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To evaluate hemodynamic markers obtained by accelerated GRAPPA (R = 2, 3, 4) and compressed sensing (R = 7.6) 4D flow MRI sequences under complex flow conditions.The accelerated 4D flow MRI scans were performed on a pulsatile flow phantom, along with a nonaccelerated fully sampled k-space acquisition. Computational fluid dynamics simulations based on the experimentally measured flow fields were conducted for additional comparison. Voxel-wise comparisons (Bland-Altman analysis,mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"mml:semanticsmml:mrowmml:msubmml:miL/mml:mimml:mn2/mml:mn/mml:msub/mml:mrowmml:annotation$$ {L}_2 $$/mml:annotation/mml:semantics/mml:math-norm metric), as well as nonderived quantities (velocity profiles, flow rates, and peak velocities), were used to compare the velocity fields obtained from the different modalities.4D flow acquisitions and computational fluid dynamics depicted similar hemodynamic patterns. Voxel-wise comparisons between the MRI scans highlighted larger discrepancies at the voxels located near the phantom's boundary walls. A trend for all MR scans to overestimate velocity profiles and peak velocities as compared to computational fluid dynamics was noticed in regions associated with high velocity or acceleration. However, good agreement for the flow rates was observed, and eddy-current correction appeared essential for consistency of the flow rates measurements with respect to the principle of mass conservation.GRAPPA (R = 2, 3) and highly accelerated compressed sensing showed good agreement with the fully sampled acquisition. Yet, all 4D flow MRI scans were hampered by artifacts inherent to the phase-contrast acquisition procedure. Computational fluid dynamics simulations are an interesting tool to assess these differences but are sensitive to modeling parameters.

YALES2BIO est un solveur multiphysique pour décrire les écoulements sanguins aux échelles micro- et macroscopiques, basé sur la méthode des volumes finis. Différents cas d'école ont été traités : rupture de jet turbulent, étirement de globule rouge par pince optique, organisation de globules rouges en écoulement, mais aussi des applications industrielles (déviateur de débit, cœur artificiel, etc.).

Objectives This study evaluated the clinical impact of the Sim&Size® simulation software on the endovascular treatment with flow-diverter stents of patients with unruptured saccular intracranial aneurysms. Methods This monocentric retrospective study evaluated a cohort of patients treated with flow-divert stents between June 1, 2014, and December 31, 2019, for cerebral aneurysms. Patients belonged to two groups, patients treated with and without the Sim&Size® simulation software. Univariate, bivariate, and multivariate analyses were used to evaluate the clinical impact of simulation software. Results Out of the 73 interventions involving 68 patients analyzed by the study, 76.7% were simulated using the Sim&Size® simulation software, and 23.3% were not. Patients treated with the simulation software had shorter stent lengths (16.00 mm vs. 20.00 mm p-value = 0.001) and surgical time (100.00 min vs. 118.00 min p-value = 0.496). Also, fewer of them required more than one stent (3.6% vs. 17.6% p-value = 0.079). Three patients belonging to the non-stimulated group presented hemorrhagic complications. Conclusions Using the Sim&Size® simulation software for the endovascular treatment of intracranial aneurysms with pipeline flow-diverter stents reduces the stent length.

The Coulter principle is a widespread technique for sizing red blood cells in hematological analyzers. It is based on the monitoring of the electrical perturbations generated by cells passing through a micro-orifice, in which a concentrated electrical field is imposed by two electrodes. However, artefacts associated with near-wall passages in the sensing region are known to skew the statistics for red blood cells sizing. This study presents numerical results that emphasize the link between the cell flow-induced rotation in the detection area and the error in its measured volume. Based on these observations, two methods are developed to identify and reject pulses impaired by cell rotation. In the first strategy, the filtering is allowed by a metric computed directly from the waveform. In the second, a numerical database is employed to train a neural network capable of detecting if the cell has experienced a rotation, given its electrical pulse. Detecting and rejecting rotation-associated pulses is shown to provide results comparable to hydrodynamical focusing, which enforces cells to flow in the center of the orifice, the gold standard implementation of the Coulter principle. This article is protected by copyright. All rights reserved.

