8th International ERCOFTAC Symposium on Engineering Turbulence Modelling and Measurements June 9-11, 2010, Marseille, France

LES OF HIGH-REYNOLDS-NUMBER COANDA FLOW SEPARATING FROM A ROUNDED TRAILING EDGE OF A CIRCULATION CONTROL AIRFOIL Takafumi Nishino1, Seonghyeon Hahn2,* and Karim Shariff1 1

2

NASA Ames Research Center, Moffett Field, CA 94035, USA Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA [email protected] ; [email protected]

Abstract A recent LES study of flow around a circulation control airfoil (Nishino et al., AIAA Paper 2010-347) is further extended, with a particular focus on the characteristics of a Coanda wall jet separating from a rounded trailing edge of the airfoil. A number of backward-tilted hairpin vortices are observed in the outer shear layer of the wall jet; these hairpins create a strong upwash between their legs and thereby lift the high-momentum jet flow below the hairpins upward. The LES results are then compared with 2D RANS simulations employing the Spalart-Allmaras model and Menter’s SST model. The Reynolds shear stresses predicted by the two models are both found to be too small in the outer shear layer of the wall jet, resulting in smaller jet spreading rates, larger peak jet velocities, and hence stronger circulations around the airfoil compared with the LES.

1

Introduction

Separation of turbulent flows over a curved surface is important in many engineering applications, and yet is difficult to accurately predict using existing RANS-based turbulence models. Further improvement of RANS models for separated turbulent flows is crucial, since DNS/LES of full-scale engineering applications, such as aircraft, is infeasible for the foreseeable future. In this study, we investigate the characteristics of turbulent Coanda flow separating from a rounded trailing edge of a circulation control (CC) airfoil by using LES. The concept of CC is to increase aerodynamic circulation around the airfoil by applying a Coanda wall jet blowing over the rounded trailing edge, thereby enhancing the lift for short-distance takeoff and landing (see, e.g., Englar, 2000). It is known that the separation location of the Coanda jet, which is critical to the performance of CC devices, is difficult to predict by using existing RANS models (Swanson and Rumsey, 2009). Recent LES studies of flow around a CC airfoil (Slomski et al., 2006; Hahn and Shariff, 2008) have shown that it is not trivial even for LES to obtain a *

solution that agrees well with wind tunnel tests. Two major issues are: (i) wind tunnel wall effects, which are of particular importance in high jet-blowing cases, and (ii) the locations of laminar-to-turbulent transition. More recently, a new set of wind tunnel tests of a CC airfoil was initiated at NASA Langley (Jones et al., 2008), and our research team at NASA Ames performed LES of the same flow configuration, including the top and bottom walls of the wind tunnel (as inviscid walls) as well as a transition strip attached on the airfoil near the leading edge (Nishino et al., 2010). The LES results agreed well with the wind tunnel tests (for a relatively low jet-blowing but still challenging case), providing a useful dataset for the improvement of existing RANS models especially for the separation of turbulent wall jets. In this paper, we further report the results of our LES with a particular focus on the characteristics of the turbulent Coanda jet. Two-dimensional RANS simulations of the same flow configuration are also performed to be compared with the LES.

2

Flow Configuration

Figure 1 describes the geometry of the CC airfoil investigated in this study. The airfoil was designed by Dr. Englar's research group at Georgia Tech Research Institute (GTRI), and is also being tested in the Basic Aerodynamics Research Tunnel (BART) at NASA Langley (Jones et al., 2008). This non-cambered CC airfoil has two independent Coanda jet slots, one each on the upper and lower sides of the semi-circular trailing edge; however the lower jet slot is not used (i.e., closed) in the present study. The airfoil chord, c, is 218.3 mm, the trailing-edge radius, r, is 0.09463c (20.66 mm), the upper jet-slot height, h, is 0.02433r (0.503 mm), and the thickness of the jet-slot blade, b, is 0.01229r (0.254 mm). Note that a wavy transition strip is attached on the airfoil lower surface near the leading edge; see Nishino et al. (2010) for details. Figure 2 shows the computational domain for the present study. As mentioned in the introduction, our LES (and also RANS simulations) include the top and bottom walls of the wind tunnel. The airfoil is located

