arXiv subjects

Denis Sipp

Publications and source records attributed to Denis Sipp.

23 records · Page 2Linked to original sources

arXiv2020

Mean-flow Data Assimilation based on minimal correction of turbulence models: application to turbulent high-Reynolds number backward-facing step

In this article, we provide a methodology to reconstruct high-Reynolds number turbulent mean-flows from few time-averaged measurements. A turbulent flow over a backward-facing step at Re = 28275 is considered to illustrate the potential of the approach. The data-assimilation procedure, based on a variational approach, consists in correcting a given baseline model by tuning space-dependent source terms such that the corresponding solution matches available measurements (obtained here from direct-numerical simulations). The baseline model chosen here consists in Reynolds-Averaged-Navier-Stokes (RANS) equations closed with the turbulence Spalart-Allmaras model. We investigate two possible tuning functions: a source term in the momentum equations, which is able to compensate for the deficiencies in the modeling of the Reynolds stresses by the Boussinesq approximation and a source term in the turbulence equation, which modifies the balance between the eddy-viscosity production and dissipation. The quality of the mean-flow reconstruction strongly depends on the baseline model and on the quantity of measurements. In the case of many measurements, very accurate reconstructions of the mean-flow are obtained with the model corrected by the source term in the momentum equations, while the reconstruction is more approximate when tuning the source term in the turbulence model. In the case of few measurements, this "rigidity" of the corrected turbulence model is favourably used and allows the best mean-flow reconstruction. The flexibility / rigidity of a model is further discussed in the light of a singular-value decomposition of the linear input / output operator between source term and measurements.

physics.flu-dyn↗

arXiv2020

Nonlinear model reduction: a comparison between POD-Galerkin and POD-DEIM methods

Several nonlinear model reduction techniques are compared for the three cases of the non-parallel version of the Kuramoto-Sivashinsky equation, the transient regime of flow past a cylinder at $Re=100$ and fully developed flow past a cylinder at the same Reynolds number. The linear terms of the governing equations are reduced by Galerkin projection onto a POD basis of the flow state, while the reduced nonlinear convection terms are obtained either by a Galerkin projection onto the same state basis, by a Galerkin projection onto a POD basis representing the nonlinearities or by applying the Discrete Empirical Interpolation Method (DEIM) to a POD basis of the nonlinearities. The quality of the reduced order models is assessed as to their stability, accuracy and robustness, and appropriate quantitative measures are introduced and compared. In particular, the properties of the reduced linear terms are compared to those of the full-scale terms, and the structure of the nonlinear quadratic terms is analyzed as to the conservation of kinetic energy. It is shown that all three reduction techniques provide excellent and similar results for the cases of the Kuramoto-Sivashinsky equation and the limit-cycle cylinder flow. For the case of the transient regime of flow past a cylinder, only the pure Galerkin techniques are successful, while the DEIM technique produces reduced-order models that diverge in finite time.

physics.comp-ph↗

arXiv2020

Non-linear input/output analysis: application to boundary layer transition

We extend linear input/output (resolvent) analysis to take into account nonlinear triadic interactions by considering a finite number of harmonics in the frequency domain using the harmonic balance method. Forcing mechanisms that maximize the drag are calculated using a gradient-based ascent algorithm. By including nonlinearity in the analysis, the proposed frequency-domain framework identifies the worst-case disturbances for laminar-turbulent transition. We demonstrate the framework on a flat-plate boundary layer by considering three-dimensional spanwise-periodic perturbations triggered by a few optimal forcing modes of finite amplitude. Two types of volumetric forcing are considered, one corresponding to a single frequency/spanwise-wavenumber pair, and a multi-harmonic where a harmonic frequency and wavenumber are also added. Depending on the forcing strategy, we recover a range of transition scenarios associated with K-type and H-type mechanisms, including oblique and Tollmien-Schlichting waves, streaks and their breakdown. We show that nonlinearity plays a critical role in optimizing growth by combining and redistributing energy between the linear mechanisms and the higher perturbation harmonics. With a very limited range of frequencies and wavenumbers, the calculations appear to reach the early stages of the turbulent regime through the generation and breakdown of hairpin and quasi-streamwise staggered vortices.

physics.flu-dyn↗

arXiv2019

A tale of two airfoils: resolvent-based modelling of an oscillator vs. an amplifier from an experimental mean

The flows around a NACA 0018 airfoil at a Reynolds number of 10250 and angles of attack of alpha = 0 (A0) and alpha = 10 (A10) are modelled using resolvent analysis and limited experimental measurements obtained from particle image velocimetry. The experimental mean velocity profiles are data-assimilated so that they are solutions of the incompressible Reynolds-averaged Navier-Stokes equations forced by Reynolds stress terms which are derived from experimental data. Spectral proper orthogonal decompositions (SPOD) of the velocity fluctuations and nonlinear forcing find low-rank behaviour at the shedding frequency and its higher harmonics for the A0 case. In the A10 case, low-rank behaviour is observed for the velocity fluctuations in two bands of frequencies. Resolvent analysis of the data-assimilated means identifies low-rank behaviour only in the vicinity of the shedding frequency for A0 and none of its harmonics. The resolvent operator for the A10 case, on the other hand, identifies two linear mechanisms whose frequencies are a close match with those identified by SPOD. It is also shown that the second linear mechanism, corresponding to the Kelvin-Helmholtz instability in the shear layer, cannot be identified just by considering the time-averaged experimental measurements as a mean flow due to the fact that experimental data are missing near the leading edge. The A0 case is classified as an oscillator where the flow is organised around an intrinsic instability while the A10 case behaves like an amplifier whose forcing is unstructured. For both cases, resolvent modes resemble those from SPOD when the operator is low-rank. To model the higher harmonics where this is not the case, we add parasitic resolvent modes, as opposed to classical resolvent modes which are the most amplified, by approximating the nonlinear forcing from limited triadic interactions of known resolvent modes.

physics.flu-dyn↗

arXiv2014

Computation of eigenvalue sensitivity to base flow modifications in a discrete framework: Application to open-loop control

A fully discrete formalism is introduced to perform stability analysis of a turbulent compressible flow whom dynamics is modeled with the Reynolds-Averaged Navier-Stokes (RANS) equations. The discrete equations are linearized using finite differences and the Jacobian is computed using repeated evaluation of the residuals. Stability of the flow is assessed solving an eigenvalue problem. The sensitivity gradients which indicate regions of the flow where a passive control device could stabilize the unstable eigenvalues are defined within this fully discrete framework. Second order finite differences are applied to the discrete residual to compute the gradients. In particular, the sensitivity gradients are shown to be linked to the Hessian of the RANS equations. The introduced formalism and linearization method are generic: the code used to evaluate the residual of the RANS equations can be used in a black box manner, and the complex linearization of the Hessian is avoided. The method is tested on a two dimensional deep cavity case, the flow is turbulent with a Reynolds number equal to 860 000 and compressible with a Mach number of 0.8. Several turbulence models and numerical schemes are used to validate the method. Physical features of the flow are recovered, such as the fundamental frequency of the natural flow as well as acoustic mechanisms, suggesting the validity of the method. The sensitivity gradients are then computed and validated, the error in predicting the eigenvalue variation being found less than 3\%. Control maps using a small steady control device are finally obtained, indicating that the control area should be chosen in the vicinity of the leading edge of the cavity.

physics.flu-dyn↗