focused on to evaluate the turbine efficiency by Venable et al. [8] and Busby et al. [9]. They claimed that there is no definite trend in the adiabatic efficiencies regarding the axial gap. Effects of the axial gap on turbine performance and blade loading were examined by Chang and Tavoularis [10]. The case with normal axial gap size was found to have the highest efficiency in their study, and increased turbulence in the endwall boundary layers provided an explanation for the increased losses in the small and large gap cases. Park et al. [11] discussed in detail effects of axial gap on unsteady secondary flow in the axial turbine. The loss owing to stator wake/rotor passage vortex interaction and the stator/rotor passage vortices interaction were closely analyzed to explain the turbine efficiency. Gaetani et al. [12] pointed out that the secondary flows in the rotor passage are affected by axial gap. Kikuchi et al. [13] explained their conclusions regarding the impact of stator flow on the rotor secondary flow strength. Restemeier et al. [14] observed a decrease in the rotor passage vortex intensity with the axial gap decreasing, which can explain the increase in efficiency. Cizmas et al. [15] showed that the turbine efficiency increases as the axial gap between the first rotor and the second stator increases. However, the quasi-three-dimensional calculation in the investigation did not take into account the endwall losses and secondary flows [16]. Tang et al. [16] showed that increasing the axial distance leads to turbine efficiency reduction, but that is not applicable for very small gaps. In addition, pressure fluctuation of a pump turbine was numerically and experimentally studied by Li et al. [17] and Guo et al. [18]. The existing studies about the effects of axial gap are mostly focused on the unsteady interaction and turbine aerodynamic performance. However, few studies focus on how blade response was affected by axial gap. Considering that periodic flow induced by rotor-stator interaction causes blade vibration, effects of axial gap on aerodynamic forces, and blade response under the aerodynamic excitation were investigated in this work. The research herein was conducted on a rocket engine turbine. The integral blisk is usually employed for rocket engine turbines. Sometimes the rotor blade is designed with a shroud, and sometimes it is not. In view of this, effects of axial gap on the shrouded rotor blade and on the unshrouded rotor blade were analyzed and compared in this study. Since turbine blades for rocket engines are usually short, the stiffness of the blade is high enough to result in small vibratory movements of blade [19]. Therefore, the fluid calculation was not coupled with the structure calculation, which greatly reduced computational costs. Aerodynamic forces acting on the rotor blade were obtained using 3D time-resolved flow simulations. The
resulting aerodynamic forces were interpolated to the FE model through surface effect elements prior to conducting forced response calculations.
Computational procedures 2 CFD calculation 2.1 Reynolds time-averaged Navier-Stokes equations were solved using CFX, a commercially available finite volume solver. The general form of governing equations for compressible viscous unsteady flow in a Cartesian coordinate is expressed as follows (
) (1) + div( U ) = div( grad ) + S , t where is the general variable for the different equations, is general diffusion coefficient, and S is a general source term. Conservation equations for mass, momentum and energy can be obtained by setting to 1, u, v , w and h. Turbulence models can be obtained when setting to k and . The upwind schemes were applied to discrete advection terms. The second-order implicit schemes were adopted for temporal discretization. The k-ω based shear stress transport (SST) turbulence model was employed in this study, since it can give highly accurate predictions of the onset and the amount of flow separation under adverse pressure gradients. The SST model combines the advantages of the k-ω model in the near-wall region and the k-ε model in the bulk domain, and it accounts for the transport of turbulent shear stress. The single-stage turbine studied here is used for a stagedcombustion cycle rocket engine oxygen turbopump, containing 17 vanes for stator and 29 blades for rotor. In the current effort, a 16 vane-32 blade count approximation was made, allowing a simulation with 1 stator passage and 2 rotor passages according to the periodicity. To keep the pitch-to-chord ratio (blockage) constant, the vane airfoil was scaled by a factor of 17/16, and the blade airfoil was scaled by a factor of 29/32. The tip clearance in the rotor was set at the design value of approximately 1% of the rotor height. The working gas in the turbine is an oxygen-rich gas. The specific heat capacity at constant pressure was 1058 J/(kg K), and the specific heat ratio was 1.326. Due subsonic inlet flow, the total pressure, 47.5 MPa, and total temperature, 771 K, were specified at the inlet. The flow direction was normal to the inlet boundary, and 5% turbulent intensity was set. The static pressure 24.5 MPa was imposed at the outlet for the subsonic outlet. Periodicity is enforced along the outer boundaries in the circumferential direction. No-slip and adiabatic boundary conditions were enforced along all the solid surfaces. In the shrouded configuration, the shroud wall rotated at the speed of rotor rotation. However, the casing wall remained static in a stationary frame for the unshrouded config-
