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A large-eddy simulation of laminar transonic buffet on an airfoil at a Mach number $M=0.735$, an angle of attack $\unicode[STIX]{x1D6FC}=4^{\circ }$, a Reynolds number $Re_{c}=3\times 10^{6}$ has been carried out. The boundary layer is laminar up to the shock foot and laminar/turbulent transition occurs in the separation bubble at the shock foot. Contrary to the turbulent case for which wall pressure spectra are characterised by well-marked peaks at low frequencies ($St=f\cdot c/U_{\infty }\simeq 0.06{-}0.07$, where $St$ is the Strouhal number, $f$ the shock oscillation frequency, $c$ the chord length and $U_{\infty }$ the free-stream velocity), in the laminar case, there are also well-marked peaks but at a much higher frequency ($St=1.2$). The shock oscillation amplitude is also lower: 6 % of chord and limited to the shock foot area in the laminar case instead of 20 % with a whole shock oscillation and intermittent boundary layer separation and reattachment in the turbulent case. The analysis of the phase-averaged fields allowed linking of the frequency of the laminar transonic buffet to a separation bubble breathing phenomenon associated with a vortex shedding mechanism. These vortices are convected at $U_{c}/U_{\infty }\simeq 0.4$ (where $U_{c}$ is the convection velocity). The main finding of the present paper is that the higher frequency of the shock oscillation in the laminar regime is due to a different mechanism than in the turbulent one: laminar transonic buffet is due to a separation bubble breathing phenomenon occurring at the shock foot.

International audience; The scattering of an acoustic wave by a 3D spatially-developing plane turbulent mixing layer is investigated by means of a Large Eddy Simulation (LES). First, a plane turbulent mixing layer of initial Reynolds number Reω, 0 ≈ 1200 and convective Mach number Mc ≈ 0.12 is computed and its characteristics are validated by comparisons to experimental and numerical studies. Then, an acoustic source is introduced in the computational domain and the LES of both the turbulent mixing layer and the acoustic field is carried out, allowing the direct computation of the scattered pressure field. Computational Aero Acoustics (CAA) methods have been implemented to minimize spurious pressure fluctuations created while the turbulent structures leave the computational domain. The side-lobes of the scattered pressure power spectral density are recovered and a parametric study, involving the convection velocity of the large turbulent structures, the amplitude and the tonal frequency of the source is carried out. The part of scattered energy, the frequency shift of the side-lobes and the spectra decrease are found to be correctly estimated. Analysis of directivity at the side-lobes frequencies show a progressive re-distribution of the acoustic energy, as the acoustic wave propagates through the turbulent shear layer.

An improvement of the efficiency of implicit schemes based on Newton-like methods for the simulation of turbulent flows by compressible LES or DNS is proposed. It hinges on a zonal Self-Adaptive Newton method (hereafter denoted SAN), capable of taking advantage of Newton convergence rate heterogeneities in multi-scale flow configurations due to a strong spatial variation of the mesh resolution, such as transitional or turbulent flows controlled by small actuators or passive devices. Thanks to a predictor of the local Newton convergence rate, SAN provides computational savings by allocating resources in regions where they are most needed. The consistency with explicit time integration and the efficiency of the method are checked in three test cases: – The standard test-case of 2-D linear advection of a vortex, on three different two-block grids. – Transition to 3-D turbulence on the lee-side of an airfoil at high angle of attack, which features a challenging laminar separation bubble with a turbulent reattachment. – A passively-controlled turbulent transonic cavity flow, for which the CPU time is reduced by a factor of 10 with respect to the baseline algorithm, illustrates the interest of the proposed algorithm.

Large Eddy Simulation of the bubble bursting process over a NACA-0012 airfoil at $Re_{c}=10^{5}$ indicates that the flow at a fixed angle of attack below the critical stall value exhibits a short (with respect to Gaster’s criteria, Gaster, Number CP-4 in AGARD, 1966) Laminar Separation Bubble (LSB) at the leading edge of the airfoil. The airfoil is smoothly pitched-up through the static stall angle to reproduce the bursting process of the short LSB that initiates a leading edge stall typical of low Reynolds number airfoil. The temporal evolution of characteristic length scales is monitored during the transient flow. Particular attention is paid to the characteristic time involved during the growth and bursting of the LSB. A recent empirical bursting criterion is used to analyse the LES results.

