Marianna Braza

Physical analysis of the transition to turbulence in the wake of a circular cylinder by three-dimensional Navier–Stokes simulation

The transition to turbulence of the flow around a circular cylinder is studied by a three-dimensional numerical simulation of the Navier–Stokes equations system in the Reynolds number range 100–300. The numerical method is second-order accurate in space and time and Neumann boundary conditions are used at the two boundaries in the spanwise direction; non-reflecting boundary conditions are specified for the outlet downstream boundary. This study predicts the frequency modulation and the formation of a discontinuity region delimited by two frequency steps within the present Reynolds number range. These features are related to the birth of streamwise vorticity and to the kinetic energy distribution in the near wake. The development of the mean dynamic quantities, the Reynolds stress correlations and the variation of their maximum values are provided in this region, where the similarity laws do not hold. The spatial evolution of the von Karman mode and of its spectral amplitude are quantified and the variation laws of the maximum spectral amplitude and of its location as a function of Reynolds number are established. The critical Reynolds number for the appearance of the first discontinuity in the present flow system is evaluated by the fully nonlinear approach.

Successive stages and the role of natural vortex dislocations in three-dimensional wake transition

The time-history of the development of the three-dimensional transition features in a nominally two-dimensional flow configuration is established for Reynolds number 220 in a cylinder wake. The identification of the successive stages that evolve very fast during experiments is possible by means of direct numerical simulation. The physical processes related to the creation of streamwise and vertical vorticity components and their impact on the spanwise waviness of the main von Karman vortex filaments are analysed by means of the Craik–Leibovich shearing instability mechanism and a comparative discussion is given with respect to the elliptic stability theory. This study proves the existence of a further stage in the three-dimensional transition, which substantially modifies the regular spanwise undulation. This is a systematic and repetitive development of natural vortex dislocations in the near wake. The definition of this kind of structure is provided, as well as its properties related to a drastic reduction of the fundamental frequency and to the selection of a lower path in the Strouhal–Reynolds number relation. The induced amplitude modulation of the flow properties along the span is also evaluated. Quantification of these properties is carried out by using wavelet analysis and autoregressive modelling of the time series. The reasons for the development of natural vortex dislocations are analysed and related to specific modulations of the spanwise structure of the longitudinal velocity upstream separation. From this part of the study an optimum shape for the spanwise distribution of this component can be specified, able to trigger the vortex dislocations in wake flows and therefore useful to apply in the context of stability theory analyses and in further DNS studies.

Organized modes and the three-dimensional transition to turbulence in the incompressible flow around a NACA0012 wing

The transition to turbulence in the incompressible flow around a NACA0012 wingat high incidence is studied by DNS in the Reynolds number range 800–10000. Twomain routes are identified for the two-dimensional transition mechanisms: that toaperiodicity beyond the von Karm´ an mode via a period-doubling scenario and the´development of a shear-layer instability, forced by the fundamental oscillation ofthe separation point downstream of the leading edge. The evolution of the globalparameters as well as the variation law of the shear-layer instability wavelengthare quantified. The history of the three-dimensional transition mechanisms from anominally two-dimensional flow structure is identified beyond the first bifurcation, aswell as the preferred spanwise wavelengths.

The three-dimensional transition in the flow around a rotating cylinder

The flow around a circular cylinder rotating with a constant angular velocity, placed in a uniform stream, is investigated by means of two- and three-dimensional direct numerical simulations. The successive changes in the flow pattern are studied as a function of the rotation rate. Suppression of vortex shedding occurs as the rotation rate increases (>2). A second kind of instabilty appears for higher rotation speed where a series of counter-clockwise vortices is shed in the upper shear layer. Threedimensional computations are carried out to analyse the three-dimensional transition under the effect of rotation for low rotation rates. The rotation attenuates the secondary instability and increases the critical Reynolds number for the appearance of this instability. The linear and nonlinear parts of the three-dimensional transition have been quantified by means of the amplitude evolution versus time, using the Landau global oscillator model. Proper orthogonal decomposition of the three-dimensional fields allowed identification of the most energetic modes and three-dimensional flow reconstruction involving a reduced number of modes.

Near-Wake Turbulence Properties around a Circular Cylinder at High Reynolds Number

The present study investigates the turbulent properties of the flow around a circular cylinder in the near-wake and in the near-wall upstream region at the Reynolds number 140,000. A detailed cartography of the mean and turbulent velocity fields using a moderate blockage and aspect ratio is provided in order to use the present results for direct comparisons with realisable 3D Navier-Stokes computations. The flow structure is analysed by means of two experiments using respectively the LDV and the PIV techniques, both providing a refined grid of measurement points. The dynamics of the separation region, the growth and decay of turbulence in the near wake, as well as the spatial growth of the organised mode are analysed.