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uration. A counter rotating wall was set in the rotating frame for the casing wall. Sliding mesh was used to model the interface region between the stator and rotor to obtain a time-accurate solution. The vane passing period was defined as the period of time required for one blade to pass one vane. The rotational speed of rotor at design point was 16000 r/min. 100 time steps were set in a vane passing period. The convergence criteria for the root mean square residual was set to 1×10−5. Since the number of time steps in a vane passing period was large enough, 20 iterations were performed for each time step to ensure the convergence. The computational grids were generated via the IGG/Autogrid software package. Structured grid systems were created in the computational domain with O-type grids near the blade surface and H-type grids in the other regions. Butterfly mesh was used to discretize the tip clearance. Computational grids for the stator and rotor are shown in Figure 1. The grid-dependency check was conducted by simulating steady flow of the shrouded model while varying the number of grid nodes. Figure 2 shows the comparison of the turbine total-to-total efficiency. The total-to-total efficiency of the turbine is defined as
tip clearance. Boundary conditions were set as mentioned above. The experimental choking mass flow rate was 20.93 kg/s. The computed choking mass flow rate was 20.66 kg/s, which is 1.3 percent below the experimental value. Figure 3 shows the normalized total pressure and total temperature (normalized by total pressure and total temperature at rotor inlet) as a function of normalized mass flow rate (normalized by choking mass flow rate). Simulation results by Glenn-HT Code [21] are also plotted in the figures. As can be seen, the CFX code gave reasonable results compared with experimental data. The three cases considered include a small gap configuration (30% of the blade axial chord), a normal gap configuration (40% of the blade axial chord), and a large gap configuration (50% of the blade axial chord). The axial gap sizes for all three cases are 0.3 br (small gap), 0.4 br (normal gap) and 0.5 br (large gap), respectively (br is the blade axial chord). It should be noted that the axial gap was changed by shifting the stator axially. The casing and hub sections in the stator domain were either elongated or shortened, while the rotor domain stayed the same. By doing so, the axial distances between the stator-rotor interface and the blade leading edges were the same for all computational configurations. However, the distances between the vane trailing edge and the stator-rotor interfaces were different.
=
1 1
Tt 2 / Tt 0
(Pt 2 / Pt 0) (
1) /
,
(2)
where the Tt0, Pt0 are the total temperature and total pressure at the turbine inlet, respectively, Tt2, Pt2 are total temperature and total pressure at the turbine outlet, and γ is specific heat ratio. It can be seen from Figure 2 that efficiency varied significantly with as the number of grid nodes increased from Level 1 to Level 3. However, the number of grid nodes had little impact on the predicted turbine efficiency between the Level 4 case and the Level 5 case. The mesh used in the Level 4 case was selected taking into account the computational costs and accuracy. The total number of grid nodes was approximately 1.0 million for the shrouded configurations and about 1.3 million for the unshrouded configurations with tip clearance. The CFX code was validated using available experimental data from tests conducted by Lewis Research on the NASA Rotor 37 [20]. The tip gap was accounted for by meshing the
CFD Figure 1 grids. (a) Stator; (b) shrouded rotor; (c) unshrouded rotor.
FE calculation 2.2 A single blade was used for modal analysis and forced response analysis. The blade models were meshed using the brick element (ANSYS Element solid 186), as shown in Figure 4. A total of 2597 elements comprised the shrouded blade and 1925 elements comprised the unshrouded blade. The mesh of the blade section for the shrouded blade was the same as the mesh for the unshrouded blade. The rotor blade was fully restrained at the hub nodes. Circumferential cyclic symmetry was maintained for the shroud in the shrouded rotor blade model by imposing a coupling constraint in a cylindrical coordinate system. The aerodynamic forces on the blade surface resulting from flow simulations were interpolated to the FE model through surface effect elements.
