Effect of fan exit guide vane placement on fan broadband interaction noise

Fan-stage configuration

The NASA SDT rig provides the initial fan-stage configurations used in this study. Some details of the three SDT FEGV configurations are listed in Table 1. Several modified FEGV placements that were not part of the SDT experiment are then constructed. The FEGV placements for the baseline, low-count, and low-noise SDT FEGVs in the experiment are shown in Figure 1(b). Figure 1(a) shows the same FEGVs moved to the closest FEGV placement considered in this paper. The FEGV location is expressed as the ratio Δx/c _tip , the change in axial placement of the FEGV normalized by the fan tip chord length. The design placement, Δx/c _tip = 0, is used as the reference. At the design location, the baseline FEGV leading edge is placed 1.65 chords downstream of the fan tip trailing edge.

OPEN IN VIEWER

Table 1.

SDT FEGV configurations.

SDT R4, 22-blade, 11-in radius
FEGV type	FEGV count	Chord (in)	Sweep angle (deg)
Baseline (BL)	54	1.57	0
Low-count (LC)	26	3.26	0
Low-noise (LN)	26	3.26	30

OPEN IN VIEWER

Figure 1.

SDT fan stage configuration. (a) Closest modeled location of the FEGV. (b) SDT FEGV location in the experiment. From top to bottom: baseline, low-count, low-noise.

The operating conditions used in this study are three acoustic points, namely Approach (AP), Cutback (CB), and Sideline/Take-off (SL/TO). ¹⁹ They are reported in Table 2. The table also gives the stage total pressure ratios calculated from RANS simulations for the design FEGV location and when the FEGV is moved very close to the fan. Only a slight drop in pressure ratio is observed when shortening the gap. A negligible difference in thrust was also noted. While in practice, if a shorter stage were truly designed from scratch, the FEGV would most likely be created with a different stagger due to the change in inflow angle. Here though, we simply move and slightly scale the original SDT FEGV baseline geometry. The 0.5%-1% change in total pressure ratio and the very slight change in thrust were deemed close enough to allow for comparison of the acoustic outcomes from the contrived stages.

OPEN IN VIEWER

Table 2.

Operating points and baseline vane stage pressure ratios from RANS.

Operating point	Rpm	Corrected mass flow (lbm/s)	Total pressure ratio Δx/c tip = −1.25	Total pressure ratio Δx/c tip = 0
Approach (AP, 61.7%)	7809	58.3	1.152	1.156
Cutback (CB, 87.5%)	11,075	83.91	1.343	1.350
Sideline (SL, 100%)	12,657	97.18	1.479	1.495

Analytical methods

The broadband noise analysis presented in this paper focuses solely on the interaction noise produced by the interaction of the fan-wake turbulence with the FEGV. The predictions from two low-order cascade models are compared: (1) the BU-RSI model that is based on Ventres’ cascade response function and uses duct mode propagation via the Green’s method, and (2) the OptiSound/Hanson’s model that is based on Glegg’s cascade response function and uses free-field propagation.

RANS data extraction

The wake flow parameters downstream of the fan are simulated using the UTCFD code, ²³ by solving the steady RANS equations (k − ω turbulence model) in a rotating frame of reference. The flow parameters are extracted from the RANS solution at the location where the leading edge of the FEGV would be. It is noted though that this method ignores any potential field effects that the FEGV's presence has on the fan wake. This method has been employed in previous work. The grid and the computational method are described in Li et al. ²⁴

Figure 4 depicts the downstream duct geometry as well as the circumferentially averaged flow fields for the SDT configuration at the Approach condition. The horizontal axis represents the nondimensional relative FEGV location. The vertical axis represents the nondimensional radius. The duct area slightly pinches as the distance from the fan increases. This pinching effect becomes much greater beyond the design FEGV location, which leads to a notable axial flow acceleration. This is captured in Figure 4(a).OPEN IN VIEWER

Isotropic turbulence is assumed, and the turbulent velocity fluctuation u′ is equal to 2 3 T K E . Circumferentially averaged inputs are used. Note that obtaining the average u′ using the circumferentially averaged TKE can be considerably different than calculating the isotropic u′ at every circumferential point then averaging as discussed in Li et al. ¹⁰ The former averaging approach is used in this study. The circumferentially averaged u′ at the Approach speed is plotted in Figure 4(c). A high u′ near the shroud is observed due to a combination of tip separation and leakage which decays as the wake evolves downstream.