Prediction of Transonic Buffet by Delayed Detached-Eddy Simulation

A delayed detached-eddy simulation of the transonic buffet over a supercritical airfoil is performed. The turbulence modeling approach is based on a one-equation closure, and the results are compared to an unsteady Reynolds-averaged Navier–Stokes simulation using the same baseline model as well as experimental data. The delayed detached-eddy simulation successfully predicts the self-sustained unsteady shock-wave/boundary-layer interaction associated with buffet. When separation occurs, the flow exhibits alternate vortex shedding and a spanwise undulation. The method also captures secondary fluctuations in the boundary layer that are not predicted by unsteady Reynolds-averaged Navier–Stokes simulation. A map of flow separation emphasizes the differences between the delayed detached-eddy simulation and unsteady Reynolds-averaged Navier–Stokes flow topologies. Statistical pressure distributions and velocity profiles help assess the performance of each model. They indicate that the delayed detached-eddy simul...

Reduced-order modeling of transonic flows around an airfoil submitted to small deformations

A reduced-order model (ROM) is developed for the prediction of unsteady transonic flows past an airfoil submitted to small deformations, at moderate Reynolds number. Considering a suitable state formulation as well as a consistent inner product, the Galerkin projection of the compressible flow Navier-Stokes equations, the high-fidelity (HF) model, onto a low-dimensional basis determined by Proper Orthogonal Decomposition (POD), leads to a polynomial quadratic ODE system relevant to the prediction of main flow features. A fictitious domain deformation technique is yielded by the Hadamard formulation of HF model and validated at HF level. This approach captures airfoil profile deformation by a modification of the boundary conditions whereas the spatial domain remains unchanged. A mixed POD gathering information from snapshot series associated with several airfoil profiles can be defined. The temporal coefficients in POD expansion are shape-dependent while spatial POD modes are not. In the ROM, airfoil deformation is introduced by a steady forcing term. ROM reliability towards airfoil deformation is demonstrated for the prediction of HF-resolved as well as unknown intermediate configurations.

Reduced-order modeling for unsteady transonic flows around an airfoil

High-transonic unsteady flows around an airfoil at zero angle of incidence and moderate Reynolds numbers are characterized by an unsteadiness induced by the von Karman instability and buffet phenomenon interaction. These flows are investigated by means of low-dimensional modeling approaches. Reduced-order dynamical systems based on proper orthogonal decomposition are derived from a Galerkin projection of two-dimensional compressible Navier-Stokes equations. A specific formulation concerning density and pressure is considered. Reduced-order modeling accurately predicts unsteady transonic phenomena.

Capturing transition features around a wing by reduced-order modeling based on compressible Navier-Stokes equations

The three-dimensional transition in the flow around a NACA0012 wing of constant spanwise section at Mach number 0.3, Reynolds number 800, and incidence 20° is investigated by direct numerical simulation and reduced-order modeling. The interaction between the von Karman and the secondary instabilities is analyzed. Irregular events in the flow transition modulating the spanwise undulation are highlighted and quantified. These transition features, including “local intermittencies” in the secondary instability pattern, are efficiently captured by a reduced-order model derived by means of the Galerkin projection of the compressible flow Navier–Stokes equations onto a truncated proper orthogonal decomposition basis.

Anisotropic eddy-viscosity concept for strongly detached unsteady flows

The accurate prediction of the flow physics around bodies at high Reynolds number is a challenge in aerodynamics nowadays. In the context of turbulent flow modeling, recent advances like large eddy simulation (LES) and hybrid methods [detached eddy simulation (DES)] have considerably improved the physical relevance of the numerical simulation. However, the LES approach is still limited to the low-Reynolds-number range concerning wall flows. The unsteady Reynolds-averaged Navier–Stokes (URANS) approach remains a widespread and robust methodology for complex flow computation, especially in the near-wall region. Complex statistical models like second-order closure schemes [differential Reynolds stress modeling (DRSM)] improve the prediction of these properties and can provide an efficient simulationofturbulent stresses. Fromacomputational pointofview, the main drawbacks of such approaches are a higher cost, especially in unsteady 3-D flows and above all, numerical instabilities.