# Delayed Detached-Eddy Simulation and Particle Image Velocimetry Investigation of S-Duct Flow Distortion

## Summary (5 min read)

### Introduction

- Delayed Detached-Eddy Simulation and Particle Image Velocimetry Investigation of S-Duct Flow Distortion Daniel Gil-Prieto,∗David G.MacManus,† Pavlos K. Zachos,‡Geoffrey Tanguy,§ FrançoisWilson,¶ and Nicola Chiereghin¶ Cranfield University, Cranfield, England MK43 0AL, United Kingdom DOI: 10.2514/1.J055468.
- The flowfieldmechanisms responsible for the main perturbations at the duct outlet are identified.
- Complex intake configurations promote high levels of dynamic total pressure and swirl distortion, which can adversely affect the engine stability [3].
- §Ph.D. Student, Propulsion Engineering Centre, Building 52.
- The switching mode promoted the swirl-switching mechanism, by which one of the Dean vortices observed in the mean flow alternately dominates the flowfield [17].

### A. Studied Case

- The S-duct geometry is a scaled-down version of the geometry investigated by Garnier [13].
- The S-duct has a circular cross section, and the main geometrical parameters are an area ratio ofAR 1.52, an axial length of L∕Din 4.95, a centerline offset ofH∕L 0.50, and an outlet diameter of Dout 150 mm (Fig. 1).
- The S-duct centerline is composed of two consecutive 52 deg arcs with curvature ratios Rin∕Rc of γ 0.16.
- The flow condition is determined by the Mach number at the reference plane, which is located 0.9Din upstream of the S-duct inlet.
- The computational and experimental results presented in thiswork correspond to a referenceMach number of Mref 0.27, which is associated with a ReD 7.1 × 105.

### B. Stereo Particle Image Velocimetry Experiment

- A detailed description of the experimental facility is reported by Zachos et al. [14], and only the key aspects of the experiment are reported here.
- The rig is calibrated to provide the requiredMach number at the reference plane (0.9Din upstream of the S-duct inlet).
- The laser light sheet was delivered by an articulated light arm, which provides a light sheet with a thickness of approximately 2 mm.
- TSI Insight 4G software was used for the calibration of the cameras, the acquisition, and the processing of the images.
- The overall uncertainty was approximately 6 and 8% for the in-plane and out-of-plane components of the velocity, respectively.

### C. Delayed Detached-Eddy Simulation

- The numerical computation is performed using a detached-eddy simulation (DES), for which the unsteady Reynolds-averaged Navier–Stokes equations are applied in the boundary layer, whereas the large-eddy simulation (LES) method is employed in the highly unsteady regions away from the wall [21].
- This profile could not be applied directly as the inlet boundary condition for the computational domain because this region was affected by the pressure gradient established in the first bend of the S-duct.
- For the mesh used in this investigation, the determinant 2 × 2 × 2 was greater than 0.83 over the domain, which indicates a good quality mesh.
- The corresponding values of SIstd were 1.9, 1.9, and 1.5 deg, whereas for SImax, the values were 17.5, 16.8, and 15.7 deg.
- The impact of the time-step choice was also assessed atMref 0.60, and the DDES simulation with the medium mesh was computed at a doubled time step of Δt 1.2 × 10−5 s, which equates to Δt∕tc 3.72 × 10−3.

### D. Proper Orthogonal Decomposition

- Turbulent flows are characterized by the presence of coherent structures that are obscured by small-scale turbulent fluctuations.
- Therefore, ai t represents the instantaneous weight of each flow feature at the different instants of time.
- The temporal coefficients are uncorrelated to each other, so that the different flow features described by the POD modes occur uncorrelated in time [26].
- Themodes are then ordered by the associated hKEi contribution.
- This permits an optimum representation in terms of kinetic energy in the sense that, for a given number of terms in the series, the POD maximizes the kinetic energy content in the reconstruction [Eq. (2)] [28].