The k − ω-based turbulence length scale, Λ _k , is estimated by Pope’s ²⁵ formula, 0.43 T K E 0.09 ω , where ω is the turbulence dissipation rate from the RANS k − ω model. Again, averaging over a passage can be done in different ways. Here Λ _k is found using Pope’s formula at every point, then the averaged Λ _k is computed. Figure 4(d) shows the averaged Λ _k and how it expands as the wake evolves.

The turbulent kinetic energy and turbulence length scale on a passage extracted at the constant axial location of Δx/c _tip = 0 are shown in Figure 5. In Hanson’s model, when turbulence inhomogeneity across the passage is included, the turbulence intensity is modeled via the Gaussian function. This is done by fitting the computed passage TKE to the expected form:

T K E ( r , θ ) = T K E b ( r ) + T K E w ( r ) e − θ 2 σ 2

(1)

OPEN IN VIEWER

Figure 5.

Turbulent kinetic energy and length scale passage fields at the Approach condition and design location. (a)TKE (b)Λ.

OPEN IN VIEWER

Figure 6.

Inhomogeneous wake modeling. Design location mid-span shown.

Likewise, the passage turbulence length scale can be either represented by a homogeneous value or separated into wake and background components. Figure 5(b) shows the Λ _k passage slice. The fully averaged value at midspan is shown as the orange line in Figure 6(b). For the discriminate-average method, two averages are computed as in Leonard et al. ²⁶ The vertical dashed lines in Figure 6 denote the threshold determined by the 20% Gaussian amplitude. Figure 6(b) shows passage Λ _k where the background and wake averaged Λ _k are represented by the shaded values. However, the Gaussian function is unsuitable at certain locations where the wake is not well-defined, such as near the shroud and hub as shown in Figure 5(a). The discriminate approach therefore is only being applied at radial locations where the passage TKE can be fit by a Gaussian function. The cut-off criteria are determined by the Gaussian fitting error as well as the ratio between the TKE _b and TKE _w to avoid locations where the wake is contaminated by the wall boundary layer and tip vortices.

Effect of modeling passage-wise inhomogeneous turbulence

As discussed in the previous section, Hanson’s method models passage-wise inhomogeneous wake flow, though one could also use it to model locally homogeneous wake flow by defining just background turbulence parameters. Figure 7 shows the predicted broadband noise for the SDT baseline vane configuration at the Approach condition fan speed when the fan wake is modeled in different ways. The homogeneous method is plotted as the solid line (uniform), and the two inhomogeneous methods described above are plotted as dashed and dotted lines. The largest difference is attributed to modeling the u′ as inhomogeneous on the passage (difference between solid and dotted lines). It leads to a slight tilt in the sound power spectra. Typically, the tilt is attributed to the turbulence length scale. However, here, the different wake and background turbulence intensities influence the upwash velocity spectra in a way that also tilts the spectrum.OPEN IN VIEWER

The influence of modeling passage-wise inhomogeneity of the turbulence intensity depends on the wake width. A thinner wake width leads to a larger impact on the result. This effect can be better seen in two ways. First, the wake at the Sideline condition is much thinner than at the Approach condition. The results for the Sideline condition in Figure 8(b) can be compared to the results for the Approach condition in Figure 7. For the Sideline condition, it is easily seen that there is a large difference between the time-averaged turbulence intensity case and the Gaussian distribution case (solid vs dotted lines). Second, the fan wake is thinner nearer the fan. Figure 8(a) shows the results when the SDT FEGV is moved upstream towards the fan (solid and dotted lines). Comparing Figure 8(a) & (b) shows that there is a larger difference in PWL between the different methods when the FEGVs are positioned closer to the fan.OPEN IN VIEWER

Effect of turbulence length scale estimation methods

In the previous section, the influence of allowing the turbulence length scale to vary between the background and wake center values was shown to have insignificant impact as seen in the dashed and dotted lines in Figures 7 and 8. In this section, the effect of using a completely different method to estimate the length scale is investigated. The first method was described above and uses time-averaged turbulence kinetic energy and dissipation rate from the RANS simulation, Λ k = 0.43 T K E 0.09 ω . Alternatively, the turbulence length scale can be obtained from the wake width. Here the wake width is computed using L w = 2 2 l n 2 σ where σ is the Gaussian standard deviation. An empirical relationship suggested by Jurdic ²⁷ Λ _w = 0.21L _w is used to estimate the length scale. The measured length scale was obtained by hot-wire data using velocity cross-correlation method:

Λ i = U ∫ 0 ∞ u i ' ( t ) u i ' ( t + τ ) u i ' 2 d τ ,

(2)

OPEN IN VIEWER

Figure 9.

