Proceedings of Meetings on Acoustics

Proceedings of Meetings on Acoustics Volume 19, 2013 http://acousticalsociety.org/ ICA 2013 Montreal Montreal, Canada 2-7 June 2013 Noise Session 3aNSb: Aviaton, Aviation Engines, and Flow Noise 3aNSb3. Improved Delayed Detached Eddy Simulation modeling and far-field trailing-edge noise estimation of a sharp-edged symmetric strut Patrick Marshallsay, Laura A. Brooks, Alex Cederholm*, Con J. Doolan, Danielle J. Moreau and Cristobal Albarracin *Corresponding author's address: Deep Blue Tech, 694 Mersey Road North, Osborne, 5017, South Australia, Australia, alex.cederholm@deepbluetech.com.au This paper presents results of a Computational Fluid Dynamic (CFD) study of a sharp-edged symmetric flat strut at Reynolds number 500,000 based on chord at zero degrees angle of attack, and the subsequent estimation of far-field noise generated at the trailing-edge. Flow field results obtained using Improved Delayed Detached Eddy Simulation (IDDES) modelling and Reynolds-Averaged Navier Stokes (RANS) modelling techniques are compared with empirical wind-tunnel data. The flow is observed to be physically complex in nature, exhibiting numerical solutions that are sensitive to the mesh grid and freestream turbulence intensity. Although originally developed for use specifically with RANS-generated flow data, the RANS-based Statistical Noise Model (RSNM) technique, which estimates far-field noise from mean turbulence data via an acoustic Green's function and a statistical turbulence correlation model, is used here to estimate far-field noise spectra from both RANS and IDDES flow data. Far-field noise is also estimated from the IDDES model using the permeable surface form of the Ffowcs Williams and Hawkings (FWH) solver. The FWH estimate gives the closest match to experimental data, while the RSNM-generated noise estimate from the IDDES data appears to be more successful at capturing the large turbulent structures within the flow than the RANS data. Published by the Acoustical Society of America through the American Institute of Physics 2013 Acoustical Society of America [DOI: 10.1121/1.4800456] Received 21 Jan 2013; published 2 Jun 2013 Proceedings of Meetings on Acoustics, Vol. 19, 040070 (2013) Page 1

INTRODUCTION Stealth is critical for the safe operation of submarines and therefore their underwater radiated noise signature must be minimized. One aspect of a submarine s signature is self-noise produced from flow past the hull and various external appendages. The flow Mach number is low, and the Reynolds number is high, and hence boundary layer turbulence in the flow over submarine appendages can create a fluctuating surface pressure in the vicinity of the trailing edge, which couples into high levels of broadband noise via a trailing edge scattering mechanism [Howe, 1998; Albarracin et al., 2012a]. Submarine trailing edge noise therefore has the potential to be a significant noise source. In order to design for low submarine self-noise, it is thus important to have the capability to predict trailing edge noise of various appendage arrangements in a timely manner. In submarine concept development, multiple designs must be assessed rapidly over a range of flow conditions using tools which have been verified and validated. Trailing edge noise can be predicted using semi-empirical models such as the BPM model [Brooks et al., 1989]. These models are popular due to their computational efficiency and are relatively straightforward to apply. However, they are based on specific test cases and thus are not sufficiently accurate for design purposes when applied to more generalized geometries and flow conditions. Direct Numerical Simulation (DNS) is a fully numeric approach which uses Computational Fluid Dynamics (CFD) simulations to solve both the flow field and the resulting acoustic field directly. It is the highest-fidelity of the modeling approaches. However, it is far too computationally-demanding to use for design purposes. Another relatively high-fidelity approach uses unsteady CFD simulations such as Large Eddy Simulations (LES) to model the flow-field. This method solves for the acoustic field using the Linearized Euler Equations (LEE) or a time domain acoustic analogy such as the Ffowcs Williams and Hawkings solution to the Lighthill Equation (e.g., Wang et al. (2009)). Although significantly less computationally intensive than DNS, solution times are still