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This paper presents the numerical study of the Source Diagnostic Test fan rig of the NASA Glenn (NASA SDT). Large-Eddy Simulations (LES) based on a finite volume approach are performed for the three different Outlet Guide Vane (OGV) geometries (baseline, low-count and low-noise) and three rotational speeds corresponding to approach, cutback and sideline operating conditions respectively. The full stage and nacelle geometries are considered in the numerical simulations, and results are compared to available measurements. The NASA SDT configuration is equipped respectively with 22 fan blades and either 26 of 54 vanes depending on the OGV geometry. The simulation domain could only be reduced to half of the full annulus and would still be a significant cost for the LES. In order to reduce computational cost, an LES with phase-lagged assumption approach is used. This method allows to perform unsteady simulations of multistage turbomachinery configurations including multiple frequency flows with a reduced computational domain composed of one single blade passage for each row. The large data storage required by the phase-lagged approach is handled by a compression method based on a Proper Orthogonal Decomposition replacing the traditional Fourier series decomposition. This compression method improves the signal spectral content especially at high frequency. Based on the numerical simulations, the flow field is described and used to assess the losses generated in the turbofan configuration based on an entropy approach. The results show different flow topologies for the fan depending on the rotational speed with a leading edge shock at high rotational speed. The fan boundary layer contributes strongly to losses with the majority of the losses being generated close to the leading edge for the dissipation due to mean strains and close to the recirculation zone occurring on the suction side for the turbulent kinetic energy production.

International audience; This paper presents the broadband noise analysis of a Counter Rotating Open Rotor (CROR) configuration. The numerical study is based on a hybrid approach: a Large Eddy Simulation (LES) code solves the near-flow field of the CROR configuration and the near-to-far-field propagation is then predicted by a Ffowcs Williams-Hawkings analogy either based on a solid or porous formulation. The LES solver uses a phase-lagged assumption with a proper orthogonal decomposition for the data storage. The numerical approach is validated against wind tunnel experimental data of a CROR configuration (AI-PX7) at three different operating points focused on the broadband noise. The analysis of the numerical simulations shows the predominant effect of the rear rotor suction side on the radiated broadband noise with an increasing contribution with span location. This source is related to the impingement of front rotor wakes and the development of leading edge vortices that induce large pressure fluctuations close to the leading edge on the suction side.

International audience; This paper presents the study of the losses generated in a Counter Rotating Open Rotor (CROR) configura- tion at three different operating conditions (approach, cutback and sideline). Unsteady Reynolds Averaged Navier-Stokes (URANS) and Large-Eddy Simulation (LES) approaches are used and compared to describe the flow field and the mechanisms of loss. Since no common circumferential periodicity occurs in the two blade rows of the configuration (11 blades for the front rotor and 9 for the rear rotor), a full 360 ◦simu- lation would be required. In order to reduce the related computational cost, a phase-lagged assumption approach is used. This method enables to perform unsteady simulations on multi-stage propulsive con- figurations including multiple frequency flows with a computational domain reduced to one single blade passage for each row. The phase-lagged approach requires a large data storage reduced in the study by a data compression method. The data compression method is based on a Proper Orthogonal Decomposition (POD) replacing the traditional Fourier Series Decomposition (FSD). The inherent limitation of the phase- shifted periodicity assumption remains with the POD data storage but this compression method alleviates some issues associated with the FSD, especially spectrum content issues. The analysis of the losses gen- erated in the configuration is based on an entropy formulation. In particular, the losses are split between boundary layer contributions and the remaining domain where wakes and secondary flows occur. The study shows the influence of the leading edge vortex on the suction side boundary layer transition of the front and rear rotor blades at high rotational speed (cutback and sideline). The main source of losses is associated with the suction side boundary layer over the front and rear rotor blades with a main peak of loss production at around 75% of the blade chord.