Comparison of turbulence length scale estimation methods. Approach condition at Δx/c _tip = 0 showed.

The predictions when using different length scale definitions are shown in Figure 10 for the (a) Approach and the (b) Sideline conditions. Both models show that the wake width method for defining the length scale, Λ _w , leads to higher sound power predictions at low frequencies and slightly lower sound power predictions at high frequencies. The trend agrees with what was presented by Leonard et al. ²⁶ and Lewis et al. ²⁸ Figure 9 includes the experimentally measured spectra. Based on the experimental data, both methods seem to predict reasonable length scales. A drawback to the k − ω-based method is that Λ _k is highly dependent on the RANS turbulence model. A good demonstration of this point can be found in the ACAT1 benchmark summary, ²⁹ which shows that the Menter SST k − ω model typically predicts lower length scale compared to the Wilcox k − ω model. The difference between acoustic predictions using Λ _w and Λ _k , shown in Figure 10, is mainly driven by the length scale near the tip, where the wake shape is not well-defined due to tip vortices, leading to a larger Λ _w estimation. It is also questionable whether or not Jurdic’s empirical model is applicable in the tip region. Therefore, in this work where we have a reliable Wilcox k − ω model, we chose to use the k − ω-based method.OPEN IN VIEWER

Figure 10 shows the predictions from both the Hanson and BU-RSI methods when using different length scale determination methods, together with the experiment-measured stage exhaust sound power. Interestingly, Hanson’s method appears to predict the Approach condition well, while the BU-RSI method predicts the Sideline condition well. As expected, the RSI model predicts lower power compared to Hanson’s model at low frequency because very few annular modes are cut-on. However, the difference between the two models at high frequencies is still under investigation.

Effect of vane sweep

The influence of sweep on broadband noise can be broken down into two components: (1) The effect of mean flow at the leading edge and (2) the vane response due to a skewed gust. The difference in mean flow is being discussed first. The inputs used for the acoustic models are extracted from the CFD solutions along the vane leading edge at the design location (Δx/c _tip = 0). Figure 11 shows that the longer distance between the swept vane LE and the fan results in a slight decay in the circumferentially averaged turbulence intensity (f) and expanded turbulence length scale (i). The swept vane extends further downstream where the axial mean flow (a) accelerates due to the pinched duct geometry.OPEN IN VIEWER

The results for the power spectrum computed using the BU-RSI and Hanson’s method for three characteristic operating conditions and the LC (blue) and LN (cyan) vanes are shown in Figure 12. If one just changes the inflow to reflect the change in the wake flow along the leading of the FEGV, but treats the vane as a straight vane in the model, one would obtain broadband noise predictions shown as the black dashed lines in Figure 12. An argument for such a calculation is the fact that the turbulence is supposed to be decorrelated from strip to strip and so each cascade could be seen to act similarly whether it was part of a straight or swept vane. Comparing the black line to the red line, which gives the results for a straight FEGV with the wake flow along its actual leading edge, one sees the inflow difference leads to higher broadband noise with the swept vane inputs. This does not reflect the experimental results.OPEN IN VIEWER

Fully modeling the swept FEGV however, leads to the more physical prediction of a slightly lower broadband noise level represented as the black solid line. The difference seen with the Hanson model, which adopts Glegg’s coordinate system as shown in Figure 3, comes from the reduction in the chordwise mean velocity component and the effective chord length together with the addition of the spanwise flow component and wavenumber. The BU-RSI model utilizes the same rotated coordinate system (see Appendix) such that sweep transforms the effective chordwise wave number and the range of spanwise wavenumbers that can radiate but does not directly utilize the spanwise flow component to redefine the effective frequency.

