Jean-Camille Chassaing

Efficient and robust Reynolds-stress model computation of three-dimensional compressible flows

Thepurposeofthiswork isthedevelopmentofanefe cientand robustimplicitmethodology fortheintegration of the three-dimensional compressible Favre ‐Reynolds-averaged Navier ‐Stokes equations with near-wall Reynoldsstressclosure.Thee vemean-e owandseventurbulencetransportequationsarediscretizedinspace,ona structured multiblock grid,using an O(¢x 3)e nitevolumeupwind-biased MUSCL schemewithVanLeere ux vectorsplitting and Van Albada limiters. Time integration is based on an implicit dual-time-stepping procedure with alternating direction implicit subiterations. A particular treatment of the approximate Jacobians used in the subiterations substantiallydiminishesthecomputing timerequirementsoftheimplicitphase,sothatthecomputationaloverhead of the Reynolds-stress seven-equation closure, compared to a two-equation closure, is less than 30% per iteration. For steady e ow computations local time steps are used, for both the subiterations and the time marching, with Courant‐Friedrichs‐Lewynumbersof O(10‐20)fortheO(1‐20)subiterationsneededand O(100‐500)forthetime marching. The robustness of the method is ensured by appropriate positivity, boundedness, and Reynolds-stress realizability constraints. The numerical method is illustrated by computing (and conducting numerical studies ) for a high subsonic (M » 0:7) three-dimensional e ow with large separation and for a transonic three-dimensional shock-wave/boundary-layer interaction.

Reynolds-Stress Model Dual-Time-Stepping Computation of Unsteady Three-Dimensional Flows

An efficient and robust implicit methodology for the integration of the unsteady three-dimensional compressible Favre-Reynolds-averaged Navier-Stokes equations with near-wall Reynolds-stress closure is developed. The five mean-flow and seven turbulence transport equations are discretized on a structured deforming grid, using an O(Δx 3 ) finite volume upwind-biased MUSCL scheme. Time integration uses an implicit O(Δt 2 ) dual-time-stepping procedure with alternating-direction-implict subiterations (with approximate Jacobians designed to minimize the computing time requirements of the implicit phase for the Reynolds stresses, so that the computational overhead of the Reynolds-stress seven-equation closure, compared to a two-equation closure, is less than 30% per iteration), based on a dynamic criterion of subiterative convergence. Grid-deformation velocities associated with solid-wall displacement are computed using a Laplacian operator. The method is validated by comparison with experimental data for 1) two-dimensional pitching oscillations of a NACA-0012 airfoil and 2) three-dimensional shock-wave oscillation in a transonic channel. The influence of the various parameters of the method is analyzed in detail

Stochastic Investigation of Flows About Airfoils at Transonic Speeds

aerodynamics nonlinearities are reported in the uncertain probabilistic space. The efficiency of the present methodology are evaluated for the propagation of random disturbances associated with the angle of attack and the freestreamMachnumber.Anerroranalysisiscarriedoutinordertodetermineappropriatephysicalandstochastic discretization levels. Different stochastic flow regimes are analyzed in details by means of various postprocessing procedures, including error bars, probabilistic density function of the aerodynamic field, and Sobol’s coefficients.

Reconstruction of unsteady viscous flows using data assimilation schemes

This paper investigates the use of various data assimilation (DA) approaches for the reconstruction of the unsteady flow past a cylinder in the presence of incident coherent gusts. Variational, ensemble Kalman filter-based and ensemble-based variational DA techniques are deployed along with a 2D compressible Navier-Stokes flow solver, which is also used to generate synthetic observations of a reference flow. The performance of these DA schemes is thoroughly analyzed for various types of observations ranging from the global aerodynamic coefficients of the cylinder to the full 2D flow field. Moreover, different reconstruction scenarios are investigated in order to assess the robustness of these methods for large scale DA problems with up to 105 control variables. In particular, we show how an iterative procedure can be used within the framework of ensemble-based methods to deal with both non-uniform unsteady boundary conditions and initial field reconstruction. The different methodologies developed and assessed in this work give a review of what can be done with DA schemes in computational fluid dynamics (CFD) paradigm. In the same time, this work also provides useful information which can also turn out to be rational arguments in the DA scheme choice dedicated to a specific CFD application.