greater than desirable for design purposes. Due to their ability to perform analyses in a timely manner, coupled with an acceptable level of accuracy, Reynolds-Averaged Navier-Stokes (RANS)-based methods for solving the flow field are feasible for concept design applications. The acoustic field can be estimated by analytical formulations applied to the RANS solution mean flow statistics. Commonly used acoustic formulations include Amiet s theory for trailing edge noise [Amiet, 1976] and surface pressure spectrum models (e.g., Kamruzzaman et al. (2012)). However, these methods assume homogeneous turbulence in the span-wise and chord-wise directions, conditions which may not hold in cases where the appendage geometry is non-symmetric in the span-wise direction or when there are adverse pressure gradients. In order to overcome the homogenous turbulence assumption, the RANS-based Statistical Noise Model (RSNM) has been postulated as an alternative means of calculating trailing edge noise [Albarracin et al., 2012a]. RSNM combines mean flow data with statistical turbulence models to form acoustic source terms, and then solves for the acoustic field using an analytical acoustic model [Ffowcs Williams and Hall, 1970]. RSNM has previously been used to estimate the sound radiated by the trailing edge of a sharp-edged symmetric strut [Albarracin et al., 2012b]. Comparison to experimental data showed an underestimation of the acoustic spectrum at low frequencies. One possible reason for this is that the RANS solution may struggle to accurately predict large turbulent structures present in this particular flow case. As such, higher-fidelity means for calculating the flow field are being investigated in the present paper for the sharp-edged symmetric strut. Improved Delayed Detached Eddy Simulation (IDDES) [Shur et al., 2008] is a hybrid RANS-LES (Large Eddy Simulation) model based on the original Detached Eddy Simulation (DES) formulation. A particularly appealing aspect of this model in the present application is the fact that, when stimulated by fluctuating turbulent flow in the flow field external to a boundary layer, within the boundary layer IDDES behaves as a Wall-Modeled LES (WMLES) model, as opposed to previous versions of DES, which show RANS behavior under similar circumstances. IDDES has previously been successfully applied to trailing edge noise modeling [Greschner et al., 2010]. In the present paper, IDDES is used to model the flow field and RSNM is then applied to the IDDES results. The reason for using RSNM here is to further understand and verify its abilities at predicting far-field trailing edge noise, given an accurate flow solution. The IDDES RSNM solution is compared directly to the RANS RSNM solution. For comparison purposes, the acoustic far-field solution is also estimated from the IDDES model using the permeable surface form of the Ffowcs Williams and Hawkings (FWH) solver [Ffowcs Williams and Hawkings, 1969; Lockard and Casper, 2005]. This paper is structured as follows: the test case, CFD methodologies, noise prediction methodologies and experimental data are first described. Results from the RANS-based and IDDES-based computations are then described and discussed. Finally, conclusions and scope for future work are highlighted. Proceedings of Meetings on Acoustics, Vol. 19, 040070 (2013) Page 2

METHODOLOGY Test Case The test case, which is shown schematically in Figure 1, comprises a flat plate airfoil model immersed in a freestream air flow of U = 38 m/s. The flat plate has a 200 mm chord, a 450 mm span, and a 5 mm thickness. Its leading edge is semi-circular and the trailing edge is a symmetric wedge shape with an included angle of 12. Experimental noise and flow-field measurements for this geometry have been presented by Moreau et al. (2011). FIGURE 1. Schematic of the test case (span into page). Flow Modeling Flow over the flat plate was modeled numerically using a commercial CFD code STAR-CCM+ [CD-adapco, 2012]. In order to limit the cell count to a reasonable level the computations considered a quasi two-dimensional slice of thickness 0.015 m through the airfoil s span. In the computational model a slightly blunted trailing edge of thickness 0.00025 m was used. Inclusion of this bluntness resulted in a substantial improvement in the quality of the mesh attainable at the trailing edge. The computational domain was meshed in two regions, where the inner region