Edouard Boujo

Sensitivity of aerodynamic forces in laminar and turbulent flow past a square cylinder

We use adjoint-based gradients to analyze the sensitivity of the drag force on a square cylinder. At Re = 40, the flow settles down to a steady state. The quantity of interest in the adjoint formulation is the steady asymptotic value of drag reached after the initial transient, whose sensitivity is computed solving a steady adjoint problem from knowledge of the stable base solution. At Re = 100, the flow develops to the time-periodic, vortex-shedding state. The quantity of interest is rather the time-averaged mean drag, whose sensitivity is computed integrating backwards in time an unsteady adjoint problem from knowledge of the entire history of the vortex-shedding solution. Such theoretical frameworks allow us to identify the sensitive regions without computing the actually controlled states, and provide a relevant and systematic guideline on where in the flow to insert a secondary control cylinder in the attempt to reduce drag, as established from comparisons with dedicated numerical simulations of the two-cylinder system. For the unsteady case at Re = 100, we also compute an approximation to the mean drag sensitivity solving a steady adjoint problem from knowledge of only the mean flow solution, and show the approach to carry valuable information in view of guiding relevant control strategy, besides reducing tremendously the related numerical effort. An extension of this simplified framework to turbulent flow regime is examined revisiting the widely benchmarked flow at Reynolds number Re = 22 000, the theoretical predictions obtained in the frame of unsteady Reynolds-averaged Navier–Stokes modeling being consistent with experimental data from the literature. Application of the various sensitivity frameworks to alternative control objectives such as increasing the lift and reducing the fluctuating drag and lift is also discussed and illustrated with a few selected examples.

Controlled reattachment in separated flows: a variational approach to recirculation length reduction

A variational technique is used to derive analytical expressions for the sensitivity of recirculation length to steady forcing in separated flows. Linear sensitivity analysis is applied to the two-dimensional steady flow past a circular cylinder for Reynolds numbers

Open-loop control of noise amplification in a separated boundary layer flow

40 \leq Re \leq 120

Quantifying acoustic damping using flame chemiluminescence

, both in the subcritical and supercritical regimes. Regions which are the most sensitive to volume forcing and wall blowing/suction are identified. Control configurations which reduce the recirculation length are designed based on the sensitivity information, in particular small cylinders used as control devices in the wake of the main cylinder, and fluid suction at the cylinder wall. Validation against full non-linear Navier-Stokes calculations shows excellent agreement for small-amplitude control. The linear stability properties of the controlled flow are systematically investigated. At moderate Reynolds numbers, we observe that regions where control reduces the recirculation length correspond to regions where it has a stabilising effect on the most unstable global mode associated to vortex shedding, while this property does not hold any more at larger Reynolds numbers.

Sensitivity and open-loop control of stochastic response in a noise amplifier flow: the backward-facing step

Linear optimal gains are computed for the subcritical two-dimensional separated boundary-layer flow past a bump. Very large optimal gain values are found, making it possible for small-amplitude noise to be strongly amplified and to destabilize the flow. The optimal forcing is located close to the summit of the bump, while the optimal response is the largest in the shear layer. The largest amplification occurs at frequencies corresponding to eigenvalues which first become unstable at higher Reynolds number. Nonlinear direct numerical simulations show that a low level of noise is indeed sufficient to trigger random flow unsteadiness, characterized here by large-scale vortex shedding. Next, a variational technique is used to compute efficiently the sensitivity of optimal gains to steady control (through source of momentum in the flow, or blowing/suction at the wall). A systematic analysis at several frequencies identifies the bump summit as the most sensitive region for control with wall actuation. Based on ...

Manipulating flow separation: sensitivity of stagnation points, separatrix angles and recirculation area to steady actuation

Thermoacoustic instabilities in gas turbines and aeroengine combustors falls within the category of complex systems. They can be described phenomenologically using nonlinear stochastic differential equations, which constitute the grounds for output-only model-based system identification. It has been shown recently that one can extract the governing parameters of the instabilities, namely the linear growth rate and the nonlinear component of the thermoacoustic feedback, using dynamic pressure time series only. This is highly relevant for practical systems, which cannot be actively controlled due to a lack of cost-effective actuators. The thermoacoustic stability is given by the linear growth rate, which results from the combination of the acoustic damping and the coherent feedback from the flame. In this paper, it is shown that it is possible to quantify the acoustic damping of the system, and thus to separate its contribution to the linear growth rate from the one of the flame. This is achieved by post-processing in a simple way simultaneously acquired chemiluminescence and acoustic pressure data. It provides an additional approach to further unravel from observed time series the key mechanisms governing the system dynamics. This straightforward method is illustrated here using experimental data from a combustion chamber operated at several linearly stable and unstable operating conditions.

Output-only parameter identification of a colored-noise-driven Van-der-Pol oscillator: Thermoacoustic instabilities as an example

The two-dimensional backward-facing step flow is a canonical example of noise amplifier flow: global linear stability analysis predicts that it is stable, but perturbations can undergo large amplification in space and time as a result of non-normal effects. This amplification potential is best captured by optimal transient growth analysis, optimal harmonic forcing, or the response to sustained noise. In view of reducing disturbance amplification in these globally stable open flows, a variational technique is proposed to evaluate the sensitivity of stochastic amplification to steady control. Existing sensitivity methods are extended in two ways to achieve a realistic representation of incoming noise: (i) perturbations are time-stochastic rather than time-harmonic, (ii) perturbations are localised at the inlet rather than distributed in space. This allows for the identification of regions where small-amplitude control is the most effective, without actually computing any controlled flows. In particular, passive control by means of a small cylinder and active control by means of wall blowing/suction are analysed for Reynolds number

Experiments and modelling of rate-dependent transition delay in a stochastic subcritical bifurcation

Re=500

Saturation of a turbulent mixing layer over a cavity: response to harmonic forcing around mean flows

and step-to-outlet expansion ratio

Robust identification of harmonic oscillator parameters using the adjoint Fokker–Planck equation

\Gamma=0.5