Davide Lasagna

Bio: Davide Lasagna is an academic researcher from University of Southampton. The author has contributed to research in topics: Flow (mathematics) & Galerkin method. The author has an hindex of 8, co-authored 40 publications receiving 189 citations. Previous affiliations of Davide Lasagna include Polytechnic University of Turin.

Multi-time delay, multi-point linear stochastic estimation of a cavity shear layer velocity from wall-pressure measurements

Abstract: In this paper, the recently introduced multi-time-delay linear stochastic estimation technique is thoroughly described, focusing on its fundamental properties and potentialities. In the multi-time-delay approach, the estimate of the temporal evolution of the velocity at a given location in the flow field is obtained from multiple past samples of the unconditional sources. The technique is applied to estimate the velocity in a cavity shear layer flow, based on wall-pressure measurements from multiple sensors. The cavity flow was investigated by performing simultaneous measurements of a single hot-wire probe, traversed on a fine grid in the shear layer, and of multiple wall-mounted condenser microphones in the cavity region. The paper compares classical high-order single-time-delay estimation approaches with the multi-time-delay technique, which is significantly more accurate as it produces a much lower mean-square estimation error, thus providing a faithful reconstruction of the time-evolution of the velocity field. This improved accuracy is strongly dependent on the number n of past wall-pressure samples used in the estimate. In this paper, we also demonstrate that the estimated velocity field only contains the signature of the relevant flow mechanisms which correlate well with the wall-pressure, while incoherent components are filtered out. The multi-time-delay approach successfully captures the spatio-temporal dynamics of the velocity fluctuation distribution in the shear layer, as it clearly resolves the dynamics of the relevant flow structures. The effect of the number of sensors used in the estimate was also considered. In general, it was evident that use of more sensors leads to better accuracy, but as the number n of past values increases, the gain becomes marginal.

Sum-of-squares of polynomials approach to nonlinear stability of fluid flows: an example of application.

Abstract: With the goal of providing the first example of application of a recently proposed method, thus demonstrating its ability to give results in principle, global stability of a version of the rotating Couette flow is examined. The flow depends on the Reynolds number and a parameter characterizing the magnitude of the Coriolis force. By converting the original Navier–Stokes equations to a finite-dimensional uncertain dynamical system using a partial Galerkin expansion, high-degree polynomial Lyapunov functionals were found by sum-of-squares of polynomials optimization. It is demonstrated that the proposed method allows obtaining the exact global stability limit for this flow in a range of values of the parameter characterizing the Coriolis force. Outside this range a lower bound for the global stability limit was obtained, which is still better than the energy stability limit. In the course of the study, several results meaningful in the context of the method used were also obtained. Overall, the results obtained demonstrate the applicability of the recently proposed approach to global stability of the fluid flows. To the best of our knowledge, it is the first case in which global stability of a fluid flow has been proved by a generic method for the value of a Reynolds number greater than that which could be achieved with the energy stability approach.

Effects of a trapped vortex cell on a thick wing airfoil

Abstract: The effects of a trapped vortex cell (TVC) on the aerodynamic performance of a NACA0024 wing model were investigated experimentally at Re = 106 and $$6.67\times 10^{5}$$ . The static pressure distributions around the model and the wake velocity profiles were measured to obtain lift and drag coefficients, for both the clean airfoil and the controlled configurations. Suction was applied in the cavity region to stabilize the trapped vortex. For comparison, a classical boundary layer suction configuration was also tested. The drag coefficient curve of the TVC-controlled airfoil showed sharp discontinuities and bifurcative behavior, generating two drag modes. A strong influence of the angle of attack, the suction rate and the Reynolds number on the drag coefficient was observed. With respect to the clean airfoil, the control led to a drag reduction only if the suction was high enough. Compared to the classical boundary layer suction configuration, the drag reduction was higher for the same amount of suction only in a specific range of incidence, i.e., α = −2° to α = 6° and only for the higher Reynolds number. For all the other conditions, the classical boundary layer suction configuration gave better drag performances. Moderate increments of lift were observed for the TVC-controlled airfoil at low incidence, while a 20% lift enhancement was observed in the stall region with respect to the baseline. However, the same lift increments were also observed for the classical boundary layer suction configuration. Pressure fluctuation measurements in the cavity region suggested a very complex interaction of several flow features. The two drag modes were characterized by typical unsteady phenomena observed in rectangular cavity flows, namely the shear layer mode and the wake mode.