consisted of 3.09 million cells while the outer region consisted of 1.53 million cells. The interface between the two regions (which is visible in Figure 3) was placed sufficiently far from the airfoil surface to enclose the boundary layer. Figure 2a shows a cross-section through the mesh. Enlarged sections through areas around the entire flat plate, and its leading and trailing edges, are shown in Figures 2b, c and d, respectively. A common mesh was used for both the RANS and IDDES computations. As seen in Figure 2, this consisted of a hexagonal core mesh, with a prism layer adjacent to the solid boundary of the airfoil. The prism layer was tailored to provide a non-dimensional thickness of the layer adjacent to the wall of y + 1, with a small expansion factor being specified to provide smooth blending between the prism layer and the core mesh. The mesh has been locally refined over several RANS runs, with no significant variations observable in fluctuating velocity and RSNM results from meshes of lesser resolution; however, a formal grid refinement study has not been performed. A non-slip boundary condition was imposed at the wall, and a hybrid wall treatment was specified [CD-adapco, 2011]. A periodic boundary condition was imposed between the two x-y planes defining the exterior boundaries (limits of modeled plate span) of the computational domain. For the steady RANS flow solution the turbulence model used was k-ω SST with 2 nd order convection and with the Realizability-option set to Durbin-Scale-Limiter and Low-Reynolds damping modification turned on. In this case incompressible flow was specified. The right-hand boundary was specified to be a pressure outlet, while velocity inlet boundary conditions (with a specified velocity vector) were imposed on the left, top and bottom boundaries (where the named directions correspond to the perspectives shown in Figures 1 and 2). Similar RANS results have previously been reported in a companion study [Albarracin et al., 2012b]. Inlet turbulence levels were selected to provide a match between the measured and simulated free-stream rms (root mean square) velocity fluctuations. Proceedings of Meetings on Acoustics, Vol. 19, 040070 (2013) Page 3

(a) (b) (c) (d) FIGURE 2. (a) Overall mesh, (b) Mesh around flat plate, (c) Mesh around leading edge of flat plate, (d) Mesh around trailing edge of flat plate. The second method used was an unsteady IDDES model using the k-ω SST model to provide the RANS component. Compressible flow was assumed, and freestream boundary conditions were imposed with Mach number and pressure specified for the inlet and outlet boundaries. A Synthetic Eddy Method [Jarrin et al., 2009] was used to introduce turbulent fluctuations in the flow into the computational domain. This provided the stimulation required to induce LES behavior in the wall region adjacent to the airfoil. Proceedings of Meetings on Acoustics, Vol. 19, 040070 (2013) Page 4

Noise Prediction The RSNM method used to obtain the sound radiated by the trailing edge uses a statistical model that relies on mean flow parameters (mean velocity, turbulent kinetic energy and turbulent dissipation) in the near vicinity of the region encompassing the trailing edge. These flow parameters are used to estimate the turbulence velocity crossspectrum, from which a noise estimate is derived via a summation procedure. The method is described in detail, with supporting equations, by Albarracin et al. (2012a) and thus is not repeated here. The Ffowcs-Williams and Hawkings (FWH) noise predictions used Star-CCM+ s inbuilt permeable FW-H solver. The interface between the two regions described in the previous section was used as the permeable FW-H integration surface. Experimental Data The simulated data were compared with the experimental data of Moreau et al. (2011). The simulated geometry and flow conditions were purposefully matched to those of the experiment, which consisted of a physical rig set up in an anechoic wind tunnel. Experimental data were collected using hot-wires and microphones. The experimental setup together with the flow and noise measurements are detailed in Moreau et al. (2011) and thus are not repeated here. RESULTS AND DISCUSSION Figure 3a shows the mean velocity field in the vicinity of the plate for the RANS solution. Figure 3b shows an instantaneous realization of the velocity field as predicted using IDDES. Details of the instantaneous flow around