International audience; The Reynolds-Averaged Navier-Stokes equations and the Large-Eddy Simulation equations can be coupled using a transition function to switch from a set of equations applied in some areas of a domain to the other set in the other part of the domain. Following this idea, different time integration schemes can be coupled. In this context, we developed a hybrid time integration scheme that spatially couples the explicit scheme of Heun and Crank-Nicolson's implicit scheme using a dedicated transition function. This scheme is linearly stable and second-order accurate. In this paper, an extension of this hybrid scheme is introduced to deal with a temporal adaptive procedure. The idea is to treat the time integration procedure with unstructured grids as it is performed with Cartesian grids and local mesh refinement. Depending on its characteristic size, each mesh cell is assigned to a rank. And for two cells from two consecutive ranks, the ratio of the associated time steps for time marching the solutions is 2. As a consequence, the cells with the lowest rank iterate more than the other ones to reach the same physical time. In a finite-volume context, a key ingredient is to keep the conservation property for the interfaces that separate two cells of different ranks. After introducing the different schemes, the paper recalls briefly the coupling procedure, and details the extension to the temporal adaptive procedure. The new time integrator is validated with the propagation of 1D wave packet, the Sod's tube, and the advection of 2D vortex.

International audience; This paper addresses how two time integration schemes, the Heun's scheme for explicit time integration and the second-order Crank-Nicolson scheme for implicit time integration, can be coupled spatially. This coupling is the prerequisite to perform a coupled Large Eddy Simulation / Reynolds Averaged Navier-Stokes computation in an industrial context, using the implicit time procedure for the boundary layer (RANS) and the explicit time integration procedure in the LES region. The coupling procedure is designed in order to switch from explicit to implicit time integra-tions as fast as possible, while maintaining stability. After introducing the different schemes, the paper presents the initial coupling procedure adapted from a published reference and shows that it can amplify some numerical waves. An alternative procedure, studied in a coupled time/space framework, is shown to be stable and with spectral properties in agreement with the requirements of industrial applications. The coupling technique is validated with standard test cases, ranging from one-dimensional to three-dimensional flows.; Ce papier explique comment deux schémas d'intégration temporelle (schéma de Heun en explicite et schéma de Crank-Nicolson en implicite) peuvent être couplés spatialement. Ce couplage est un prérequis pour faire des simulations couplées LES / RANS dans un contexte industriel pour lequel la couche limite (RANS) est calculée en implicite et l'intégrateur explicite est utilisé pour la LES. La méthodologie de couplage est choisie pour passer très vite de l'explicite à l'implicite tout en garantissant la stabilité. Après avoir introduit les deux schémas, le papier présente une méthode de couplage adaptée de la littérature qui amplifie certains nombres d'onde. Une approche alternative, étudiée dans un contexte couplé espace/temps, est stable et présente des propriétés spectrales en accord avec les prérequis des applications industrielles. Le couplage est validé sur des cas tests classiques en 1D et 3.

The performance of a system designed for given functioning conditions often seriously degrades, when operated at other conditions. Therefore, a system operating over a continuous range of conditions should be designed over this range. The aerodynamic shape optimization of an aircraft at multiple altitudes, angles of attack and Mach numbers is a typical case in aerospace. This paper links parametric and multipoint optimizations by the sampling of the operating condition ranges. It is demonstrated that this discrete set of operating conditions, used to formulate a composite objective function, must adequately be chosen. An algorithm is proposed to select these conditions, which ensures a minimal computational cost to the robust optimization. Wing aerodynamic multipoint optimizations using a lifting line model and Reynolds-averaged Navier---Stokes equations, derived with a discrete adjoint formulation, are given as examples.

A framework is proposed for the spectral analysis of the numerical scheme applied on a nonconforming grid interface between two structured blocks for the two-dimensional advection equation, in a cell-centered finite-volume formalism. The conservative flux computation on the nonconforming grid interface is based on the sum of partial fluxes computed with the same numerical scheme used for a standard cell interface. This framework is used to analyze the effect of grid refinement or coarsening on the stability of the second-order centered scheme. New theoretical results are given and compared to numerical results. Considering the convection of a two-dimensional isentropic vortex, the refinement/coarsening are shown to be the cause of instabilities, poor accuracy and reflection of high-frequency waves. A new approach to compute partial fluxes, which is based both on a high-order extrapolation that accounts for the local metric and on a Riemann solver, is then proposed to reduce spurious modes.

