publications

2024

1. 

   Bayesian inference of mean velocity fields and turbulence models from flow MRI

   A. Kontogiannis, P. Nair, M. Loecher, D. B. Ennis, and 2 more authors

   2024

   Abs arXiv

   We solve a Bayesian inverse Reynolds-averaged Navier-Stokes (RANS) problem that assimilates mean flow data by jointly reconstructing the mean flow field and learning its unknown RANS parameters. We devise an algorithm that learns the most likely parameters of an algebraic effective viscosity model, and estimates their uncertainties, from mean flow data of a turbulent flow. We conduct a flow MRI experiment to obtain mean flow data of a confined turbulent jet in an idealized medical device known as the FDA (Food and Drug Administration) nozzle. The algorithm successfully reconstructs the mean flow field and learns the most likely turbulence model parameters without overfitting. The methodology accepts any turbulence model, be it algebraic (explicit) or multi-equation (implicit), as long as the model is differentiable, and naturally extends to unsteady turbulent flows.

2. 

   Learning rheological parameters of non-Newtonian fluids from velocimetry data

   A. Kontogiannis, R. Hodgkinson, and E. L. Manchester

   2024

   Abs arXiv

   We solve a Bayesian inverse Navier-Stokes (N-S) problem that assimilates velocimetry data in order to jointly reconstruct the flow field and learn the unknown N-S parameters. By incorporating a Carreau shear-thinning viscosity model into the N-S problem, we devise an algorithm that learns the most likely Carreau parameters of a shear-thinning fluid, and estimates their uncertainties, from velocimetry data alone. We then conduct a flow-MRI experiment to obtain velocimetry data of an axisymmetric laminar jet through an idealised medical device (FDA nozzle) for a blood analogue fluid. We show that the algorithm can successfully reconstruct the flow field by learning the most likely Carreau parameters, and that the learned parameters are in very good agreement with rheometry measurements. The algorithm accepts any algebraic effective viscosity model, as long as the model is differentiable, and it can be extended to more complicated non-Newtonian fluids (e.g. Oldroyd-B fluid) if a viscoelastic model is incorporated into the N-S problem.

3. 

   Bayesian inverse Navier–Stokes problems: joint flow field reconstruction and parameter learning

   A. Kontogiannis, S. V. Elgersma, A. J. Sederman, and M. P. Juniper

   Inverse Problems, Dec 2024

   Abs HTML

   We formulate and solve a Bayesian inverse Navier–Stokes (N–S) problem that assimilates velocimetry data in order to jointly reconstruct a 3D flow field and learn the unknown N–S parameters, including the boundary position. By hardwiring a generalised N–S problem, and regularising its unknown parameters using Gaussian prior distributions, we learn the most likely parameters in a collapsed search space. The most likely flow field reconstruction is then the N–S solution that corresponds to the learned parameters. We develop the method in the variational setting and use a stabilised Nitsche weak form of the N–S problem that permits the control of all N–S parameters. To regularise the inferred geometry, we use a viscous signed distance field as an auxiliary variable, which is given as the solution of a viscous Eikonal boundary value problem. We devise an algorithm that solves this inverse problem, and numerically implement it using an adjoint-consistent stabilised cut-cell finite element method. We then use this method to reconstruct magnetic resonance velocimetry (flow-MRI) data of a 3D steady laminar flow through a physical model of an aortic arch for two different Reynolds numbers and signal-to-noise ratio (SNR) levels (low/high). We find that the method can accurately (i) reconstruct the low SNR data by filtering out the noise/artefacts and recovering flow features that are obscured by noise, and (ii) reproduce the high SNR data without overfitting. Although the framework that we develop applies to 3D steady laminar flows in complex geometries, it readily extends to time-dependent laminar and Reynolds-averaged turbulent flows, as well as non-Newtonian (e.g. viscoelastic) fluids.

2023

1. 

   Physics-informed compressed sensing for PC-MRI: an inverse Navier-Stokes problem

   A. Kontogiannis, and M. P. Juniper

   IEEE Transactions on Image Processing, Jan 2023

   Abs arXiv HTML

   We formulate a physics-informed compressed sensing (PICS) method for the reconstruction of velocity fields from noisy and sparse phase-contrast magnetic resonance signals. The method solves an inverse Navier-Stokes boundary value problem, which permits us to jointly reconstruct and segment the velocity field, and at the same time infer hidden quantities such as the hydrodynamic pressure and the wall shear stress. Using a Bayesian framework, we regularize the problem by introducing a priori information about the unknown parameters in the form of Gaussian random fields. This prior information is updated using the Navier-Stokes problem, an energy-based segmentation functional, and by requiring that the reconstruction is consistent with the k -space signals. We create an algorithm that solves this inverse problem, and test it for noisy and sparse k -space signals of the flow through a converging nozzle. We find that the method is capable of reconstructing and segmenting the velocity fields from sparsely-sampled (15% k -space coverage), low ( ∼10 ) signal-to-noise ratio (SNR) signals, and that the reconstructed velocity field compares well with that derived from fully-sampled (100% k -space coverage) high ( >40 ) SNR signals of the same flow.