the leading and trailing edges are shown in Figures 3b and 3c, respectively. The permeable surface used in IDDES FWH is indicated as the black rectangle around the flat plate (labeled in Figure 3b). Figure 3c indicates the existence of a separation bubble immediately downstream of the leading edge. Further downstream the separation bubble reattaches. However, it appears to periodically break away, giving rise to large-scale structures that propagate downstream. These undergo intensification when they encounter the adverse pressure gradient associated with the wedge upstream of the trailing edge of the airfoil. Given the assumptions inherent in the formulation of RANS models, it is probably unreasonable to expect that a steady RANS model will provide an accurate statistical description of a flow field exhibiting the large-scale flow structures that are seen here. This assertion is borne out by a comparison of Figures 3a and 3b. The large-scale flow structures can be expected to be a source of low-frequency noise, and the failure of the RANS model to predict their presence suggests that a RSNM estimation of the noise spectrum based on a RANS simulation may well underpredict the noise levels at lower frequencies. As will be shown in Figure 6, this behavior has been observed in the present study. Further insight into the nature of the flow can be gained from an examination of the normalized cross-stream (z) vorticity (Figure 4). Figure 5 shows profiles of mean velocity and rms velocity fluctuation measured at a point immediately downstream of the trailing edge of the airfoil [Moreau et al., 2011]. These are compared with predictions made using the RANS and IDDES simulations. The mean velocities in Figure 5 show close agreement overall, except in a small region close to the center-line, where both the RANS and the IDDES models underpredict the measured mean velocity. The RANS estimates for the rms velocity fluctuations also compare well with the experimental measurements, as do the independent estimates of Albarracin et al. (2012b). However, a substantially lower level of agreement is observed in respect of the IDDES simulations. The high levels of rms velocity fluctuation predicted by the IDDES model are attributed to the large-scale structures observed in Figures 3 and 4. However, as already noted, the present experimental data are insufficient to confirm or refute the existence of these proposed flow structures. Further investigations comparing experimental and simulated velocity spectra at identical points in the boundary layer could potentially be used to resolve this issue. Proceedings of Meetings on Acoustics, Vol. 19, 040070 (2013) Page 5

(a) (b) (c) (d) FIGURE 3. Velocity field (a) Mean RANS, (b) Instantaneous IDDES, (c) Leading edge instantaneous IDDES, (d) Trailing edge instantaneous IDDES. Proceedings of Meetings on Acoustics, Vol. 19, 040070 (2013) Page 6

(a) (b) (c) FIGURE 4. Normalized cross-stream vorticity ( z c/u ), where z is cross-stream (z) vorticity, c is chord, and U is freestream velocity (a) Instantaneous IDDES, (b) Leading edge instantaneous IDDES, (c) Trailing edge instantaneous IDDES. (a) (b) FIGURE 5. (a) Trailing edge mean velocity (U) normalized with respect to freestream velocity (U ) as a function of distance above plate (y (see Figure 1)) normalized with respect to chord (c), (b) Trailing edge fluctuating velocity (u ) normalized with respect to freestream velocity (U ) as a function of distance above plate (y) normalized with respect to chord (c); (Experiment blue, RANS red, IDDES green). Figure 6 shows the noise spectrum measured at a location of y = 585 mm directly above the trailing edge of the plate [Moreau et al., 2011], and predictions made using a number of methods, namely RANS post-processed using RSNM (see also Albarracin et al. (2012b)), and IDDES post-processed using RSNM and FWH. Note that the RANS RSNM results differ slightly from those shown in Albarracin et al. (2012b). The present data are for a later RANS simulation in which several small modifications have been made. These refinements have resulted in the RSNM Proceedings of Meetings on Acoustics, Vol. 19, 040070 (2013) Page 7