A large eddy simulation (LES) of a turbulent flow past a 70° sweep angle delta wing is performed and compared with wind tunnel experiments. The angle of attack and the Reynolds number based on the root chord are equal to 27° and 1.6×10 6 , respectively. Due to the high value of the Reynolds number and the three-dimensional geometry, the mesh resolution usually required by LES cannot be reached. Therefore a local mesh refinement technique based on semi-structured grids is proposed, whereas different wall functions are assessed in this paper. The goal is to evaluate if these techniques are sufficient to provide an accurate solution of such flow on available supercomputers. An implicit Miles model is retained for the subgrid scale (SGS) modelling because the resolution is too coarse to take advantage of more sophisticated SGS models. The solution sensitivity to grid refinement in the streamwise and wall normal direction is investigated.

Large-eddy simulation ofcompressible Navier-Stokes equations is used to study flows where a laminar boundary-layer separation is followed by a turbulent reattachment. The aim of the present work is to predict and describe the transition process and its interaction with the wake dynamics for a subsonic blade turbine configuration. Indeed, a better knowledge of this mechanism can help to improve the accuracy of a Reynolds-averaged Navier-Stokes turbulence model for such a flow case. High-resolution large-eddy-simulation-type computations have been carried out for the T106 low-pressure blade turbine at inlet Mach number of 0.1 and chord Reynolds number of 1.6 x 10 5 based on the exit isentropic velocity. The simulated mean and turbulent quantities compare well with the available experimental data. The primary two-dimensional instability that originates from the free shear in the bubble is unstable via the Kelvin-Helmholtz mechanism. Then, the three-dimensional motions spread on the boundary layer, leading to full breakdown to turbulence after the reattachment point

Large-eddy simulations of the flow over a deep cavity are performed. The computations reproduce identically all the parameters of the experiment by Forestier and co-workers [J. Fluid Mech. (to be published)], including the high Reynolds number ReL=8.6×105. Spectra show an accurate prediction of the peak levels of the fundamental frequency and its first harmonics. Results are also analyzed both in terms of Reynolds and phase averages, the procedure used to compute phase averages being identical to the one used during the experiment. Agreement with the experimental data is found to be excellent. The expansion rate of the shear layer is accurately described, and the temporal physics of the flow, including the dynamics of the coherent structures, is fully recovered. By comparison with an auxiliary computation wherein the wind-tunnel upper wall is not taken into account, the cavity is found to oscillate in a flow-acoustic resonance mode. New values for the γ constant of Rossiter’s model are then proposed for a...

A large eddy simulation (LES) of a turbulent flow past an airfoil near stall at a chord Reynolds number of 2.1 x 10 6 is performed and compared with wind-tunnel experiments. This configuration still constitutes a challenging test case for Reynolds-averaged Navier-Stokes (RANS) simulation and LES as a result of the complexity of the suction side boundary layer: an adverse pressure gradient creates successively a laminar separation bubble, a turbulent reattachment, and a turbulent separation near the trailing edge. To handle this high-Reynolds-number flow with LES on available supercomputers, a local mesh-refinement technique and a discretization of the convective fluxes are developed in a block-structured finite volume code to reduce the total number of grid points and the numerical dissipation acting on the small scales, respectively. Influence of subgrid scale modeling (SGS) is assessed through the comparisons of explicit selective mixed scale model (SMSM) and implicit monotone-integrated LES model results. Moreover, the solution sensitiveness to grid refinement and spanwise extent is investigated

An algorithm for the simulation of unsteady, viscous, stratified compressible flows, which remains valid at all speeds, is presented. The method is second-order accurate in both space and time and is independent of the Mach number. In order to remove the stiffness of the numerical problem due to the large disparity between the flow speed and the acoustic wave speed at low Mach number, an approximate Newton method, based on artificial compressibility, is proposed. Additionally, a modified advection upstream splitting method (AUSM +) scheme is used, which permits accurate computations of both compressible and incompressible flows. A detailed description of the method and an efficiency comparison with other approximate Newton methods described in the literature are given. Furthermore, it is shown that the accuracy of the algorithm is not dependent on the Mach number through the computations of various benchmark test cases. Copyright (C) 2000 John Wiley & Sons, Ltd.

