Fulvio Martinelli

Modal and non-modal stability analysis of electrohydrodynamic flow with and without cross-flow

We report the results of a complete modal and non-modal linear stability analysis of the electrohydrodynamic flow for the problem of electroconvection in the strong-injection region. Convective cells are formed by the Coulomb force in an insulating liquid residing between two plane electrodes subject to unipolar injection. Besides pure electroconvection, we also consider the case where a cross-flow is present, generated by a streamwise pressure gradient, in the form of a laminar Poiseuille flow. The effect of charge diffusion, often neglected in previous linear stability analyses, is included in the present study and a transient growth analysis, rarely considered in electrohydrodynamics, is carried out. In the case without cross-flow, a non-zero charge diffusion leads to a lower linear stability threshold and thus to a more unstable flow. The transient growth, though enhanced by increasing charge diffusion, remains small and hence cannot fully account for the discrepancy of the linear stability threshold between theoretical and experimental results. When a cross-flow is present, increasing the strength of the electric field in the high-Re Poiseuille flow yields a more unstable flow in both modal and non-modal stability analyses. Even though the energy analysis and the input‐output analysis both indicate that the energy growth directly related to the electric field is small, the electric effect enhances the lift-up mechanism. The symmetry of channel flow with respect to the centreline is broken due to the additional electric field acting in the wall-normal direction. As a result, the centres of the streamwise rolls are shifted towards the injector electrode, and the optimal spanwise wavenumber achieving maximum transient energy growth increases with the strength of the electric field.

Feedback control of transient energy growth in subcritical plane Poiseuille flow

Subcritical flows may experience large transient perturbation energy amplifications, that could trigger nonlinear mechanisms and eventually lead to transition to turbulence. In plane Poiseuille flow, controlled via wall blowing/suction with zero net mass flux, optimal and robust control theory has been recently applied to a state-space representation of the Orr-Sommerfeld-Squire equations, leading to reduced transient growth as well as increased transition thresholds. However, to date no feedback control law has been found that is capable of ensuring the closed-loop Poiseuille flow to be monotonically stable. The present paper addresses first the possibility of complete feedback suppression of the transient growth mechanism in subcritical plane Poiseuille flow when wall actuation is available, and demonstrates that closed-loop monotonic stability cannot be achieved in such a case. Secondly, a Linear Matrix Inequality (LMI) technique is employed to design controllers that directly target the energy growth mechanism. The performance of such control laws is quantified by using Direct Numerical Simulations of transitional plane Poiseuille flow, and the increase in transition thresholds due to the control action is assessed.

Linear stability of plane Poiseuille flow over a generalized Stokes layer

Linear stability of plane Poiseuille flow subject to spanwise velocity forcing applied at the wall is studied. The forcing is stationary and sinusoidally distributed along the streamwise direction. The long-term aim of the study is to explore a possible relationship between the modification induced by the wall forcing to the stability characteristic of the unforced Poiseuille flow and the signifcant capabilities demonstrated by the same forcing in reducing turbulent friction drag. We present in this paper the statement of the mathematical problem, which is considerably more complex that the classic Orr-Sommerfeld-Squire approach, owing to the streamwise-varying boundary condition. We also report some preliminary results which, although not yet conclusive, describe the effects of the wall forcing on modal and non-modal characteristics of the flow stability.

Modeling Arterial Wall Transport for Drug-Eluting Stents

Drug-eluting stents (DES) are very commonly used for treating coronary atherosclerotic lesions. Despite the broad effectiveness of DES, ∼5% of treated patients experience complications including in-stent restenosis and late-stent thrombosis. The occurrence of these complications depends on various factors including the concentration of the eluted drug in the arterial wall and the rate of arterial re-endothelialization. Drug concentration in the arterial wall needs to be sufficiently high to be efficacious while remaining sufficiently low to avoid compromising wall stability (leading to stent malapposition). Furthermore, because drugs used in DES modulate proliferation rates of not only smooth muscle cells but also endothelial cells, the drug concentration affects re-endothelialization rates. Drug concentration in the arterial wall is determined by the transport and metabolism of the drug and may also be affected by the flow field in the lumen of the stented vessel. In the present study, we develop a computational model of drug transport in the arterial wall. Previous models have typically treated the arterial wall as a homogeneous porous medium [1] and have often ignored drug reaction with cells in the arterial wall [2]. In the present study, we have developed a model that incorporates the multi-layer structure of the arterial wall and have compared its predictions for the distribution of an eluted drug within the arterial wall with those of the single-layer homogeneous wall model.Copyright

Turbulent drag reduction by feedback: a Wiener-filtering approach

In an attempt to devise control laws for reducing drag in turbulent wall ows, modern control theory has recently been employed for the design of linear controllers [1], state estimators [2], and compensators [3; 4]. These approaches led to encouraging results, revealing the potential of linear control in targeting significant dynamics in wall turbulence [5]. All the aforementioned works, however, rely on an approximate statespace representation of the system dynamics, obtained by linearization of the governing equations about a base ow profile. The state-space formulation reduces the compensator design problem to the solution of two matrix Riccati equations, a procedure that becomes computationally cumbersome for high-dimensional systems. Effects of nonlinearities and modeling errors are accounted for by introducing state and measurement noises with known (approximately modeled) statistics.