2022

1. 

   Joint reconstruction and segmentation of noisy velocity images as an inverse Navier–Stokes problem

   A. Kontogiannis, S. V. Elgersma, A. J. Sederman, and M. P. Juniper

   Journal of Fluid Mechanics, Jul 2022

   Abs arXiv HTML

   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 (≃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.

2021

1. 

   Inverse problems in magnetic resonance velocimetry: shape, forcing and boundary condition inference

   A. Kontogiannis, and M. P. Juniper

   ASME, Fluids Engineering Division (Publication) FEDSM, Oct 2021

   Abs HTML PDF

   We derive and implement an algorithm that takes noisy magnetic resonance velocimetry (MRV) images of Stokes flow and infers the velocity field, the most likely position of the boundary, the inlet and outlet boundary conditions, and any body forces. We do this by minimizing a discrepancy norm of the velocity fields between the MRV experiment and the Stokes problem, and at the same time we obtain a filtered (denoised) version of the original MRV image. We describe two possible approaches to regularize the inverse problem, using either a variational technique, or Gaussian random fields. We test the algorithm for flows governed by a Poisson or a Stokes problem, using both real and synthetic MRV measurements. We find that the algorithm is capable of reconstructing the shape of the domain from artificial images with a low signal-To-noise ratio.

2. 

   Adjoint state of nonlinear vortex-lattice method for aerodynamic design and control

   A. Kontogiannis, and E. Laurendeau

   AIAA Journal, Feb 2021

   Abs HTML

   The adjoint state of a nonlinear vortex-lattice method, coupled with sectional polars obtained with an infinite swept-wing (2.5D) Reynolds-averaged Navier–Stokes (RANS) solver, is presented as an interactive method for preliminary aerodynamic design and control of moderate-to-high aspect ratio wings in subsonic and transonic flows. First, the nonlinear vortex-lattice method is described, augmented with a Prandtl–Glauert compressibility correction and regularized so that poststall solutions can be recovered. The linearization of the coupled system of equations is formulated using a Newton method, and the adjoint state is obtained for lift, drag, and inverse design functionals. Numerical results show that the aerodynamic model approximates well the forces predicted by three-dimensional (3D) RANS simulations for the Common Research Model wing, and that the adjoint-state gradients agree well with finite difference tests for a plethora of test cases. More interesting examples are shown, ranging from the optimal unstalling of wings to the assimilation of 3D RANS data into the present model, as well as its ability to extrapolate.

2018

1. 

   Robust fluid-structure interaction analysis of an adaptive airfoil using shape memory alloy actuators

   T. Machairas, A. Kontogiannis, A. Karakalas, A. Solomou, and 2 more authors

   Smart Materials and Structures, Sep 2018

   Abs HTML

   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.

2021

1. arXiv Draft

   Simultaneous boundary shape estimation and velocity field de-noising in magnetic resonance velocimetry using physics-informed neural networks

   U. Sengupta, A. Kontogiannis, and M. P. Juniper

   2021

   Abs arXiv

   Magnetic resonance velocimetry (MRV) is a non-invasive experimental technique widely used in medicine and engineering to measure the velocity field of a fluid. These measurements are dense but have a low signal-to-noise ratio (SNR). The measurements can be de-noised by imposing physical constraints on the flow, which are encapsulated in governing equations for mass and momentum. Previous studies have required the shape of the boundary (for example, a blood vessel) to be known a priori. This, however, requires a set of additional measurements, which can be expensive to obtain. In this paper, we present a physics-informed neural network that instead uses the noisy MRV data alone to simultaneously infer the most likely boundary shape and de-noised velocity field. We achieve this by training an auxiliary neural network that takes the value 1.0 within the inferred domain of the governing PDE and 0.0 outside. This network is used to weight the PDE residual term in the loss function accordingly and implicitly learns the geometry of the system. We test our algorithm by assimilating both synthetic and real MRV measurements for flows that can be well modeled by the Poisson and Stokes equations. We find that we are able to reconstruct very noisy (SNR = 2.5) MRV signals and recover the ground truth with low reconstruction errors of 3.7 - 7.5%. The simplicity and flexibility of our physics-informed neural network approach can readily scale to assimilating MRV data with complex 3D geometries, time-varying 4D data, or unknown parameters in the physical model.

2019

1. 

   Viscous-inviscid analysis of transonic swept wings using 2.5D RANS and parametric shapes

   A. Kontogiannis, M. Parenteau, and E. Laurendeau

   In AIAA Scitech 2019 Forum, Jan 2019

   HTML

2018

1. 