Numerical Simulation of Transit-Time Ultrasonic Flowmeters by a Direct Approach

This paper deals with the development of a computational code for the numerical simulation of wave propagation through domains with a complex geometry consisting in both solids and moving fluids. The emphasis is on the numerical simulation of ultrasonic flowmeters (UFMs) by modeling the wave propagation in solids with the equations of linear elasticity (ELE) and in fluids with the linearized Euler equations (LEEs). This approach requires high performance computing because of the high number of degrees of freedom and the long propagation distances. Therefore, the numerical method should be chosen with care. In order to minimize the numerical dissipation which may occur in this kind of configuration, the numerical method employed here is the nodal discontinuous Galerkin (DG) method. Also, this method is well suited for parallel computing. To speed up the code, almost all the computational stages have been implemented to run on graphical processing unit (GPU) by using the compute unified device architecture (CUDA) programming model from NVIDIA. This approach has been validated and then used for the two-dimensional simulation of gas UFMs. The large contrast of acoustic impedance characteristic to gas UFMs makes their simulation a real challenge.

A discontinuous galerkin approach for the numerical simulation of transit-time ultrasonic flowmeters

A Discontinuous Galerkin approach is presented for the numerical simulation of acoustic waves propagation in transit-time ultrasonic flowmeters with clamp-on transducers. In this configuration, the ultrasonic beam crosses multiple solid-solid and fluid-solid interfaces which generate complex physical phenomena with an important impact on the flow rate measurement. To capture all these phenomena, the employed physical model is based on the wave theory. The wave propagation in the fluid part is described by the linearized Euler equations and in the solid part by the equations of linear elasticity. Considering the good parallelization properties of the numerical method, the simulation code was implemented to run on graphical processing units. To validate it, several test cases are performed for both separated and coupled fluid-solid media. Furthermore, a study on the impact of pipe flow profiles on the flow rate measurement is carried out.

Low Mass-Damping Vortex-Induced Vibrations of a Single Cylinder at Moderate Reynolds Number.

The feasibility and accuracy of large eddy simulation is investigated for the case of three-dimensional unsteady flows past an elastically mounted cylinder at moderate Reynolds number. Although these flow problems are unconfined, complex wake flow patterns may be observed depending on the elastic properties of the structure. An iterative procedure is used to solve the structural dynamic equation to be coupled with the Navier-Stokes system formulated in a pseudo-Eulerian way. A moving mesh method is involved to deform the computational domain according to the motion of the fluid structure interface. Numerical simulations of vortex-induced vibrations are performed for a freely vibrating cylinder at Reynolds number 3900 in the subcritical regime under two low mass-damping conditions. A detailed physical analysis is provided for a wide range of reduced velocities, and the typical three-branch response of the amplitude behavior usually reported in the experiments is exhibited and reproduced by numerical simulation.

A Moving Least Squares-Based High-Order-Preserving Sliding Mesh Technique with No Intersections

The sliding mesh approach is widely used in numerical simulation of turbomachinery flows to take in to account the rotor/stator or rotor/rotor interaction. This technique allows relative sliding of one grid adjacent to another grid (static or in motion). However, when a high-order method is used, the interpolation used in the sliding mesh model needs to be of, at least, the same order than the numerical scheme, in order to prevent loss of accuracy. In this work we present a sliding mesh model based on the use of Moving Least Squares (MLS) approximations. It is used with a high-order ( > 2) finite volume method that computes the derivatives of the Taylor reconstruction inside each control volume using MLS approximants. Thus, this new sliding mesh model fits naturally in a high-order MLS-based finite volume framework (Cueto-Felgueroso et al., Comput Methods Appl Mech Eng 196:4712–4736, 2007; Khelladi et al., Comput Methods Appl Mech Eng 200:2348–2362, 2011) for the computation of acoustic wave propagation into turbomachinery.

Vortex-Induced Vibrations of a Cylinder at Subcritical Reynolds Number

The present work focusses on the numerical study of Vortex-Induced Vibrations (VIV) of an elastically mounted cylinder in a cross flow at moderate Reynolds numbers. Low mass-damping experimental studies show that the dynamic behavior of the cylinder exhibits a three-branch response model, depending on the range of the reduced velocity. However, few numerical simulations deal with accurate computations of the VIV amplitudes at the lock-in upper branch of the bifurcation diagram. In this work, the dynamic response of the cylinder is investigated by means of three-dimensional Large Eddy Simulation (LES). An Arbitrary Lagrangian Eulerian framework is employed to account for fluid solid interface boundary motion and grid deformation. Numerous numerical simulations are performed at a Reynolds number of 3900 for both no damping and low-mass damping ratio and various reduced velocities. A detailed physical analysis is conducted to show how the present methodology is able to capture the different VIV responses.Copyright