Axial fan blade vibration under inlet cross-flow

In thermal power plants equipped with air-cooled condensers, axial cooling fans operate 1 under the influence of ambient flow fields. Under inlet cross-flow conditions, the resultant asymmetric 2 flow field is known to introduce additional harmonic forces to the fan blades. This effect has 3 previously been studied only numerically or using blade mounted strain gauges. For this study, 4 Laser Scanning Vibrometry was used to assess fan blade vibration under inlet cross-flow conditions 5 in an adapted fan test rig inside a wind tunnel test section. Two co-rotating laser beams scanned 6 a low pressure axial fan, resulting in spectral, phase resolved surface vibration patterns of the fan 7 blades. Two distinct operating points were examined, with and without inlet cross-flow influence. 8 While almost identical fan vibration patterns were found for both reference operating points, overall 9 blade vibration increased by 100% at low fan flow rate due to cross-flow, and by 20% at high fan flow 10 rate. While numerically predicted natural frequency modes could be confirmed from experimental 11 data as minor peaks in the vibration amplitude spectrum, they were not excited significantly by 12 cross-flow. Instead, primarily higher rotation rate harmonics were amplified, i.a. a synchronous blade 13 tip flapping was strongly excited at the blade pass frequency. 14


Introduction
In arid regions, ecologic and economic reasons increasingly demand the application of air-cooled condensers (ACC) in thermal power plants [1].Traditional "A-frame" designs consist of large diameter, low-pressure axial fans mounted horizontally below bundles of heat exchanger tubes where the condensate is cooled by the fans' draft [2].At the fans' inlets, the influence of cross-flow induced by neighboring fans and natural ambient winds, which typically reach magnitudes of 5 to 13 m/s or more [3,4], is a major issue.It effectively reduces the volumetric effectiveness of the cooling fans [5][6][7][8][9][10].
Cross-flow introduces asymmetric effects in the inlet flow field of the fans and cause an azimuthal dependence of the flow's angle of attack at the fan blades.This affects the pressure and velocity distribution at the rotor outlet, as well as the blade loads.The strong asymmetry of the flow field was shown early by Thiart and von Backström [11] for a wall mounted fan, indicating the mechanisms behind the reduction of volumetric effectiveness.For the shrouded peripheral fans in an array of cooling fans of an ACC, the inlet cross draft additionally causes a flow detachment at the windward edge of the nozzle or condenser bank edge.This introduces additional asymmetric effects to the inlet flow field, as shown by Meyer [12] using numerical investigations, and from experimental and numerical data by van der Spuy et al. [13,14].
Along with its negative aerodynamic influence on fan cooling performance, inlet cross-flow is also known to increase blade load and vibration.Depending on its lateral position, relative blade motion is advancing or retreating to the ambient cross-flow, which respectively results in greater or smaller angle of attack of the relative flow at the fan blade.This may result in greater or smaller blade forces and can lead to considerable stall effects [15].The upwind inlet shroud detachment can affect the load in longitudinal direction of the cross-flow decisively [16].
Hotchkiss et al. [15] found a strong azimuthal dependence of blade load due to γ = 45 • between inflow angle and fan axis in a pipe-inlet free-outlet computation.For anti-clockwise fan rotation and inlet cross-flow from the left (azimuthal position ϕ = 180 • ) to the right (ϕ = 0 • ), Hotchkiss et al. found variations in torque and thrust of more than 20% compared to the reference case without cross-flow, with maxima locating around the ϕ = 180 . . .220 • and minima around ϕ = 0 • .Similar results were found from simulation performed by Bredell et al. [16], who computed significant bending moment variations of ACC periphery fans under the influence of induced inlet cross-flow.Azimuthal variation of the load distribution was similar to the findings of Hotchkiss et al, i.e. maximum bending momentum was found at the upwind position ϕ = 180 • .It was shown that nature and magnitude of the amplification caused by induced cross-flow at the periphery fan depend strongly on ACC platform height and fan geometry.Larger hub to tip ratio fans did not show essentially smaller bending moment variations.
From measurements with strain gauges on an operating on-site periphery fan in a power plant ACC, Muiyser et al. [17] computed the azimuthal load distribution.Their experimental findings agree with the computations mentioned above.Blade load was increased dominantly by magnitudes around 20% at the upwind side of the periphery fan, with higher loads at the advancing blade side (ϕ ≈ 0 • to 180 • ) compared to the retreating blade side.Earlier potential flow computations by Muiyser et al. [18] already identified the sensitivity of blade vibration to distorted inlet flow conditions.Depending on blade stiffness, excitation due to cross-flow was found to lead to considerable damping or resonance effects.Largest strain gauge amplitudes were found where rotation rate frequency harmonics were in proximity of natural frequencies [17,18].
Inlet cross-flow can obviously cause great amplifications in fan vibration and respective blade loads.This is relevant to the effective stress in the large-diameter cantilever style fans used in conventional ACCs.It may also be a concern for larger hub to tip ratio fans, especially when operating rotation rate harmonics coincide with a natural frequency of the blade.
Rather than determining the azimuthal load distribution, this study wants to gain more spatially resolved spectral information on the influence of inlet cross-flow on the blade vibration of axial fans.
For this, blade motion was captured using Laser Scanning Vibrometry (LSV) in a wind tunnel fan test rig, as described below.Natural frequencies and mode shapes of the industrial fan were computed, and the findings are used to assess the motion patterns of peak amplitude frequencies from the measurements.