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Results and discussion 3 Flow field analysis 3.1
Grid-dependency Figure 2 check in terms of the total to total efficiency.
(Color Figure 3 online) Total pressure (a) and total temperature (b) versus mass flow.
Figure 5 presents instantaneous contours of static pressure, normalized by the inlet total pressure, at the midspan for shrouded rotor configurations with different axial gaps. High pressure behind the vane trailing edge is axially elongated as the axial gap increases. As can be seen, static pressure on the pressure side of the middle blade decreased, while static pressure on the pressure side of the top blade increased as the axial gap increased. It revealed that differences of pressure on blades at different positions became smaller as the axial gap increased. Considering that the blade passed through different positions as the rotor rotated, it can be deduced that the smaller the axial gap, the larger the pressure fluctuation on the blade surface. Figure 6 shows time-averaged blade surface static pressure normalized by the inlet total pressure at 10%, 50% and 90% spans for the shrouded rotor with different axial gap sizes. It reveals that the axial gap had little impact on the time-averaged pressure on the blade surface, which is in agreement with the finding of Venable et al. [8]. The standard deviation was selected to reflect the intensity of the pressure fluctuations on the rotor blades. It is essentially the root mean square of the difference between the latest solution value and the running arithmetic average value. Figure 7 shows the standard deviation of the surface pressure fluctuations at 10%, 50% and 90% spans for the shrouded rotor with different axial gap sizes. The pressure fluctuations are normalized by inlet total pressure. The strongest pressure fluctuations are located on the blade suction side toward the leading edge. The maximum fluctuations decrease along the spanwise. When the axial gap increases, the pressure fluctuation reduces apparently in most range of the axial chord. Figure 8 shows contours of the standard deviation of pressure fluctuations (normalized by inlet total pressure) on the suction side of the shrouded rotor blade for different axial gap sizes. It appears that pressure fluctuations generally decrease along the spanwise and axial chord. The maximum pressure fluctuation occurs on the suction side toward the leading edge and blade hub. The contours reveal that the size of high pressure fluctuation regions decreases as the axial gap increases. Aerodynamic forces on the rotor blade are calculated as follows f t = n t ( (pds ) + f visco ),
(3)
s
f z = n z( (pds ) + f visco ),
(4)
s
(Color Figure 4 online) FE meshes. (a) Shrouded blade; (b) unshrouded blade.
where f t and f z are circumferential force and axial force, respectively, f visco represents the viscous force on blade, n t and
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(Color Figure 5 online) Instantaneous static pressure contours at midspan for different axial gaps. (a) Small gap; (b) normal gap; (c) large gap.
(Color Figure 6 online) Time-averaged static pressure on the shrouded rotor blade surface at different spans. (a) 10% span; (b) 50% span; (c) 90% span.
(Color Figure 7 online) Standard deviation of static pressure on the shrouded rotor blade surface at different spans. (a) 10% span; (b) 50% span; (c) 90% span.
n z are circumferential unite vector and axial unite vector, and (pds ) represents the surface integral of static pressure on s
the rotor blade. The unsteady aerodynamic forces on the shrouded rotor blade in time domain are plotted in Figure 9. The force peaks decrease and valleys increase as the axial gap increases. Therefore, the aerodynamic force fluctuations decrease with increasing axial gap. Mean values of aerodynamic forces seem to slightly change. This can be expected, because the
time-averaged pressure on the blade surface hardly changes when the axial gap varies, as shown in Figure 6. The FFT method was used to convert the aerodynamic forces in time domain to frequency domain. Figure 10 shows the amplitude frequency characteristics of aerodynamic forces on the shrouded rotor blade. It should be noted that the frequency was normalized by the vane passing frequency. The 1st harmonic of circumferential force is clearly the dominating component, while the magnitudes of the other harmonics are small in comparison. The 1st harmonic of axial force is also
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(Color Figure 8 online) Contours of the standard deviation of static pressure fluctuations (normalized by inlet total pressure) on the suction side of shrouded rotor blade. (a) Small gap; (b) normal gap; (c) large gap.
