We formulate and solve a generalized inverse Navier–Stokes problem for the joint velocity field reconstruction and boundary segmentation of noisy flow velocity images. To regularize the problem, we use a Bayesian framework with Gaussian random fields. This allows us to estimate the uncertainties of the unknowns by approximating their posterior covariance with a quasi-Newton method. We first test the method for synthetic noisy images of two-dimensional (2-D) flows and observe that the method successfully reconstructs and segments the noisy synthetic images with a signal-to-noise ratio (SNR) of three. Then we conduct a magnetic resonance velocimetry (MRV) experiment to acquire images of an axisymmetric flow for low (
${\simeq }6$
) and high (
${>}30$
) SNRs. We show that the method is capable of reconstructing and segmenting the low SNR images, producing noiseless velocity fields and a smooth segmentation, with negligible errors compared with the high SNR images. This amounts to a reduction of the total scanning time by a factor of 27. At the same time, the method provides additional knowledge about the physics of the flow (e.g. pressure) and addresses the shortcomings of MRV (i.e. low spatial resolution and partial volume effects) that otherwise hinder the accurate estimation of wall shear stresses. Although the implementation of the method is restricted to 2-D steady planar and axisymmetric flows, the formulation applies immediately to three-dimensional (3-D) steady flows and naturally extends to 3-D periodic and unsteady flows.
In the present paper, an aero-structure interaction model for the rapid simulation of morphing structures realized through shape memory alloy (SMA) actuators is presented. The aerodynamic simulation method implements a potential flow method strongly coupled with an integral boundary layer method in the context of a viscous-inviscid interaction approach, which includes a transition prediction model and a simplified shear stress-transport equation for the turbulence closure. The structural analysis model of the airfoil integrates a well-established SMA constitutive model for the prediction of the actuator behavior into finite element software. The two numerical models are loosely interconnected by exchanging geometrical and loading data at each iteration. An articulated 2-link adaptive mechanism for load alleviation purposes in horizontal axis wind turbine blades is investigated considering two different morphing scenarios: (1) operation of a single hinged flap; (2) combined movement of two sequential airfoil segments is attempted to achieve a smoother camber variation. The present fluid-structure interaction (FSI) model is employed with the aim to quantify its effect and benefits on the active shape control of the morphing airfoil, the actuator response, and the aerodynamic performance including lift and drag coefficients. The presented results demonstrate the robustness and numerical performance of the developed FSI method.
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