Materials and Methods
Laser Scanning Vibrometry measurements were performed on an axial fan, using a fan test rig mounted inside a wind tunnel test section.Natural modes and frequencies were computed from a FEM eigenvalue computation of the fan under centripetal load.

Wind tunnel fan test rig
The influence of an inlet cross-flow on fan blade vibration was measured using LSV inside a customized fan test rig inside a Göttinger type wind tunnel with a 2.80 m long open test section and an exit nozzle of 1.87 × 1.40 m 2 .A commercial D fan = 300 mm diameter low pressure axial fan with five forward skewed blades and a hub to tip ratio of ν hub = 0.342 was examined operating with its axis perpendicular to a uniform ambient velocity U 0 .Figure 1 shows the experimental setup, and fan design is illustrated in Fig. 2.   The test fan was examined operating in its standard shroud without guard grille, held in place by four thin struts with its outlet mounted to a square duct section, 1.5 inside the 300 × 300 mm 2 square duct is described in [19].Fan flow rate V was computed from static pressure loss over five standard nozzles inside a settling chamber at the end of the outlet duct in accordance to fan test rig standard ISO 5801 (not displayed in Fig. 1).The experimental setup was previously used to investigate the integral inlet flow field influence on the characteristic fan curve, as
To measure fan rotation rate f 0 and to synchronize the test fan with the co-rotating laser scanning vibrometer's derotator, a rotary encoder was mounted directly to the fan axis at its center.With the wind tunnel either turned off or operating at U 0 = 10 m/s wind velocity, the characteristic cross-flow coefficient differed slightly around 0.25, depending on the rotation rate f 0 of the commercial fan.
At one low flow rate OP1 and a higher one OP2 with similar flow rate coefficients a total of four operating points were measured with µ = 0 (OP10 and OP20) and µ ≈ 0.25 (OP11 and OP21), as listed in Table 1 along with the respective total fan pressure coefficients