In the context of the AEROCAV French Research Program, Large-Eddy Simulations were conducted to compute the turbulent structures and the noise generated by the flow over realistic cavities, similar to those present on air craft fuselages and wings. The radiated acoustic field was computed using a Kirchhoff integ ral method. Two geometrical configurations are considered, both with cylindrical shapes but with different Depth/Diameter aspect ratio (H/D = 1 and H/D = 0.5 ) embedded in a subsonic flow ( Mach = 0.2 ) and for a Reynolds number based on the length of the cavity equal to 4.6·10 5 . Dedicated experimental aerodynamic and aeroacoustic measurements databases are used to validate the numerical computations. Experimental and numerical flows are similar except that the boundary layer upstream the cavity is turbulent in the experiments and laminar for the CFD. The aerodynamic fields in the two sets of results are in good agreement, whereas the acoustic field is largely influenced by the install ation effects. These effects are analyzed through computations based on Boundary Element Method and CAA and then corrections factors are provided. The acoustic emission for the H/D = 1 case is characterized by a discrete tonal mode, as a superposition of structur al and Rossiter resonance phenomena, while the H/D = 0.5 case presents a directive and highly dissymmetrica l broadband noise emission. A numerical process is also proposed to c ontrol this dissymmetry.

The purpose of this paper is to investigate the acoustical field generated by the flow over a cylindrical cavity on a flat plane, similar to those located on wings and fuselage of transport aircraft, using a hybrid numerical method. Firstly, a CFD computation was carried out, using a Large-Eddy Simulation method, to compute the turbulent structures and the noise generating mechanisms. Secondly, the near-field results were injected in a Kirchhoff integral method code, in order to compute the far-field noise radiation. The retained case for this study is represented by a cavity with a unitary depth/diameter ratio, in the presence of a subsonic flow with a Reynolds number based on the diameter of the cavity equal to 4.6x10 5 . As inflow condition, a fluctuation-free velocity profile was considered. Computational results were compared to experimental data measured in an anechoic wind tunnel for the same geometry configuration, but in the presence of a turbulent boundary layer. As expected, a symmetrical flow pattern was observed joined with a fluid resonant mechanism. The computation shows that the acoustical field is less influenced by the inflow condition and results are in good agreement with the experimental measurements despite a slight under-estimation of the main tone amplitude.

An algorithm is proposed for the simulation of unsteady viscous stratified compressible flows. The advantage of the method is its capability to deal with a broad range of subsonic Mach numbers, including nearly incompressible flows, with a single modelling, based on the fully compressible Navier-Stokes equations. The method is second-order accurate both in space and time. To remove the stiffness of the numerical problem due to the large disparity between the flow and the acoustic wave speeds at low Mach number, an approximate Newton method, based on artificial compressibility, is used. After a detailed description of the method, the accuracy of the algorithm is checked by computing compressible and incompressible benchmark test cases. Results of flows over a backward facing step with or without stratification effects for a Reynolds number of 800 are compared with the steady solution of incompressible methods, The computation of a compressible natural convection allows to evaluate the accuracy of the method for flow including significant compressibility effects, whereas numerical results of a Poiseuille-Benard channel flow for a Reynolds number of 10 demonstrate the efficiency of the present algorithm to compute unsteady hows. (C) 2000 Elsevier Science Ltd. All rights reserved.

An improvement of an implicit scheme for Large-Eddy Simulation is proposed in this paper. This local optimization (LO) of the convergence is based on the reduction of the high computational eort per time step inherent to the use of implicit time stepping methods. Indeed, the LO is a local adpatation of the iteration number in the inner process. Moreover an implicitation of the boundary condition between two domains where the iteration number is dieren t, is also used. This procedure is validated on two test cases. The rst one is a 2D laminar vortex advection which allows us to check the potential of this LO. On a transitional boundary layer around an airfoil near stall at a chord Reynolds number of 2:1 10 6 , it is shown that this procedure can be used without damaging the accuracy.