### A. Experimental Validation

- The mean velocity field for the DDES solution is compared with the SPIV results at the same inlet Mach number of Mref 0.27 (Fig. 4).
- The DDES also predicts a pair of regions of high lateral velocity near the wall at the top of the AIP (Fig. 4c), which results in a secondary pair of vortices (Fig. 4d).
- The maximum values are σu∕h wAIPi 0.28 and 0.22 for DDES and SPIV, respectively.
- To quantify the discrepancies between the DDES and SPIV results in terms of fluctuating flowfield, the profile of the standard deviation of the three components of the velocity is compared along the symmetry axis of the AIP (Fig. 5).
- Therefore, the instantaneous SI predicted in the DDES solution shows similar mean and peak values as well as similar probability distributions as indicated by the standard deviation, skewness, and kurtosis, compared to the SPIV measurements.

### B. Coherent Structures at the Aerodynamic Interface Plane

- POD [26] is applied to the three-component velocity vector at the AIP for both the DDES and SPIV data.
- For a consistent comparison, the DDES solution is linearly interpolated using the Delaunay triangulation method into the loci of the SPIV data points before the POD computation.
- The POD permits the identification of the flow coherent structures.
- The temporal coefficients associated with the higher modes oscillate around the null mean value.
- Therefore, the PODmodes are ordered by hTKEi content.

### 1. Delayed Detached-Eddy Simulation and Stereo Particle Image Velocimetry Coherent Structures

- The fourmost-energetic coherent structures for the streamwise and in-planevelocity fields as predicted byDDESare similar compared to SPIV data (Fig. 7).
- This inplane velocity perturbation is associated with a circumferential oscillation of the low-streamwise-velocity region that follows the swirl switching (Figs. 8a and 8b).
- When aFVM t is positive, the pair of vortices becomes stronger and moves into a more centered position in the AIP (Fig. 8g).
- The effect of this perturbation is to modulate the streamwise velocity distortion between the high- and low-streamwise-velocity regions.
- In contrast, the DDES underpredicts the energetic content of the first vertical mode (FVM) and second vertical mode (SVM), which show values of 0.76 and 0.38%, respectively, compared to the 0.93 and 0.46% obtained for the SPIV data.

### 2. Spectral Analysis

- The DDES simulations are time-resolved and therefore can be used to further develop the understanding of the temporally underresolved SPIV results through a spectral analysis of the POD temporal coefficients (Fig. 9).
- The FVM and SVM show a more broadband spectrum, even though a distinct peak can be identified around 1.06 (Figs. 9b and 9d).
- The POD analysis of the velocity field at the AIP has identified the main coherent structures that are responsible formost of the flowfield unsteadiness.
- In addition, the unsteady swirl distortion pattern deviates from the well-known symmetric vortex pair, and multiswirl structures as well as single rotating cells are promoted [16].
- The design of an efficient flow control system depends on a good understanding of the origin of the AIP perturbations upon which the flow control device has to act.

### C. Symmetry Plane Flowfield

- The mean flow at the symmetry plane is characterized by the presence of a separated flow region at the inner bend, as indicated by the reversed flow (Fig. 10a).
- The mean position of the separation and reattachment points corresponds to saddle points, where the wall shear stress is null [33].
- The separation bubble length is slightly underpredicted by the DDES solution compared to the experimental value of 1.95Din.
- The computed mean vertical velocity field shows positive values near the lower wall, which is associated with the presence of the symmetric vortices (Fig. 10c).
- Fluctuations as high as σv∕h wAIPi 0.36 are also observed for the vertical velocity field downstream of the separation bubble (Fig. 10d), at the region where the mean-flow shear layer is located (Fig. 10a).

### D. Multiplane Proper Orthogonal Decomposition

- POD is applied to the three-component velocity vector at the AIP and symmetry plane simultaneously.
- This multiplane POD permits the identification of coherent structures at the AIP and their relationship with the upstream flowfield.
- Therefore, this technique establishes a link between the upstream flow and the perturbations at the AIP.
- To the authors’ knowledge, this is the first attempt to relate AIP and symmetry plane flow characteristics using POD in S-duct research.
- Because this multiplane POD is now based on the hTKEi of both the AIP and the symmetry plane, a change in the modal distributions could be expected relative to the case where only the AIP was considered (Sec. III.B).