Laser Scanning Vibrometry
Axial blade surface velocity distribution was captured using a Polytec PSV-500 Scanning Vibrometer, coupled with a PSV-A-400 derotator.The laser beam scanned the fan blades' surface at N ScPts = 400 equally distributed probe locations with a typical distance of 10 mm as shown in Fig. 2a, at a sampling rate of 12.5 kHz.On each scanning point, 30 samples of 640 ms (around 27 full fan rotations) were successively captured and transferred to the frequency domain.Hanning windows with 70% overlap were used to average the 30 samples, resulting in frequency domain data sets of bandwidth B = 5 kHz resolved to discrete frequencies k • ∆ f , with ∆ f = 1.5625Hz.With the respective fan rotation rate f 0 , discrete Strouhal numbers resulted.Plain kinematic effects were observed at rotation rate f 0 , caused by the uncertainty in parallel alignment of laser beam and fan axis.To exclude such rigid body rotation effects from blade vibration analysis, the frequency domain was filtered to a minimum integer k 0 above the second rotation rate harmonic, such that can be computed.This allows the reconstruction of a relative motion pattern The magnitude of total fan vibration is analyzed with the surface averaged axial velocity as a function of the frequency, Using this, the integral level of overall fan blade vibration can be expressed by the root mean square value over all Strouhal numbers k 0 ∆ f / f 0 ≤ Sr k ≤ B/ f 0 with k 0 from Eq. ( 5), i.e. (9)

Numerical setup for natural frequency computation
To interpret the measured vibration shapes at dominant frequencies, the natural frequencies f e,j of the test fan were computed, along with the respective mode shapes.The finite element solver ANSYS Mechanical was used to perform the modal analysis under typical centripetal loads.
Tetrahedral triangulation of the geometric fan model was performed with typical element sizes of 10 −3 D fan , resulting in 206 802 nodes.The resulting mesh is shown in Fig. 2b.A centripetal load was inflicted on the fan at f 0 = 44.2Hz, with rigid support in all degrees of freedom at the four bolt locations marked u = 0 in Fig. 2b.This resulted in peak von-Mises equivalent stress levels of 269 MPa, located at the leading edge of the blades at around on third of the span between hub and tip.This pre-strain of the blades has a considerable influence on the fan's natural frequencies and mode shapes.

Natural frequencies
Natural frequency computation with the setup described above typically resulted in groups of five distinct frequencies in great proximity.These refer to the same natural mode for each individual blade, which differ numerically due to model and mesh asymmetries.The arithmetic mean over theses sets of joint frequencies resulted in the first eight natural frequencies f e,j listed in Table 2 along with the respective Strouhal numbers Sr e,j , which differ for the different rotation rates f 0 of the four operating points.The distinct five frequencies averaged to f e,j are listed in    Even though operating at distinctly different flow rates Φ, the reference spectra of OP10 and OP20

First natural frequency mode
The numerically predicted first natural mode is shown in Fig. 4b.As stated above, five very close frequencies were found for Sr e,1 , each with another maximum attenuated blade (see Table 3).In Fig. 4b, The remaining four non-dominant blades describe a counter-motion to the one on the upper right, with most discernible motion patterns at the two blades opposing it (bottom and left in Fig. 5b).Peer-reviewed version available at Appl.Sci.2017, 7, 862; doi:10.3390/app7080862 In reference to the associated amplitude peak v z (Sr e,2 ) in Fig. 3, the relative axial motion ṽz,i (9.620) is displayed in Fig. 5a for OP20.Again, the mode shape resembles the computation very strongly, with the dominant blade on the upper right.The single difference between measured vibration response and computation may be discerned in the motion of the remaining four blades.The two opposing blades do not show a counter-motion to the upper right one.Instead, such motion is more strongly found in the blades flanking the dominant one.This discrepancy between measurement and computation may be attributed to the differences due to manufacturing and installation, and the interaction of presumably more distinct individual natural frequencies for each blade.