The use of a database as unsteady ino w condition for turbulent boundary layers of complex o w is evaluated. This technique is employed to achieve a full zonal coupling between a Reynolds average Navier Stokes simulation (RANS) and a large-eddy simulation (LES). The database is rst extracted from a plane of a compressible turbulent at plate boundary layer and contains all conservative variables. Scaling functions are developed to use this database as ino w conditions for a at plate at dieren t Reynolds and Mach numbers. The inuence on the solution of several parameters, such as the database duration or the time-step between two samples of the database, is discussed. Some results are compared with those given by the recycling rescaling method of Lund, Wu and Squires. 9

The aim of the present work is to predict and describe the boundary layer transition process influenced by an incoming upstream turbulent wake generated by a moving cylinder for a subsonic blade turbine configuration. High-resolution Large-Eddy Simulation type computations have been carried out for the T106 low-pressure blade turbine at Mach number of 0.1 and chord based Reynolds number of 1.6 105 and have been compared with experiments.

A Large Eddy Simulation (LES) of a turbulent flow past a 70° sweep angle delta wing is performed and compared with windtunnel experiments. The angle of attack and the Reynolds number based on the root chord are equal to 27° and 1.6 × 106, respectively. Due to the high value of the Reynolds number and the three-dimensional geometry, the mesh resolution usually required by LES cannot be reached. Therefore a local mesh refinement technique, based on semi-structured grids, and some wall functions are assessed in this paper. The goal is to evaluate if these techniques are sufficient to provide accurate solution of such flow on available supercomputers. An implicit Miles model is retained for the Subgrid Scale (SGS) modelling, because the resolution is too coarse to take advantage of more sophisticated SGS models. The solution sensitiveness to grid refinement in the streamwise and wall normal direction is investigated.

A Large Eddy Simulation (LES) of a turbulent flow over the A-airfoil near stall at a chord Reynolds number of 2.1 x 10 is performed and compared with windtunnel experiments. This configuration still constitutes a challenging test case for Reynolds Average Navier-Stokes (RANS) simulation and LES due to the complexity of the suction side boundary layer: an adverse pressure gradient creates successively a laminar separation bubble, a turbulent reattachment and a turbulent separation near the trailing edge. To handle this high Reynolds number flow with LES on available supercomputer, a local mesh refinement technique and a discretization of the convective fluxes are developed in a block-structured finite volume code to reduce the total number of grid points and the numerical dissipation acting on the small scales, respectively. Influence of Subgrid Scale Modelling (SGS) is assessed through the comparisons of explicit Selective Mixed Scale Model (SMSM) and implicit MiLES model results. Moreover the solution sensitivity to grid refinement and spanwise extent is investigated. With the use of the largest grid (7.2 x 10 cells) and SMSM model, the computed mean and fluctuating velocity profiles compares favourably with experimental measurements, which constitutes to the authors knowledge the first satisfying LES of this complex flow.

A Large Eddy Simulation (LES) of a turbulent flow over the A-airfoil near stall at a chord Reynolds number of 2.1 × 106 is performed and compared to windtunnel experiments. This configuration still constitutes a challenging test case for Reynolds Averaged Navier-Stokes (RANS) simulation and LES due to the complexity of the suction side boundary layer: an adverse pressure gradient creates successively a laminar separation bubble, a turbulent reattachment and a separation near the trailing edge. To handle this high Reynolds number flow with LES on available supercomputers, a local mesh refinement technology and a low dissipative scheme are developed. It appears that the computed mean and fluctuating velocity profiles compare reasonably well with experimental measurements.

The aim of the present work is to predict and describe the transition process and its interaction with the wake dynamics for a subsonic blade turbine configuration. High-resolution Large-Eddy Simulation type computations have been carried out for the T106 low-pressure blade turbine at Mach number of 0.1 and chord Reynolds number of 1.6 105 and have been compared with experiments.