Sensitivity Analysis of Chaotic Systems using Unstable Periodic Orbits

Abstract: A well-behaved adjoint sensitivity technique for chaotic dynamical systems is presented. The method arises from the specialisation of established variational techniques to the unstable periodic orbits of the system. On such trajectories, the adjoint problem becomes a time periodic boundary value problem. The adjoint solution remains bounded in time and does not exhibit the typical unbounded exponential growth observed using traditional methods over unstable non-periodic trajectories (Lea et al., Tellus 52 (2000)). This enables the sensitivity of period averaged quantities to be calculated exactly, regardless of the orbit period, because the stability of the tangent dynamics is decoupled effectively from the sensitivity calculations. We demonstrate the method on two prototypical systems, the Lorenz equations at standard parameters and the Kuramoto-Sivashinky equation, a one-dimensional partial differential equation with chaotic behaviour. We report a statistical analysis of the sensitivity of these two systems based on databases of unstable periodic orbits of size 10^5 and 4x10^4, respectively. The empirical observation is that most orbits predict approximately the same sensitivity. The effects of symmetries, bifurcations and intermittency are discussed and future work is outlined in the conclusions.

Spectral proper orthogonal decomposition

Abstract: The identification of coherent structures from experimental or numerical data is an essential task when conducting research in fluid dynamics. This typically involves the construction of an empirical mode base that appropriately captures the dominant flow structures. The most prominent candidates are the energy-ranked proper orthogonal decomposition (POD) and the frequency-ranked Fourier decomposition and dynamic mode decomposition (DMD). However, these methods are not suitable when the relevant coherent structures occur at low energies or at multiple frequencies, which is often the case. To overcome the deficit of these ‘rigid’ approaches, we propose a new method termed spectral proper orthogonal decomposition (SPOD). It is based on classical POD and it can be applied to spatially and temporally resolved data. The new method involves an additional temporal constraint that enables a clear separation of phenomena that occur at multiple frequencies and energies. SPOD allows for a continuous shifting from the energetically optimal POD to the spectrally pure Fourier decomposition by changing a single parameter. In this article, SPOD is motivated from phenomenological considerations of the POD autocorrelation matrix and justified from dynamical systems theory. The new method is further applied to three sets of PIV measurements of flows from very different engineering problems. We consider the flow of a swirl-stabilized combustor, the wake of an airfoil with a Gurney flap and the flow field of the sweeping jet behind a fluidic oscillator. For these examples, the commonly used methods fail to assign the relevant coherent structures to single modes. The SPOD, however, achieves a proper separation of spatially and temporally coherent structures, which are either hidden in stochastic turbulent fluctuations or spread over a wide frequency range. The SPOD requires only one additional parameter, which can be estimated from the basic time scales of the flow. In spite of all these benefits, the algorithmic complexity and computational cost of the SPOD are only marginally greater than those of the snapshot POD.

Adaptive Boundary Iterative Learning Control for an Euler–Bernoulli Beam System With Input Constraint

Abstract: This paper addresses the vibration control and the input constraint for an Euler–Bernoulli beam system under aperiodic distributed disturbance and aperiodic boundary disturbance. Hyperbolic tangent functions and saturation functions are adopted to tackle the input constraint. A restrained adaptive boundary iterative learning control (ABILC) law is proposed based on a time-weighted Lyapunov–Krasovskii-like composite energy function. In order to deal with the uncertainty of a system parameter and reject the external disturbances, three adaptive laws are designed and learned in the iteration domain. All the system states of the closed-loop system are proved to be bounded in each iteration. Along the iteration axis, the displacements asymptotically converge toward zero. Simulation results are provided to illustrate the effectiveness of the proposed ABILC scheme.

Spectral proper orthogonal decomposition

Abstract: The identification of coherent structures from experimental or numerical data is an essential task when conducting research in fluid dynamics. This typically involves the construction of an empirical mode base that appropriately captures the dominant flow structures. The most prominent candidates are the energy-ranked proper orthogonal decomposition (POD) and the frequency ranked Fourier decomposition and dynamic mode decomposition (DMD). However, these methods fail when the relevant coherent structures occur at low energies or at multiple frequencies, which is often the case. To overcome the deficit of these "rigid" approaches, we propose a new method termed Spectral Proper Orthogonal Decomposition (SPOD). It is based on classical POD and it can be applied to spatially and temporally resolved data. The new method involves an additional temporal constraint that enables a clear separation of phenomena that occur at multiple frequencies and energies. SPOD allows for a continuous shifting from the energetically optimal POD to the spectrally pure Fourier decomposition by changing a single parameter. In this article, SPOD is motivated from phenomenological considerations of the POD autocorrelation matrix and justified from dynamical system theory. The new method is further applied to three sets of PIV measurements of flows from very different engineering problems. We consider the flow of a swirl-stabilized combustor, the wake of an airfoil with a Gurney flap, and the flow field of the sweeping jet behind a fluidic oscillator. For these examples, the commonly used methods fail to assign the relevant coherent structures to single modes. The SPOD, however, achieves a proper separation of spatially and temporally coherent structures, which are either hidden in stochastic turbulent fluctuations or spread over a wide frequency range.