Spectral decomposition of surface averaged vibration
The measured response in surface averaged blade vibration v z (Sr) to inlet cross-flow is shown in its spectral decomposition in Fig. 6 for OP1 and Fig. 7 for OP2.The integral root mean square measures show a distinct increase in overall blade vibration at OP1 from µ = 0.26.With 718.46 mm/s at OP11, v rms was almost double the value of reference configuration OP10 (v rms = 362.52mm/s).At OP2, µ = 0.25 cross-flow increased v rms by about 20% from 363.40 mm/s (OP20) to 436.87 mm/s (OP21).The greater overall increase in v rms also reflects in the influence of cross-flow in the spectral decomposition of v z (Sr) in Figs. 6 and 7. Amplitude gains are found at OP1 in Fig. 6 at almost each integer value Sr ≥ 4, but Sr = 5 and Sr = 6 are the rotation rate harmonics that are exited dominantly.Due to the influence of inlet cross-flow, the blade pass frequency was also measured to become the dominant amplitude peak v z at the higher flow rate operating point OP2, as visible in Fig. 7. Amplification at Sr = 6 was found for OP21 too, but to a far lesser magnitude than for OP1 in Fig. 6.The previously dominant frequency Sr = 3 was not affected in amplitude by cross-flow at either operating point.Blade vibration around the natural frequency domains cannot be discerned from the data presented in Figs. 6 and 7, the cross-flow influence appears not to excite the fan's natural modes significantly.At the blade passing frequency Sr = 5, both operating points OP11 (Fig. 8b) and OP21 (Fig. 9b) showed a synchronized blade tip flapping motion caused by the influence of cross-flow.At the blade tips, large peak velocity amplitudes ṽz,i (5) can be found.The vibration increase at blade pass frequency is not surprising.Since Sr = 5 is the frequency at which the fan blades pass the inlet cross-flow, it is also the excitation frequency of the resultant external harmonic forces, causing an in-phase motion of all blades.A blade tip flapping motion was also detected from experimental LSV data at the sixth rotation rate harmonic Sr = 6.The pattern can be seen especially clearly for the strong excitation at OP12 in Fig. 10b, but also in Fig. 11b for OP22.But while the single-blade motion with its peak at the leading edge tip resembles the first natural mode shown in Fig. 4b, the dominant blade's neighbors do not move in counter-phase to it.Instead, they have an offset of θ i,ref around 90 • , which levels the otherwise similar amplitude v z,i at the bottom and upper right blades in Figs.10b and 11b.
From the fact that blade root amplitudes ṽz,i (6) are distinctly below zero where the blade tip is maximum (bottom right blade in Fig. 10b), and above zero were blade tip velocity is minimum (left and top blade), an non-ideally stiff fixation of the fan motor to the casing is indicated.Thus, an overlying additional resonance mode of the entire fan within its casing could be the cause of the observed excitation at Sr = 6.

Discussion
Using a co-rotating LSV setup, it was possible to measure blade vibration of an axial fan with high spectral and spatial resolution.Additionally, the experiment was set up inside a wind tunnel test section to investigate the effect a uniform inlet cross-flow on fan blade vibration, which is known to introduce a significant axial asymmetry of the flow field in the rotor section [12][13][14].
Up to this point, similar investigations have only been made numerically [15,16,18] or using strain gauges on larger diameter fans [17,21].Using LSV in this setup, it was possible to gain more insight on the spatial resolution of the fan blade vibration under cross-flow influence, and to compare the resulting motion distributions to numerical mode analysis.
Two distinct fan operating points were examined, with very similar spectral distributions of surface averaged blade vibration amplitude in the reference configuration, i.e. without ambient flow field.The first and, to a smaller extend, second natural frequency showed peaks in the vibration amplitude spectrum which fitted the predicted natural mode very well in shape, but stronger blade vibration was measured at the rotation rate harmonics.Under the influence of inlet cross-flow, the blade pass frequency and the sixth rotation rate harmonic were excited strongly, while no significant amplification of the natural frequencies was measured.These findings agree with previously observed cross-flow excitation effects [17,18].Integral fan blade vibration almost doubled at low fan flow rate, and increased by 20% at the higher fan flow rate.