Current Address: Vestas Wind Systems A/S, Alsvej 21, 8940 Randers SV, Denmark

Figure 1: Geometry of the CC airfoil investigated. 3.62c downstream of the inlet of the test section at zero-degrees angle-of-attack, following the wind tunnel tests at NASA Langley. In the wind tunnel tests, this airfoil model spans the entire test section 3.26c wide, whereas the LES is performed only for a narrow mid-span region 0.0641c wide (14.0 mm, which is twice the “wavelength” of the wavy transition strip). Note, however, that this “narrow” spanwise domain size is still sufficiently large to capture the development of turbulent coherent structures for the Coanda jet flow, as will be shown later in Fig. 7.

3

Numerical Methods

The LES was performed using CDP, an incompressible Navier-Stokes code developed at the Center for Turbulence Research (CTR) at Stanford University (Ham and Iaccarino, 2004). The code employs a finite-volume scheme to spatially discretize the continuity and Navier-Stokes equations with second order accuracy, and a second order fully implicit scheme for the time integration. Subgrid-scale (SGS) stresses are modelled using the dynamic Smagorinsky model. The 2D RANS simulations to be compared with the LES were performed using SUmb, a compressible Navier-Stokes code developed at CTR (van der Weide et al., 2006). The code uses a finite-volume scheme, which spatially discretizes the compressible RANS, energy, and turbulence model equations with second order accuracy. The Spalart-Allmaras (S-A) model (Spalart and Allmaras, 1994) and the SST model of Menter (Menter, 1994) are used in this study. Figure 3 shows a snapshot of the computational mesh used in this study. Although CDP supports the use of unstructured meshes to easily handle complex geometries, the present study uses a block-structured mesh consisting of only hexahedral cells. For the semi-circular Coanda surface, 800 grid points are al-

Figure 2: Computational domain.

located in the tangential direction, 640 of which are equidistantly distributed at θ = 10 to 170 (θ is the clockwise angle from the upper jet exit) and the other 160 points are clustered at θ = 0 to 10 and 170 to 180 (80 points each). The wall-normal resolution is fine enough to resolve the viscous sublayer. For the spanwise direction, 256 grid points are equidistantly allocated over the 0.0641c (or 27.8h) wide domain. The total number of grid points is about 116 million. The subgrid-scale eddy viscosity in the LES is up to about 5 times larger than the molecular viscosity in the Coanda jet region, where the eddy viscosity in the 2D RANS simulations is about 40 to 50 times larger than the molecular viscosity. For the LES, no-slip conditions are applied at the airfoil surface, whereas slip (i.e., inviscid) conditions are used for the top and bottom walls of the wind tunnel. A uniform streamwise velocity of U∞ = 34 m/s is applied at the inlet boundary of the domain, resulting in the freestream Reynolds number of 0.49 million based on c. Also, the volume flow rate of the jet is set at 7.4210-4 m3/s, which results in a “peak” jet-exit velocity (i.e., the maximum of the time-averaged jet velocity profile at the jet exit) Uj,max = 134.5 m/s and a jet Reynolds number of about 4500 based on h. See Nishino et al. (2010) for more details. For the compressible RANS simulations, the inlet flow conditions are adjusted such that the mass flow rates (at the wind tunnel inlet and also at the jet inlet) match those in the incompressible LES, assuming that the constant air density in the incompressible LES is 1.2 kg/m3, the total temperature of the inlet air (for both the wind tunnel and the jet plenum) is 295 K, and the static pressure at the tunnel outlet is 101325 Pa.

Figure 3: Snapshot of the computational mesh.