A new resolution method for solving linear systems resulting from the discrete adjoint approach in aerodynamic shape optimization with a single objective and multiple constraint functions is presented. The steady flow is governed by the three-dimensional compressible Favre-averaged Navier–Stokes equations combined with a two-equation turbulence model. Block flexible variants of the generalized minimal residual method are Krylov methods designed for the solution of linear systems with multiple right-hand sides allowing variable preconditioning. Then, they can be applied to the discrete adjoint equations of Favre-averaged Navier–Stokes equations for all objective and constraint functions as a right-hand side. The paper focuses on the development of a new algorithm combining the three following features: flexibility, multiple right-hand-side concurrent processing, and spectral deflation. This latter property enables to recycle approximate spectral information from one restart to the next one in order to avoi...

International audience; Wall-modeling is required to make large-eddy simulations of high-Reynolds number wall-bounded turbulent flows feasible in terms of computational cost. Here, an extension of the integral wall-model for large-eddy simulations (iWMLESs) for incompressible flows developed by Yang et al. ["Integral wall model for large eddy simulations of wall-bounded turbulent flows," Phys. Fluids 27(2), 025112 (2015)] to compressible and isothermal flows is proposed and assessed. The iWMLES approach is analogous to the von Karman-Pohlhausen integral method for laminar flows: the velocity profile is parameterized, and unknown coefficients are determined by matching boundary conditions obeying the integral boundary layer momentum equation. It allows non-equilibrium effects such as pressure gradient and convection to be included at a computing cost similar to analytical wall-models. To take into account density variations and temperature gradients, the temperature profile is also parameterized and the integral compressible boundary layer energy equation is considered. Parameterized profiles are based on the usual logarithmic wall functions with corrective terms to extend their range of validity. Instead of solving a set of differential equations as wall-models based on the thin boundary layer equation approach, a simple linear system is solved. The proposed wall-model is implemented in a finite-volume cell-centered structured grid solver and assessed on adiabatic and isothermal plane channel flows at several friction Reynolds and Mach numbers. For low Mach number cases, mean profiles, wall fluxes, and turbulent fluctuations are in agreement with those of Direct Numerical Simulation (DNS). For supersonic flows, the results are in good agreement with the DNS data, especially the mean velocity quantities and the wall friction, while standard analytical wall-models show their limits.

The aim of this study is to propose a computing method to obtain a detailed simulation of the unsteady flow that develops in multistage turbomachines. The three-dimensional unsteady Reynolds-averaged Navier—Stokes equations are solved using a structured multiblock decomposition method. Although this kind of flow solver is very popular in the turbomachine community nowadays, the complex block connectivities used in meshes of industrial configurations can be penalizing for parallel computing. The computing strategy implemented in a modern flow solver is investigated in this paper, with a particular interest in mesh partitioning, communications and load balancing. Advantages and drawbacks of different computing platforms are then discussed, ranging from vector supercomputers to massively scalar platforms. Comparisons are performed regarding criteria such as the elapsed time and the electrical power consumption. The results show that the use of a large number of computing cores (>128) is heavily penalized by communications and load balancing errors, whereas computing performance with a moderate number of computing cores (

This paper deals with aerodynamic shape optimization using a high-fidelity solver. Because of the computational cost needed to solve the Reynolds-averaged Navier–Stokes equations, the performance of the shape must be improved using very few objective function evaluations, despite the high number of design variables. In our framework, the reference algorithm is a quasi-Newton gradient optimizer. An adjoint method inexpensively computes the sensitivities of the functions, with respect to design variables, to build the gradient of the objective function. As usual, aerodynamic functions show numerous local optima when the shape varies, and a more global optimizer is expected to be beneficial. Consequently, a kriging-based optimizer is set up and described. It uses an original sampling refinement process that adds up to three points per iteration by using a balancing between function minimization and error minimization. To efficiently apply this algorithm to high-dimensional problems, the same sampling process is reused to form a cokriging (gradient-enhanced model) based optimizer. A comparative study is then described on two drag-minimization problems depending on 6 and 45 design variables. This study was conducted using an original set of performance criteria, characterizing the strength and weakness of each optimizer in terms of improvement, cost, exploration, and exploitation.