( a )
Scan point distribution on rotor at inlet seen from front, anti-clockwise rotation.(b) FEM tessellation for natural frequency computation, seen from outlet, clockwise rotation.

Figure 2 .
Figure 2. Experimental subject axial fan with forward skewed blades.

3. 1 . 2 .
Spectral decomposition of the surface averaged velocity amplitudeReference results show the response of fan vibration without the presence of a uniform ambient cross-flow field at the fan inlet (U 0 = 0 m/s).Dominant amplitude peaks can be determined, and a comparison of the two operating points OP10 and OP20 can be made.Selected frequencies Sr are examined more closely, and the respective reconstructed motion pattern can be compared to associated natural modes determined from FEM simulation.

Figure 3
Figure3shows the spectral decomposition of the surface averaged fan blade velocity amplitude v z from all N ScPts scan points as defined in Eq. (8) for the frequency range 2.2 < Sr ≤ 50.As annotated above, the first two rotation rate harmonics Sr = 1 and 2 are cut off due to distortion by kinematic effects.In Fig.3, dotted vertical lines indicate the harmonics of the blade pass frequency Sr = 5.The data sets' natural frequencies Sr e,i are added in dashed vertical lines for i = 1 to 4. Due to the different rotation rates f 0 of the operating points' natural frequencies, these dashed lines do not coincide for the data sets.It becomes clear from Figure3that the measured mean surface vibration was dominated by the rotation rate harmonics, i.e.where Sr has integer values, with v z amplitudes close to zero in between.

Figure 4 .
Figure 4. Measured and computed modal shapes at first natural frequency.

Figure 5 .
Figure 5. Measured and computed modal shapes at second natural frequency.

3 Figure 6 .
Figure 6.Spectral decomposition of cross-flow influence on measured mean surface velocity amplitude at OP1.

Figure 7 .
Figure 7. Spectral decomposition of cross-flow influence on measured mean surface velocity amplitude at OP2.

Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 5 July 2017 doi:10.20944/preprints201707.0007.v1
• D fan above the wind tunnel test section's floor.Behind a short flow straightening device, stagnation pressure p m,i was captured relative to wind tunnel ambient pressure with 81 Kiel type stagnation pressure probes, and surface averaged to the total to total fan pressure ∆p tt = ∑ 81 i=1 p m,i /81.The equally spaced 9 × 9 grid of pressure probes

Table 1 .
Examined operating points

5 July 2017 doi:10.20944/preprints201707.0007.v1
Peer-reviewed version available at Appl.Sci.2017, 7, 862; doi:10.3390/app7080862Thescanning laser was accompanied by a reference beam signal v z,ref (Sr k ), which remained fixed on one probe location for phase reference to the individual measured velocities v z,i (Sr k ) (for i = 1 . . .N ScPts scan points).Using the recorded cross spectral density between the two signals G i,ref (Sr k ), a phase offset of point i at Sr k and B/∆ f = 3200 .(5) Preprints (www.preprints.org)| NOT PEER-REVIEWED | Posted:

Table 3 .
Blade specific distinct first four natural frequencies.
coincide intensely, with almost identical integral vibration measures v rms = 362.52mm and 363.40 mm, respectively.The dominant peak for both operating points is Sr = 3, with similar velocity amplitudes, but also the blade pass frequency harmonics Sr = 5, 10 and 15 are prominent.Noteworthy non-integer values Sr locate in the proximity of the first three natural frequencies, especially at Sr e,1 .

Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 5 July 2017 doi:10.20944/preprints201707.0007.v1
Peer-reviewed version available at Appl.Sci.2017, 7, 862; doi:10.3390/app7080862Inallreferenceresults (on the left in Figs. 8 to 11), the distribution of ṽz,i forms no clear pattern, and the amplitude range is comparably low.In contrast to this, the right hand graphics in Figs.8 to 11show very characteristic motion patterns of the fan blades under the influence of inlet cross-flow.
v z,i • cos(ϑ vv ref ) in mm/s