(Color Figure 9 online) Time variation of aerodynamic forces on shrouded rotor blade. (a) Circumferential forces; (b) axial forces.
(Color Figure 10 online) Harmonics of aerodynamic forces on the shrouded rotor blade. (a) Circumferential forces; (b) axial forces.
a dominating component. However, more harmonics have considerable magnitudes compared with circumferential force. In general, the amplitudes of all harmonics decrease significantly as the axial gap size increases. Structural response analysis 3.2 The first and second modal frequencies are 2467 and 4829 Hz for shrouded blades; and 3697 and 5501 Hz for unshrouded blades, respectively. It is clear that modal frequency for the
shrouded blade is lower than that for the unshrouded blade because blade stiffness increased because of the shroud. The first and second mode shapes for shrouded and unshrouded blades are presented in Figure 11. It can be seen that the maximum displacement is located at the blade tip toward the trailing edge for both blades, regardless of the shroud. Time histories of forced response displacement on the blade tip toward the trailing edge for shrouded and unshrouded rotor blades are plotted in Figure 12. Blades used here are both con-
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figurations with a small axial gap. It can be seen that the maximum displacements and amplitudes for the unshrouded rotor blade are all larger than those for the shrouded rotor blade. It seems that the shroud effectively restrains the blade deformation. The displacement responses of the unshrouded blade show obvious beat vibration phenomenon. The response amplitudes present temporal periodic change. However, fluctuations of displacement amplitudes for the shrouded rotor blade are small. It can be expected that the displacement responses for the unshrouded rotor blade have more frequency compo-
nents. The circumferential displacement (Dy) is the largest component, while the axial displacement (Dx) is the smallest component for both types of blades. All three displacement components have similar characteristics of cycle for both the shrouded rotor blade and unshrouded rotor blade. Time histories of the blade tip circumferential displacement (Dy) on the trailing edge for shrouded and unshrouded configurations with different axial gaps are shown in Figure 13(a) and (b), respectively. It can be seen from Figure 13(a) that tip displacement for shrouded rotor blade was hardly affected by
(Color Figure 11 online) The 1st and 2nd mode shapes for blades. (a) Shrouded rotor blade; (b) unshrouded rotor blade.
(Color Figure 12 online) Time history of forced response deformation. (a) Shrouded rotor blade; (b) unshrouded rotor blade.
(Color online) Time history of blade tip displacement on trailing edge for different axial gaps. (a) Shrouded rotor blade; (b) unshrouded rotor blade. Figure 13
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the axial gap. Figure 13(b) reveals that, for the unshrouded blade, displacement peaks decrease and valleys slightly increase as the axial gap increases. Therefore, amplitudes of displacement response decrease with increasing axial gap. It is clear that the shroud weakens the effect of axial gap on the rotor blade response. Figure 14 shows the FFT amplitude spectra of the blade tip circumferential displacement response for shrouded and unshrouded blades with different axial gaps. Frequency of the 1st harmonic is the first mode frequency of the rotor blade. Frequency of the 2nd harmonic is the vane passing frequency, which is the frequency of forced excitation. Frequency of the 3rd harmonic is equal to the second mode frequency of the rotor blade. Displacement response for the shrouded blade has one significant harmonic component. The 1st harmonic is absolutely dominating, while the 2nd and 3rd harmonic components are weak. Three notable harmonic components exist for the unshrouded blade. The 1st harmonic is also dominant for the unshrouded blade. However, the 2nd harmonic component is large, which is different from the shrouded blade. What is more, the 3rd harmonic is not negligible. It can
be concluded that the shroud significantly weakens the blade forced response at the exciting frequency. From the displacement harmonics for the shrouded blade we can see that amplitudes of the 1st harmonics are almost the same for different axial gaps. Although the 2nd harmonic is weak, it also reveals that amplitudes tend to decrease as the axial gap increases. As for the unshrouded blade, amplitudes of the 1st and 3rd harmonics change very little with changes in axial gap. However, amplitudes of the 2nd harmonics significantly decreased as the axial gap increased. This reveals that the axial gap has significant impact on the response harmonic at forced exciting frequency, while it has little influence on the response harmonics at natural frequency. Time histories of forced response stress on the leading edge toward the blade root for shrouded and unshrouded blades are shown in Figure 15. Just like the time history of displacement, the stress response for the unshrouded blade shows beat vibration phenomenon, while that for the shrouded blade does not show similar characteristics. The radial stress is the largest component, while the other two components are small for both kinds of blades. The blades experience alternating
(Color Figure 14 online) Harmonics of blade tip displacement on the trailing edge for different axial gaps. (a) Shrouded rotor blade; (b) unshrouded rotor blade.