Table 1 Summary of Coanda jet conditions and results Case Uj [m/s] Uj,max [m/s] θsep [deg.] xrec/c S-A (2D RANS, compressible) 106.7 133.2 75.0 1.058 SST (2D RANS, compressible) 106.7 132.9 69.0 1.080 LES (3D, incompressible) 105.4 134.5 69.5 1.060

xstag/c 0.0131 0.0098 0.0055

CL 1.85 1.60 1.36

θsep: jet separation angle, xrec: rear-end of recirculation bubble, xstag: front stagnation point, CL: lift coefficient

Results and Discussion

Table 1 summarises the Coanda jet conditions and results for the LES and 2D RANS. Note that the bulk jet-exit velocity (i.e., spatial mean of the time-averaged velocity profile at the jet exit) Uj is slightly higher in the compressible RANS than in the incompressible LES due to the compressibility effect, which, however, is practically negligible. Meanwhile, the peak jet-exit velocity, Uj,max, is slightly lower in the RANS than in the LES due to slightly different jet profiles; this difference, however, is also practically negligible, as will be shown later in Fig. 10. 4.1. LES Figure 4 shows contours of instantaneous streamwise velocity around the airfoil (as well as inside the jet plenum). The transition to turbulence is observed around x/c = 0.1 and 0.4 on the upper and lower sides of the airfoil, respectively; see Nishino et al. (2010) for details. The separation angle of the Coanda jet, θsep, is 69.5, which agrees well with the experimental estimate of about 70. Figure 5 shows the Cp distribution on the airfoil surface. The experimental and RANS results are also plotted here for comparison. The experimental data are those measured in the mid-span region, where the flow around the airfoil is statistically two-dimensional (except for the region around the wavy transition strip attached near the leading edge). The agreement between the LES and experiments is very good overall.

The time-averaged lift coefficient CL calculated in the LES is 1.36, which is also satisfactorily close to the experimental value of 1.31. Figure 6 shows time-averaged boundary layer profiles on the airfoil upper surface at several chordwise locations. Note that U+ is the velocity in wall units, n is the distance from the airfoil surface, and n+ is n in wall units. The flow accelerates as it moves downstream, especially near the jet exit located at x/c = 0.9054. A “universal” turbulent boundary layer profile is maintained only up to around x/c = 0.8, where the acceleration parameter K (cf. Jones and Launder, 1972) is about 1.010-6, and then the inner layer starts accelerating more than the outer layer, creating a velocity peak very close to the airfoil surface near the jet exit. Now we look at the Coanda jet flow around the rounded trailing edge. Figure 7(a) shows vortical flow structures in/around the jet, visualized by iso-surface of the second invariant of the velocity gradient tensor 2

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U/U∞

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Figure 4: Instantaneous streamwise velocity contours around the airfoil [LES].

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Figure 5: Cp distributions on the airfoil surface.

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Figure 6: Boundary layer profiles on the airfoil upper surface (top) and in wall units (bottom) [LES].

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Figure 7: Vortical flow structures over the Coanda surface, visualized by iso-surface of the second invariant of the velocity gradient tensor and coloured based on the velocity magnitude; (a) with the wind-tunnel stream, and (b) without the wind-tunnel stream, i.e., U∞ = 0. and coloured based on instantaneous velocity magnitude. It is remarkable that a number of hairpin-like structures are observed, and most of these hairpins are tilted backward to the Coanda surface, i.e., the head of each hairpin is located upstream of its legs. These backward-tilted hairpins are located in the outer shear layer of the wall jet, create a strong upwash between their legs, and thus lift the high-momentum jet flow below the hairpins upward (Nishino et al., 2010). Figure 7(b) shows the Coanda jet structures for a case without the wind-tunnel stream (i.e., U∞ = 0). A number of backward-tilted hairpins are still observed in this case, indicating that the formation of these hairpin structures is not relevant to the surrounding flow but intrinsic to the Coanda jet itself. The basic

Figure 8: Basic mechanism of the formation of a backward-tilted hairpin vortex.

mechanism of the formation of these hairpin vortices is speculated to be analogous (but opposite) to that of forward-tilted hairpin vortices observed in boundary layer flows (e.g., Adrian, 2007; Wu and Moin, 2009). The difference between the forward- and backwardtilted hairpins is the direction (sign) of the mean shear acting on the vortices; the sign of the mean shear in the outer shear layer of a wall jet is opposite to that in a boundary layer, as illustrated in Fig. 8. It is still unclear, however, if and how much the curvature of the wall, which is neglected in Fig. 8, affects the formation of the backward-tilted hairpin vortices. 4.2. Comparisons between LES and RANS As noted in the introduction, turbulent Coanda flow separating from a curved surface is known to be difficult to accurately predict using existing RANS models. For CC airfoil applications, this difficulty in RANS often results in an overprediction of the airfoil circulation and, correspondingly, an overprediction of the lift (cf. Table 1). It is therefore informative to make a detailed comparison of the Coanda flow between the LES and RANS simulations, and to figure out the main cause for the discrepancy between them. Figure 9 compares mean flow patterns around the Coanda trailing edge, depicted using streamlines together with Cp contours. It can be seen that both S-A and SST models qualitatively correctly predict the