A parallel automated Chimera overset grid algorithm for complex configurations is presented in this paper. The algorithm is based on the implicit hole cutting (IHC) algorithm presented by Lee and Baeder, which is enhanced by several methodologies to eliminate shortcomings in the original method. The resulting overall algorithm is more general than the IHC algorithm, while preserving the high degree of automation of the original method. The approach is well suited for handling steady flow problems. The effectiveness of the presented method is demonstrated with several aerodynamic test cases. Copyright © 2010 John Wiley & Sons, Ltd.

Many industrial applications involve flows periodic in time. Such flows are not simulated with enough efficiency when using classical unsteady techniques, as a transient regime must be bypassed. New techniques, dedicated to time-periodic flows and based on Fourier analysis, have been developed recently. Among these, the time spectral method casts a time-periodic flow computation in several coupled steady computations, corresponding to a uniform sampling of the period. Up until now, the steady states were reached using an explicit pseudotime algorithm. Thus, very small time steps were needed and the convergence rate slowed down when increasing the number of harmonics. In this paper, a block-Jacobi approach is presented to solve the stationary problems with an implicit algorithm. Numerical simulations show, on one hand, the good quality of the results and, on the other hand, the interest of the proposed method to reduce the sensitivity of computations to a large number of harmonics.

A surrogate-model based shape optimization method is presented and applied to the case of the multidisciplinary shape optimization of a 2D NACA subsonic airfoil. The cost function is designed so that both the far-field radiated noise and the aerodynamic forces are controlled. The surrogate model is based on the Kriging optimal interpolation technique. In order to increase the efficiency of the method, a dynamic Kriging method is developed, which can be interpreted as an Adaptive Mesh Refinement method in the shape optimization parameters.

International audience; This paper presents the application of the gradient span analysis (GSA) method to the multipoint optimization of the two-dimensional LS89 turbine distributor. The cost function (total pressure loss) and the constraint (mass flow rate) are computed from the resolution of the Reynolds-averaged Navier-Stokes equations. The penalty method is used to replace the constrained optimization problem with an unconstrained problem. The optimization process is steered by a gradient-based quasi-Newton algorithm. The gradient of the cost function with respect to design variables is obtained with the discrete adjoint method, which ensures an efficient computation time independent of the number of design variables. The GSA method gives a minimal set of operating conditions to insert into the weighted sum model to solve the multipoint optimization problem. The weights associated to these conditions are computed with the utopia point method. The single-point optimization at the nominal condition and the multipoint optimization over a wide range of conditions of the LS89 blade are compared. The comparison shows the strong advantages of the multipoint optimization with the GSA method and utopia-point weighting over the traditional single-point optimization.

Presently, improving the accuracy and reducing computational costs are still two major CFD objectives often considered incompatible. This paper proposes to solve this dilemma by developing an adaptive mesh refinement method in order to integrate the 3D Euler and Navier–Stokes equations on structured meshes, where a local multigrid method is used to accelerate convergence for steady compressible flows. The time integration method is a LU-SGS method (AIAA J 1988; 26: 1025–1026) associated with a spatial Jameson-type scheme (Numerical solutions of the Euler equations by finite volume methods using Runge–Kutta time-stepping schemes. AIAA Paper, 81-1259, 1981). Computations of turbulent flows are handled by the standard k–ω model of Wilcox (AIAA J 1994; 32: 247–255). A coarse grid correction, based on composite residuals, has been devised in order to enforce the coupling between the different grid levels and to accelerate the convergence. The efficiency of the method is evaluated on standard 2D and 3D aerodynamic configurations. Copyright © 2004 John Wiley & Sons, Ltd.