(Color Figure 15 online) Time history of forced response stress. (a) Shrouded rotor blade; (b) unshrouded rotor blade.
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tensile stress and compressive stress induced by the periodic aerodynamic forces. Mean stress for shrouded blade is tensile stress, while that for unshrouded blade is close to zero. Time histories of radial stress on the leading edge nearing the blade root for the shrouded and unshrouded configurations with different axial gaps are shown in Figure 16. As can be seen from Figure 16(a), the axial gap has little impact on the stress response of the shrouded blade. As for the response of the unshrouded blade shown in Figure 16(b), when the axial gap increases, the stress peaks change little and the stress valleys increase, which results in decreasing stress amplitude. FFT amplitude spectra of stress response for shrouded and unshrouded blades with different axial gaps are shown in Figure 17. The stress responses have similar amplitude-frequency characteristics with the displacement responses. Figure 17(a) reveals that the 1st harmonic is absolutely dominant, and amplitudes of the 2nd and 3rd harmonics are small for the shrouded blade. Amplitudes of harmonics are hardly influenced by the axial gap size. The 1st harmonic is dominant, the 2nd harmonic is significant, and the 3rd harmonic is weak for the unshrouded blade response shown in Figure 17(b). Amplitudes of the 1st and 3rd har-
monics are hardly affected by the axial gap size. As the axial gap increases, amplitude of the 2nd harmonic shows significant reduction. It can be concluded that the axial gap mainly affects the harmonic component at the exciting frequency.
Conclusion 4 Forced response analysis of a rocket engine turbine blade was conducted by a decoupled fluid-structure interaction procedure in time domain. The FFT method was employed to convert response from the time domain to the frequency domain. Effects of the stator-rotor axial gap on aerodynamic forces and blade response were studied. In consideration of common blade styles for rocket engine turbines, the influence of axial gap on the shrouded blade response was compared with that on the unshrouded blade response. Results demonstrated that: 1) The axial gap has little impact on the time-averaged pressure on blade surface, while the pressure fluctuations significantly decrease as the axial gap increases. Aerodynamic forces on the blade surface display periodic variation. Frequencies of harmonics are multiples of the vane passing
(Color online) Time history of radial stress on the leading edge nearing the blade root for different axial gaps. (a) Shrouded blade; (b) unshrouded Figure 16 blade.
(Color online) Harmonics of radial stress on the leading edge nearing the blade root for different axial gaps. (a) Shrouded blade; (b) unshrouded Figure 17 blade.
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frequency, and the 1st harmonic is dominant. Amplitudes of all harmonics decrease with increasing axial gap. 2) Modal frequencies for the shrouded blade are lower than those for the unshrouded blade because of increased stiffness induced by the shroud. The shroud restricts blade deformation, and responses of the shrouded blade are much lower than those of the unshrouded blade. 3) Responses of the shrouded and unshrouded blades in time domain both display periodic variation. Furthermore, the unshrouded blade responses show obvious beat vibration phenomenon, while the shrouded blade responses do not show this characteristic. FFT results reveal that frequencies of the first three harmonics are respectively corresponding to the first order frequency of blade, vane passing frequency and the second order frequency of blade. The 1st harmonic of shrouded blade response is clearly dominant, while the other harmonics are small in comparison. However, the unshrouded blade response has at least three notable harmonics. This demonstrates that the shroud restrains multiple harmonics, especially the forced harmonic at exciting frequency. 4) The axial gap mainly affects the forced harmonic at vane passing frequency, while the other two harmonics at natural frequency are hardly affected. Amplitudes of the unshrouded blade response decrease as the axial gap increases. However, amplitudes of the shrouded blade response change little with increasing axial gap because its forced harmonic is too small to influence the amplitude. 1
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