(b)

(a)

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Figure 9: Mean streamlines and Cp contours around the Coanda trailing edge: (a) S-A, (b) SST, and (c) LES. profiles at  = 70, where the SST model successfully captures the separation of the jet but the peak velocity is still too large, whereas the S-A model predicts an even larger peak velocity (and fails to capture the jet separation). These larger peak velocities of the jet are speculated to be related to the circulation around the airfoil overpredicted by both models. Finally, Reynolds shear stress profiles around the Coanda trailing edge are shown in Fig. 11. The LES results plotted here are those “resolved” only (i.e., the subgrid-scale stress, which is less than about 10% of the total shear stress, is not included), whereas the RANS results plotted are based on the eddy viscosity and velocity gradient profiles predicted. Of interest is the discrepancy in the outer shear layer of the jet. It can be seen that both S-A and SST models give much smaller Reynolds shear stress in the outer shear layer, consistent with the smaller jet spreading rates and thus the larger peak jet velocities compared with the LES shown in Fig. 10.

flow patterns; however, neither of them agrees quantitatively well with the LES. Of particular interest is that the S-A model predicts a “correct” (i.e., comparable to the LES) recirculation bubble length behind the airfoil but with a “wrong” jet separation angle, whereas the SST model predicts a “correct” jet separation angle but with a “wrong” recirculation bubble length (cf. Table 1). These results show that neither the recirculation bubble length nor the jet separation location is solely responsible for the discrepancy of the circulation around the airfoil between the LES and RANS simulations. Figure 10 compares mean tangential velocity profiles around the Coanda trailing edge. The jet profiles predicted by the S-A and SST models are practically the same as the LES at the jet exit ( = 0), but then clearly differ from the LES downstream of the jet exit ( > 0), i.e., both S-A and SST models give smaller jet spreading rates and thus larger peak jet velocities compared with the LES. Of particular interest are the 0.02 0 deg. (jet exit)

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Figure 10: Mean tangential velocity profiles around the Coanda trailing edge.

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Figure 11: Reynolds shear stress profiles around the Coanda trailing edge.

5

Conclusions

In this paper, we extended our recent LES study of flow around a circulation control airfoil (Nishino et al., 2010) with a particular focus on the turbulent Coanda jet separating from the rounded trailing edge. A number of backward-tilted hairpin vortices were found in the outer shear layer of the jet to lift the high-momentum jet flow below the hairpins upward. These hairpins were observed even for the case without the wind-tunnel stream, indicating that their formation is intrinsic to the Coanda jet. The LES results were then compared with 2D RANS simulations using the S-A and SST models. Both models predicted a stronger circulation around the airfoil than the LES, even though the SST model correctly predicted the Coanda jet separation location (demonstrating that the jet separation location is not solely responsible for the wrong circulation predicted). The Reynolds shear stresses predicted by the two models were both found to be too small in the outer shear layer of the jet, resulting in smaller jet spreading rates and the stronger circulation induced around the airfoil. It is of great interest that the outer shear layer of the Coanda jet, where the S-A and SST models were found to give too weak turbulence, is exactly where the backward-tilted hairpin vortices were observed in the LES to enhance turbulent mixing. Further investigations into this outer shear layer of the Coanda jet would be beneficial from both turbulence physics and modelling points of view.

Acknowledgements The present work has been supported by NASA’s Fundamental Aeronautics Program (Subsonic Fixed Wing Project), and T. Nishino has been supported by the NASA Postdoctoral Program (NPP) administrated by Oak Ridge Associated Universities (ORAU).

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