prediction more closely matching the experimental data at higher frequencies (a slight drop-off in amplitude was observed at higher frequencies in Albarracin et al. (2012b)). Although the RANS RSNM prediction agrees reasonably well with experimental data at frequencies above about 1000 Hz, the discrepancy at lower frequencies reported previously [Albarracin et al., 2012b] remains. The discrepancy may be due to the fact that despite the simple geometry of the flat plate, it generates complex flow patterns, particularly near the leading and trailing edges. It would be interesting to repeat the experiments and the analysis using a regular airfoil, such as one having a NACA 0012 profile. For appropriate flow conditions, the flow over such an airfoil would not separate, and the RANS/RSNM estimates could therefore be expected to show closer agreement with experiment. It is, however, also desirable that the physical underpinnings of the RSNM model be investigated further with a view to improving its performance in cases such as the one considered here. As evident in Figure 6, the IDDES RSNM shows little agreement with the measured data; although it appears to be similar at very low frequencies, it greatly underpredicts noise levels above about 500 Hz. The RSNM technique relies on CFD outputs of mean velocity, mean turbulent kinetic energy, and turbulent energy dissipation. As has already been discussed, there are some discrepancies between the fluctuating streamwise velocity component of the IDDES solution when compared to the RANS solution and the measured data. As such, discrepancies in the turbulent kinetic energy would be expected (and were observed when compared to the RANS solution), which would affect the RSNM solution. It is felt, however, that the values of turbulent energy dissipation rate extracted from the IDDES solution are the main contributors to the inability of the IDDES flow solution to model noise spectra via the RSNM method. The turbulence energy dissipation rate values from the present IDDES model were significantly lower than anticipated. Turbulent energy dissipation rate is something of an ambiguous quantity in RANS turbulence modeling, where one is mainly interested in estimating dissipation rate as an intermediate step in computing a turbulence viscosity [Mathieu and Scott, 2000]. Emphasis is therefore placed on modeling a dissipation-like quantity that will provide a plausible estimate for the turbulence viscosity, while accurate modeling of the dissipative processes occurring within the turbulent flow field tends to be a secondary consideration. The situation is exacerbated when using an IDDES model, since turbulent dissipation rate needs to be calculated separately for the RANS and LES components of the flow, and the quantities then blended in an appropriate manner. The observed discrepancies in turbulent dissipation, and means of overcoming this in the IDDES model are matters that require further investigation. The best agreement between measured and predicted noise data at low frequencies is achieved by the IDDES FWH. It should be noted that the IDDES FWH solution was obtained from a separate IDDES run, in which the same modeling methodology and boundary conditions as described in this paper were used, but with minor changes in the mesh resolution adjacent to the solid boundary (the mean and fluctuating velocity as well as RANS RSNM results corresponding to this modified mesh showed good agreement with those presented within this paper). The RSNM results for the modified IDDES solution are not presented here, but show the same trends as the presented IDDES RSNM data. The FWH solution shows good agreement with the measured data across the entire frequency range. These results suggest that even though an IDDES flow solution using RSNM is not yielding realistic results at present, the IDDES flow solution is capable of predicting flow parameters that yield an acceptable acoustic prediction (albeit using a different means of prediction). Further investigations of the robustness of the IDDES solution, as well as the generation and interpretation of IDDES flow data suitable for use with RSNM are required. Moreover, additional IDDES runs at other flow speeds would enhance understanding of the flow. FIGURE 6. Spectral density as a function of frequency for experiment (blue), RANS RSNM (red), IDDES RSNM (light green), and IDDES FWH (dark green). Proceedings of Meetings on Acoustics, Vol. 19, 040070 (2013) Page 8