For the cutback and sideline fan speeds, the predictions and experimental data diverge below 4 kHz. Others have shown that interaction noise generated by the rig support pylon is significant ³⁰ at lower frequency especially for higher fan speeds. In addition, the ACAT1 benchmark study ⁸ also reported that analytical interaction noise models typically underpredict sound power level at low frequencies because the experimental measurement often includes low frequency noise sources that are not modeled. It is believed that the notable discrepancy between measured and predicted spectra under 3 kHz in Figure 12(c)-(f) as well as Figure 10(b) is at least somewhat attributed to the rig noise contamination in the experiment.

Effect of vane placement

Previously, researchers analyzed the ACAT1 fan stage as it pertains to FEGV placement. It was found that moving the FEGV closer to the fan did not result in a large noise penalty. Behn and Tapken ⁶ pointed out that moving the FEGV closer to the fan produces slightly higher noise levels at high frequency and lower levels at low frequency. The difference across the spectrum was less than 2 dB. This effect was corroborated by Blázquez and Corral. ³¹ The low-order BU-RSI method was used in a preliminary investigation of this effect in Li et al. ¹⁰ In this section, we aim to present a more comprehensive study of this topic.

The hub and tip radii in the acoustic models are defined by the duct geometry where the FEGV leading edge is placed. This implies that the annulus geometry defined in the acoustic model changes slightly as the FEGV placement moves. In the swept FEGV cases, the outer annular radius is defined by the duct radius at a slightly further axial location compared to the straight FEGV placed at the same hub location. The effect of these slight FEGV spanwise length differences on the final acoustic outcomes have been shown to be quite small. ⁷

Specific normalized locations downstream of the fan at which the FEGV might be placed are selected. They represent three shorter interstage cases compared to the original SDT. At each location, the wake flow parameters along the leading edge of the BL or LC and along the swept leading edge of the LN FEGVs are shown as line plots in Figure 13.OPEN IN VIEWER

Again, the inputs (a), (b), (f), (i) are used when the inflow is modeled as locally homogeneous, and (a), (b), (c), (d), (e), (g), (h) are used when the Gaussian wake model is used. The line plots highlight the increase in axial velocity and turbulence length scale and a slight decay in turbulence intensity, with increased distance from the fan. For the Gaussian wake model, the decay in turbulence intensity occurs mostly in the wake amplitude while the background remains largely the same. Notably, the flow acceleration is much greater along the swept LN vane leading edge compared to the straight BL/LC vane leading edge, because part of the LN vane extends further into the region where the duct area shrinks at a steeper rate.

In Figure 14, the effect of vane placement on the downstream noise spectrum is shown for the BL vane as predicted by the different methods. The main influence on the acoustic prediction, as the location changes, comes from the turbulence length scale, which is responsible for the tilt of the spectrum. A larger length scale increases the low-frequency noise and decreases the high-frequency noise. Both models using Λ _k show consistent trends. The wake width L _w expands at a similar rate to the circumferentially averaged Λ _k . As discussed in Section Effect of turbulence length scale estimation methods, determining L _w near the tip is quite challenging, and the predictions using Λ _w lead to different trends in the spectral shapes. It is reiterated that Λ _k provides a more consistent length scale estimation.OPEN IN VIEWER

The results predicted using Λ _k are in qualitatively good agreement with the experimentally measured spectra for ACAT1 using short and long gap configurations as reported in Behn and Tapken, ⁶ where placing the vane further from the fan increases the low frequency noise, and decreases the high frequency noise. Using Hanson’s model, with the wake turbulence treated as homogeneous or inhomogeneous leads to very similar trends. Quantitatively, the discriminate-averaged length scale approach leads to slightly shifted trends at higher frequency. This trend is more noticeable for the Sideline condition.

The noise prediction for the Approach operating point is shown in a slightly different way in Figure 15. Here, the spectra obtained when the FEGV is placed at different axial locations are compared to the spectrum at the design FEGV location. Hence the colormap depicts a Δ of the sound power spectrum compared to the spectrum when the FEGV is at Δx/c _tip = 0. The BU-RSI model and Hanson’s model using the Gaussian wake and discriminate averaged Λ _k are being compared. Hanson’s model shows a smoother result compared to the BU-RSI model due to the absence of duct singularity issues. Both models show similar trends qualitatively. When the interstage gap is shorter than the design gap, i.e. Δx/c _tip < 0, the low frequency noise decreases and the high frequency noise increases. For the longer gap, i.e. Δx/c _tip > 0, both models show the noise increases, especially at low frequency. Quantitatively, the BU-RSI model shows slightly less increase for a shorter gap at high frequency. This is tied to the difference in how the inflow mean velocity affects the prediction from each model, as discussed in a previous study. ¹⁰ OPEN IN VIEWER