This paper addresses the problem of multiple operating conditions design, in the context of optimal aircraft mission performance and from the aerodynamic point of view. In particular, the choice of the flight conditions to be included in the optimization problem from desired condition ranges has to be done such that the optimization problem is wellpoised with a minimal computational cost. To this aim, a new method called Gradient Span Analysis is given, based on the analysis of the linear dependencies provided by adjoint sensitivities. A wing-body configuration is presented as test case and optimization results show the interest in terms of computational time savings. Physical interpretation of the method is also given.

International audience; A computational methodology is presented to obtain a model reduction of the steady compressible Reynolds-Averaged Navier–Stokes equations with a high-dimensional parameter space. It combines both a reduced-basis method and an adaptive sequential sampling technique. The reduced basis is made of the leading eigenvectors computed by a Singular Value Decomposition of the snapshot span basis. The sampling method uses an a posteriori error estimator combined with a leave-one-out algorithm. This methodology allows a dynamic building of surrogate models for aerodynamic flight data generation and for multidisciplinary design optimization with a small number of full numerical flow simulations. The efficiency of the method is assessed on an analytic test case and a classical aerodynamic transonic flow around a 2D profile.

We describe work performed inside the elsA (http://elsa.onera.fr) block-structured CFD software to analyse and improve parallel computation efficiency. Details of MPI implementation are discussed. Computational results are given for realistic industrial configurations (28 106 mesh points) on several massively parallel platforms up to 1024 processors.

This study deals with unsteady numerical simulation of casing treatment in a stage of an axial compressor. The stall inception process is first investigated in the compressor with smooth wall. At low mass flow, the simulation shows the development of large reversed flow regions near the casing that leads to rotating stall. Then, a simulation is performed for a compressor stage with casing treatment. Despite a strong impact on the rotor casing flow, the operating range extension is low, meaning that other processes like rotor/stator interactions may play a role in the loss of stability.

This study takes place in the frame of a research project to simulate the flow in a multistage High Pressure Compressor (HPC). The present paper focuses on the effect of tip gap deteriorations that occur in a high pressure compressor due to thermal constraints. To simulate this challenging industrial problem, the compressor is considered with two radial tip gap dimensions. The flow is computed by the mean of a 3D unsteady RANS calculation and is compared with experimental measurements, showing that a good decription of the mean flow is obtained with the proposed numerical model. The results show that the last stage is responsible for the loss of stability. An increase of the radial tip gap leads to a dramatic reduction of operability (by 20%), pressure ratio and efficiency. Finally, detailed investigation of the flow at offdesign conditions are presented to obtain a better understanding of the flow in this multistage compressor.

Efficient numerical tools coupled with high-performance computers, have become a key element of the design process in the fields of energy supply and transportation. However flow phenomena that occur in complex systems such as gas turbines and aircrafts are still not understood mainly because of the models that are needed. In fact, most computational fluid dynamics (CFD) predictions as found today in industry focus on a reduced or simplified version of the real system (such as a periodic sector) and are usually solved with a steady- state assumption. This paper shows how to overcome such barriers and how such a new challenge can be addressed by developing flow solvers running on high-end computing platforms, using thousands of computing cores. Parallel strategies used by modern flow solvers are discussed with particular emphases on mesh-partitioning, load balancing and communication. Two examples are used to illustrate these concepts: a multi-block structured code and an unstructured code. Parallel computing strategies used with both flow solvers are detailed and compared. This comparison indicates that mesh-partitioning and load balancing are more straightforward with unstructured grids than with multi-block structured meshes. However, the mesh-partitioning stage can be challenging for unstructured grids, mainly due to memory limitations of the newly developed massively parallel architectures. Finally, detailed investigations show that the impact of mesh-partitioning on the numerical CFD solutions, due to rounding errors and block splitting, may be of importance and should be accurately addressed before qualifying massively parallel CFD tools for a routine industrial use.