### 1. Swirl Switching

- The first switching mode (FSM) does not show any perturbations either in the vertical or streamwise velocity components at the symmetry plane.
- The FSM shows a series of alternate positive and negative lateral velocity regions along the symmetry plane, which are tilted by about 25–30 deg relative to the streamwise axis.
- This indicates the dominance of one of the two secondary flow vortices, which migrate toward a more central position in the cross section, whereas the other vortex is confined to the opposite wall, as observed in Sec. III.
- This perturbation shows the same periodic behavior at St 0.53 as the FSM (Fig. 11f).
- The swirl switching is accompanied by a lateral oscillation of the low-streamwisevelocity region (Figs. 13a, 13d, 13g, 13j, and 13m).

### 2. Shear-Layer Oscillations

- The AIP perturbation promoted by the first vertical mode (FVM) of the multiplane POD (Fig. 12a) is similar to that obtained with the POD applied just at the AIP (Fig. 7e), even though in the multiplane POD the central region of the modal shape is more spread vertically.
- The vortex shedding occurs mainly at a frequency of about St 1.06 (Fig. 12i), which is exactly twice the value for the swirl-switching mechanism (Figs. 11e and 11f).
- The AIP perturbation associated with the SVM (Fig. 12b) is similar to that obtained when only the AIP was considered (Fig. 7d).
- Therefore, the AIP perturbations represented by the FVM and SVM are promoted by the same flow mechanism, which is the roll-up of alternating D ow nl oa de d by C ra nf ie ld U ni ve rs ity ( A K A D E FE N C E A C A D E M Y O F T H E U K ) on A pr il 10 , 2 01 7 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /1 .J 05 54 68 spanwise vortices through the shear layer.
- D ow nl oa de d by C ra nf ie ld U ni ve rs ity ( A K A D E FE N C E A C A D E M Y O F T H E U K ) on A pr il 10 , 2 01 7 | h ttp :// ar c. ai aa .o rg | D O I: 1 0. 25 14 /1 .J 05 54 68.

### IV. Conclusions

- The unsteady flowfield in an S-duct with a centerline offset of H∕L 0.50, area ratio ofAR 1.52, and lengthL∕Din 4.95 has been simulated atMref 0.27 andReD 7.1 × 105 using a delayed detached-eddy simulation (DDES) approach.
- Very good agreement has been found between computational and Fig. 13 FVM and SVM of the combined AIP and symmetry plane velocity field POD (DDES,Mref 0.27).
- Therefore, the capability ofDDES simulations to capture the main unsteady characteristics of flows within S-duct intakes has been demonstrated.
- The streamwise vortices are then convected downstream and promote a swirl-switching oscillation in the AIP velocity field.
- The identification of the source of theAIP perturbations may facilitate the design of more efficient flow control systems.

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##### Citations

18 citations

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...The use of proper orthogonal decomposition (POD) applied to the S-PIV measured velocity data [9] and unsteady CFD simulations [19] revealed that the velocity flow field unsteadiness was dominated by the swirl switching mechanism [28]....

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...Previous Stereoscopic Particle Image Velocimetry (PIV) and CFD analysis [9][19] found that the unsteady distortion characteristics of the velocity field were associated with different flow modes....

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...Duct B was also evaluated through steady and unsteady CFD simulations [11,19] as well as with S-PIV measurements [8,9]....

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^{1}, Pavlos K. Zachos

^{1}, David G. MacManus

^{1}, Grant McLelland

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16 citations

^{1}, David G. MacManus

^{1}, Pavlos K. Zachos

^{1}, Abian Bautista

^{1}•Institutions (1)

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...3° for the fine, medium and coarse meshes, respectively, and similar results were obtained for std(S?̅?) and max(S?̅?) [29]....

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...[29], and the time-averaged and fluctuating velocity fields at the AIP are only briefly described in this section for completeness....

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...22, for DDES and SPIV, respectively [29]....

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...9Din upstream of the S-Duct inlet plane was matched in the DDES [29]....

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...2 Flow field statistics at the AIP for DDES (top) and SPIV (bottom), including the time-averaged w-velocity (left), timeaveraged swirl angle (centre) and standard-deviation of the w-velocity (right) [29]...

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