The overall sound power level (OAPWL) is calculated by integrating the spectrum up to 20 kHz. Figure 16 shows the predictions for the SDT BL vane from the BU-RSI model and Hanson’s model, using a Gaussian wake with discriminate averaged Λ _k . Both models predict that the OAPWL change is basically less than 1 dB as the vane placement changes. Hanson’s model predicts overall lower OAPWL compared to the BU-RSI model. The difference in OAPWL, ΔOAPWL, referenced by the design location is depicted in Figure 17. At the Approach condition, the BU-RSI predicted values show that the OAPWL barely changes from Δx/c _tip = −0.4 to 0, while Hanson’s model shows a slight decrease in OAPWL with distance of the FEGV from the fan. In this region the duct area change is small. Beyond the design location, Δx/c _tip > 0, the duct area reduces rapidly and both models show an increase in OAPWL with distance due to flow acceleration. Modeling the inhomogeneous wake turbulence intensity has a rather small effect on ΔOAPWL at the Approach condition. At the Sideline condition, a Gaussian modeled wake with discriminate averaged length scale used in Hanson’s model leads to a slightly larger difference in ΔOAPWL compared to the other inflow definition options.OPEN IN VIEWER

OPEN IN VIEWER

Figure 17.

ΔOAPWL using baseline vane at Approach speed. Black: BU-RSI model, blue: Hanson model with homogeneous turbulence, blue-dashed: Hanson model using Gaussian turbulence with discriminate averaged Λ, blue-dotted: Hanson model using Gaussian turbulence with fully averaged Λ.

Figure 18 shows the predicted spectrum for the LC and LN FEGVs placed at the same axial locations. Results for the Approach operating condition are shown, and the methods being compared are the BU-RSI model with Λ _k , and the Hanson’s model with Gaussian modeled wake and discriminate averaged Λ _k . The same tilting in the spectrum with increasing axial distance is seen for both models. The trends show that the spectral shapes produced by the LC vane are rather similar to those produced by the BL vane. The LN vane on the other hand exhibits less tilting. This is mainly attributed to the turbulent length scale at the vane leading edge. At the position closest to the fan, the length scale is small along most of the span and increases steeply near the shroud. Along the swept FEGV, the vane leading edge extends further downstream where the turbulent flow from the tip leakage is more developed such that the length scale expands at a slower rate. This tilts the spectrum for the LN vane less as compared to the LC vane spectrum. However, the change in the axial velocity is slightly greater for the LN vane when shifting from the design location to 1.25 chord lengths upstream. These effects are seen in Figures 4 and 13. This leads to smaller spectral changes for the LN FEGV as it moves towards the fan. The BU-RSI predicts that, as both the LC and LN vanes are moved closer to the fan, the OAPWL decreases slightly, while Hanson’s model predicts a slight increase for the LC vane and a slight decrease for the LN vane.OPEN IN VIEWER

The OAPWL for LN and LC vanes are shown in Figure 19. The LN vane is only investigated up to the design location due to the simulation domain. Similar to the LC and BL vanes, both models show that the broadband OAPWL predicted using the swept LN vane is not strongly affected by the vane placement. Also Hanson’s model tends to predict lower overall sound power compared to BU-RSI. For the LC vane, the difference between the two models increases with speed, whereas the LN vane shows similar differences between the two models across the three operating conditions.OPEN IN VIEWER

In Figure 20, the trends are compared across all three vane types at the Approach condition. Again, the BU-RSI is being compared to Hanson’s model with a Gaussian modeled wake and discriminate averaged Λ _k . Hanson’s model shows that the BL vane case changes the most in the region Δx/c _tip = −1.25 to 0, while BU-RSI shows that the LN vane changes the most. All of the changes however are within roughly |1 dB|.OPEN IN VIEWER

Hanson’s model shows slightly more decrease in OAPWL from Δx/c _tip = −1.25 to 0, and both models show that the LC vane has slightly lower Δ in this region. The trend of the swept LN vane is quite different from the BL and LC vanes, due to the leading edge location, which extends much further downstream such that the LN vane experiences less change in turbulence length scale and more flow acceleration.