CONCLUSION Predicted flow field and noise estimates based on IDDES have been presented and compared to previously reported results from measurements and RANS combined with RSNM. The IDDES flow field suggests the existence of large structures; however, they have not been confirmed in the experiments. The IDDES are in good agreement with measured mean velocity in the near vicinity of the trailing edge; however, IDDES overpredicts the corresponding fluctuating velocity (when compared to the experimental data). The IDDES RSNM solution is currently poor; however, the IDDES FWH shows great promise. Hypotheses for the poor performance of the IDDES RSNM solution have been postulated and will be further investigated in the future. The paper indicates that the flow could be more complex than previously envisaged and it would be worthwhile investigating the possibility of using two different formulations of RANS RNSM further, one covering low frequency, and one covering high frequency. The present paper is a report on work in progress and as already discussed, further investigation of IDDES combined with RSNM and FWH is required. A systematic variation of the mesh resolution in the vicinity of the acoustic sources will be performed. Additional IDDES runs at other flow speeds would also be beneficial. In addition, it would be beneficial to carry out measurements with accompanying simulations on test cases where the flat plate has a smooth surface without a wedge preceding the trailing edge. ACKNOWLEDGMENTS This work has been supported by the Australian Research Council under Linkage Grant LP110100033 Understanding and predicting submarine hydrofoil noise. REFERENCES Albarracin, C. A., Doolan, C. J., Jones, R. F., Hansen C. H., Brooks, L. A., and Teubner, M. D. (2012a). A RANS-based statistical noise model for trailing edge noise, in Proceedings of the 18 th AIAA/CEAS Aeroacoustics Conference (33 rd AIAA Aeroacoustics Conference), Colorado Springs, Colorado, USA, 4-6 June 2012, Paper AIAA 2012-2181. Albarracin, C. A., Marshallsay, P., Brooks, L. A., Cederholm, A., Chen, L., and Doolan, C. J. (2012b). Comparison of aeroacoustic predictions of turbulent trailing edge noise using three different flow solutions, in Proceedings of the 18 th Australasian Fluid Mechanics Conference, Launceston, Australia, 3-7 December 2012, Paper 223. Amiet, R. K. (1976). Noise due to turbulent flow past a trailing edge, J. Sound Vib. 47, 387-393. Brooks, T. F., Pope, D. S., and Marcolini, M. A. (1989). Airfoil self-noise and prediction, NASA Reference Publication 1218. CD-adapco (2012). User Guide, Star-CCM+, Version 7.04. Ffowcs Williams, J. E., and Hall, L. H. (1970). Aerodynamic sound generation by turbulent flow in the vicinity of a scattering half plane, J. Fluid Mech. 40, 657-670. Ffowcs Williams, J. E., and Hawkings, D. L. (1969). Sound generation by turbulence and surfaces in arbitrary motion, Phil. Trans. R. Soc. A. 264, 321-342. Greschner, B., Grilliat, J., Jacob, M. C., and Thiele, F. (2010). Measurements and wall modeled LES simulation of trailing edge noise caused by a turbulent boundary layer, Int. J. Aeroacoust. 9, 329-355. Howe, M. S. (1998). Acoustics of Fluid-Structure Interactions (Cambridge University Press, Cambridge, United Kingdom), Chap. 3, pp. 215-218. Jarrin, N., Prosser, R., Uribe, J.-C., Benhamadouche, S., and Laurence, D. (2009). Reconstruction of turbulent fluctuations for hybrid RANS/LES simulations using a Synthetic-Eddy Method, Int. J. Heat Fluid Fl. 30, 435-442. Kamruzzaman, M., Lutz, T., Herrig, A. and Krämer, E. (2012). Semi-empirical modeling of turbulent anisotropy for airfoil selfnoise predictions, AIAA J. 50, 46-60. Lockard, D. P., and Casper, J. H. (2005). Permeable surface corrections for Ffowcs Williams and Hawkings integrals, in Proceedings of the 11 th AIAA/CEAS Aeroacoustics Conference (26 th AIAA Aeroacoustics Conference), Monterey, California, USA, 23-25 May 2005. Mathieu, J., and Scott, J. (2000). An Introduction to Turbulent Flow (Cambridge University Press, Cambridge, United Kingdom), Chap. 8, pp. 356-358. Moreau, D. J., Brooks, L. A., and Doolan, C. J. (2011). Broadband trailing edge noise from a sharp-edged strut, J. Acoust. Soc. Am. 129, 2820-2829. Shur, M. L., Spalart, P. R., Strelets, M. K., and Travin, A. K. (2008). A hybrid RANS-LES approach with delayed-des and wall-modelled LES capabilities, Int. J. Heat Fluid Fl. 29, 1638-1649. Wang. M., Moreau, S., Iaccarino, G., and Roger, M. (2009). LES prediction of wall-pressure fluctuations and noise of a lowspeed airfoil, Int. J. Aeroacoust. 8, 177-198. Proceedings of Meetings on Acoustics, Vol. 19, 040070 (2013) Page 9