   Sensitivity of glaze ice accretion and iced aerodynamics prediction to roughness

   A. Kontogiannis, A. Prakash, E. Laurendeau, and F. Moens

   In 26th Annual Conf. of the Computational Fluid Dynamics Society of Canada, Jan 2018

   Abs PDF

   A study of the effect of the assumed ice roughness on ice shape prediction and aerodynamic performance degradation has been conducted to quantify the sensitivity of glaze ice accretion prediction according to the value of equivalent sand grain roughness height (ks). The motivation stems from the fact that a good representative value of ks is almost never known a priori, and usually crude roughness models are employed. First, a validation of the icing suite NSCODE-ICE is presented, for both ice-accretion and aerodynamic performance degradation, using three icing experiments performed in the Icing Research Tunnel (IRT) of NASA. Then, a sensitivity study is conducted for a range of ks values that are most common for ice formation on transport aircraft wings, encountering atmospheric icing conditions. The goal is to quantify the variation of aerodynamic performance loss due to the uncertainty introduced by the choice of the ks value

2. An extended rough-wall model for an integral boundary layer model intended for ice accretion calculations

   E. Radenac, A. Kontogiannis, C. Bayeux, and P. Villedieu

   In 10th AIAA Atmospheric and Space Environments Conf., Jan 2018

2017

1. Description and assessment of the new ONERA 2D icing suite IGLOO2D

   P. Trontin, A. Kontogiannis, G. Blanchard, and P. Villedieu

   In 9th AIAA Atmospheric and Space Environments Conf., Jan 2017

   Abs

2. A robust fluid-structure interaction numerical tool for the analysis of airfoil morphing structures with shape memory alloy actuators

   A. Karakalas, A. Kontogiannis, T. Machairas, A. Solomou, and 2 more authors

   In VIII ECCOMAS Thematic Conf. on Smart Structures and Materials (SMART), Jan 2017

2022

1. 

   Methods and systems for improved reconstruction of magnetic resonance velocimetry data and a method of compressing flow data of a fluid

   M. Juniper, and A. Kontogiannis

   2022

   HTML

2023

1. 

   Inverse problems in fluid dynamics for magnetic resonance velocimetry

   A. Kontogiannis

   Cambridge University Engineering Department, Mar 2023

   Abs HTML

   I formulate a digital twin approach to the reconstruction of velocity fields from noisy and sparse magnetic resonance velocimetry signals. The method learns the most probable fluid dynamics model that fits the data by solving a Bayesian inverse Navier–Stokes boundary value problem. This jointly reconstructs and segments the velocity field, and at the same time infers hidden quantities such as the hydrodynamic pressure and the wall shear stress, as well as their uncertainties. Using a Bayesian framework, I regularize the problem by introducing a priori information about the unknown parameters in the form of Gaussian random fields. This prior information is updated using the Navier–Stokes problem, an energy-based segmentation functional, and by requiring that the reconstruction is consistent with the signals. I create an algorithm that solves this inverse problem, and first test it for noisy synthetic images of 2D flow in a simulated aortic aneurysm. I then extend the method to noisy, sparsely-sampled signals, and test it for experimental flow through a converging nozzle. I find that the method is capable of reconstructing and segmenting the velocity fields from sparsely-sampled (15% sampling), low (∼10) signal-to-noise ratio (SNR) signals, and that the reconstructed velocity field is almost identical to that derived from fully-sampled (100% sampling) high (>40) SNR signals of the same flow. Finally, I implement the same algorithm in 3D and test it for an experimental flow through a 3D-printed physical model of an aortic arch. I show that the method can successfully reconstruct noisy flows in realistic geometries and high Reynolds numbers. Further, the method naturally extends to 3D periodic and unsteady flows, and its computational complexity can be substantially decreased if an adaptive discretization method (e.g. wavelets) is used. The reconstruction of in vivo cardiovascular and porous media flows are among the most exciting applications of this work.

2017

1. 

   Viscous-inviscid fluid-structure interaction method for the analysis of multielement morphing airfoils

   A. Kontogiannis

   School of Mechanical Engineering and Aeronautics, University of Patras, Mar 2017

   Abs HTML PDF

   In the present diploma thesis, the development of a two-body viscous-inviscid interaction method (Foil2E) is described as an extension of the Foil2W code of the Laboratory of Aerodynamics of the School of Mechanical Engineering of National Technical University of Athens, based on the XFOIL code. The method is weakly coupled with ABAQUS to perform fluid-structure interaction analysis for morphing multielement airfoils using Nitinol wire actuators. Firstly, the basic principles of VII methods and the fluid phenomena that occur and need to be modeled are presented. Then, the panel method for the purely inviscid flow is described as well as the viscous displacement model for the equivalent inviscid flow (EIF) and the integral boundary layer model including the e^n transition criterion. Finally, the thesis concludes with the numerical formulation for the VII as it was implemented in Foil2E, the validation of the code using experimental data from AGARD and the results of the FSI analysis of an airfoil with morphing fowler flap. Viscous-inviscid interaction codes are well suited for rapid and interactive aerodynamic analysis. Hence, Foil2E code could be of great use in the analysis of high-lift slotted airfoils, biplane and canard configurations. Moreover, due to the low computational cost and time of VII methods, the present method is promising for rapid quasi-3D FSI computations including the material models for Nitinol, as developed by the Structural Analysis and Smart Materials (SAAM) group of the department.