Large eddy simulation of a forward–backward facing step for acoustic source identification
Introduction
Computational fluid dynamics (CFD) is now a common design tool for road vehicles. Powerful and lower cost computers enable parametric studies for improving performance and safety, but the next challenging issue that can lead to significant commercial advantages is comfort of passengers and nuisance reductions for communities nearby roads and rail tracks. With this objective, SNCF (French trains), PSA (Peugeot-Citroen), EDF (Electricité de France) and ECL (Ecole Centrale de Lyon) embarked on a project aiming at numerical prediction of noise (PREDIT 2.2), supported by the French state.
Aerodynamic noise is generated by turbulent structures, but the acoustic energy radiated is a very small fraction of the total flow energy, or even of the turbulent kinetic energy. The non-linear nature of turbulence being so different from that of propagation, hybrid methods are commonly used whereby the flow features and turbulence are computed on the one hand, then introduced as a transporting media and source terms, in a separate acoustic calculation. Some groups, including ECL (Gloerfelt et al., 2001) have resorted to a direct simulation of both phenomena, but this approach is based on high order schemes which cannot be easily extended to industrial geometries. In the present hybrid approach, the linearized Euler equations (LEE) are used for the propagation of noise. The LEE consist of propagation equations for velocity, density and pressure fluctuations, where all non-linear terms are excluded with the notable exception of a source term . This term is a fluctuation and as such must be “reconstructed” when a RANS model is used to compute the aerodynamic flow, for instance by the Stochastic Noise Generation and Radiation (SNGR) model (Longatte et al., 1998). Alternatively as in the present project, this source term is evaluated from the instantaneous flow-fields of a large eddy simulation (LES). A similar method was successfully applied by Kato et al. (2000) to the flow around an insulator, for a high-speed train also. However, the far-field sound was in this case computed from the instantaneous surface pressure on the insulator. Using the LES + LEE approach, the acoustic power spectrum was successfully predicted for the case of a duct flow obstructed by a 2D diaphragm (Crouzet et al., 2002), and the finite element LES code N3S (Rollet-Miet et al., 1999) was accurate in generating the acoustic source term. The second test case of the PREDIT project, presented hereafter, is a forward backward facing step. A first LES calculation performed by Lazure (2000) was based on the N3S-LES code. The tetrahedral FE mesh was not warranted for this rectangular geometry, nor was it ideal for the interpolation of the source terms onto the Cartesian mesh used for the acoustic propagation calculation. A second simulation was thus undertaken, at the same time evaluating the LES capabilities of the commercial code, Star-CD, commonly used by SNCF.
Section snippets
Numerical method
The Star-CD code uses the conservative finite volume method, and an unstructured collocated grid is used to store velocities and scalars at cell centres. To minimize the truncation errors in the convective term of the filtered equations, the central second order-differencing scheme is used preferentially to the default upwind or QUICK scheme. To ensure stability, the so-called centred scheme uses in fact an upwind scheme on the implicit part of the equations (i.e. evaluated at time step n+1),
Determination of the constant Cs
Prior to any LES application of a commercial or industrial code, its performance on homogeneous isotropic turbulence (HIT) should be established. As shown by Rollet-Miet et al. (1999), this can be extremely informative. Moreover, the quality of the predicted acoustic power spectrum is obviously highly dependent on the quality of the source term spectrum. As no such information was available for Star-CD, Y. Addad first undertook the LES simulation of the classical HIT test, using the
The forward–backward facing step
The case selected in the present study is a flow over a forward–backward facing step, of height h=50 mm and l=10h long. The external flow velocity is 50 m/s resulting in Reynolds number Reh=1.7×105 (based on the external velocity and the obstacle height). The upstream boundary layer thickness reported in Leclercq et al. for the LDA measurements was about 0.7h.
The geometric parameters of the present application are presented in Fig. 3. The domain height is 10h, the spanwise width of the domain
Results and discussion
The flow develops three recirculation zones around the step. Fig. 5 shows streamlines obtained from the averaged field where the three distinct recirculation zones are observed. The separation and reattachment points of the first bubble in the region before the forward step are in good agreement with the experimental data of Leclercq et al. (2001) and Moss and Baker (1980). In the experiments, the flow detaches at 0.8–1.5h before the step to reattach on the vertical wall at 0.6–0.65h. The
Conclusion
The calibration of the classical Smagorinsky subgrid model constant was carried out using the homogeneous turbulence decay and taking in account the numerical dissipation identified in the commercial code. Then, results from two large eddy simulations of a flow over forward–backward facing step at Reynolds number Re=1.7×105 are presented. Running two independent calculations simultaneously, starting from very different initial conditions was found useful in monitoring statistical convergence.
Acknowledgements
C. Talotte and M.C. Jacob gratefully acknowledge support from the PREDIT programme of the French Ministère de l’Education Nationale, de la Recherche et de la Technologie. Y. Addad and D. Laurence gratefully acknowledge support from the Algerian Ministère de l’Enseignement et de la Recherche scientifique, and are thankful to Dr. A. Ghobadian, Dr. R. Clayton (Computational Dynamics Ltd.), S. Benhamadouche, and F. Crouzet (EDF) for assistance and helpful discussions.
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