Large Eddy Simulations are used to study the heat-release response to fuel inflow acoustic harmonic oscillations, in a coaxial jet flame where both reactants (O2 and CH4) are injected in a dense cryogenic state. The geometry is that of the academic test rig Mascotte, operated by ONERA (France), which high pressure operating conditions are relevant for the characterization of flame dynamics in Liquid Rocket Engines (LREs). The simulations, which are carried out with a real-gas fluid solver using a detailed kinetic scheme for CH4 high-pressure oxycombustion, provide a thorough insight into the flame response for a wide range of forcing frequencies, spanning from approximately 1kHz to 20kHz. Local Flame Transfer Functions (FTF) are computed and analyzed: regions of preferential heat-release response are observed to be highly dependent on the forcing frequency. An analysis based on a flame sheet assumption is conducted to distinguish the main sources of heat release fluctuations: the primary contribution comes from the species diffusivity oscillations, while the density variations have a negligible effect. The second largest contributor is either the mixture fraction gradient or the flame surface area, depending on the forcing frequency. The FTFs are expected to be useful for thermoacoustic Low-Order Models or Helmholtz solvers, and the subsequent analysis has the potential to guide future development of analytical models for flame dynamics in LREs.

Introduction The Woven EndoBridge device (WEB) was developed as an alternative to treat Wide-Necked bifurcation aneurysms. It has proven to be effective and safe, however, cases of recanalization have been reported. The purpose of this study was to evaluate and quantify hemodynamic parameters and indexes with CFD of the intracranial aneurysms before and after WEB simulation and to establish their relationship to complete occlusion. Materials and methods Using the heterogeneous model based on the marching cubes algorithm, we created 3D representations of 27 bifurcated intracranial aneurysms treated with the single-layer WEB device to evaluate hemodynamics parameters with CFD, calculated with and without the WEB. Results We observed a lower treatment entry concentration indices (ICI) (2.12 ± 1.31 versus 3.14 ± 0.93, p-value: 0.029) previous to placement of WEB and higher pre-treatment FN (7.56 ± 5.92 versus 3.35 ± 1.51, p-value: 0.018) and post-treatment FN (5.34 ± 5.89 versus 1.99 ± 0.83, p-value: 0.021) for cases with successful occlusions. Lower post-treatment SRa (197.81 ± 221.29 versus 80.02 ± 45.25, p-value: 0.044) and higher pre (0.11 ± 0.07 versus 0.25 ± 0.19, p-value: 0.011) and post-treatment MATT (0.69 ± 1.23 versus 1.02 ± 0.46, p-value: 0.006) were observed in non-occluded cases. Conclusions In our CFD analysis of the hemodynamic parameters of IA, we found lower ICI before the placement of the WEB device and higher FN pre- and post-treatment for cases with successful occlusions. Non-occluded cases had lower post-treatment SRa and higher pre-treatment and post-treatment MATT.

Introduction The Woven EndoBridge device (WEB) is used to treat wide-neck bifurcation aneurysms. These devices are deployed inside the sac. Therefore, the mesh structure provides apposition with the aneurysm wall and induces aneurysmal thrombosis. The objective of our study was to evaluate the anatomic and device-related parameters and indexes with Computational Fluid Dynamics (CFD) of the intracranial aneurysms before and after WEB simulation and find their relationship to complete occlusion. Materials and methods Using the heterogeneous model based on the marching cubes algorithm, we created 3D representations of 27 bifurcated intracranial aneurysms treated with the single-layer WEB device to evaluate anatomic and device-related parameters with CFD. Results In our CFD analysis, we observed higher large volumes (Va) (0.25 ± 0.18 versus 0.39 ± 0.09, p-value= 0.025) and higher volume to neck surface ratio (Ra) (1.32 ± 0.17 versus 1.54 ± 0.14, p-value= 0.021) in cases with occlusion failure. Conclusions Large aneurysm volumes (Va) and higher volume to neck surface ratio (Ra) could be associated with occlusion failure in aneurysms treated with the WEB device.

International audience; Color Doppler imaging (CDI) is the modality of choice for simultaneous visualization of myocardium and intracavitary flow over a wide scan area. This visualization modality is subject to several sources of error, the main ones being aliasing and clutter. Mitigation of these artifacts is a major concern for better analysis of intracardiac flow. One option to address these issues is through simulations. In this article, we present a numerical framework for generating clinical-like CDI. Synthetic blood vector fields were obtained from a patient-specific computational fluid dynamics CFD model. Realistic texture and clutter artifacts were simulated from real clinical ultrasound cineloops. We simulated several scenarios highlighting the effects of 1) flow acceleration; 2) wall clutter; and 3) transmit wavefronts, on Doppler velocities. As a comparison, an “ideal” color Doppler was also simulated, without these harmful effects. This synthetic dataset is made publicly available and can be used to evaluate the quality of Doppler estimation techniques. Besides, this approach can be seen as a first step toward the generation of comprehensive datasets for training neural networks to improve the quality of Doppler imaging

International audience; A methodology is developed where the acoustic response of a swirl stabilized flame is obtained from a reduced set of simulations. Building upon previous analytical flame transfer functions, a parametrization of the flame response is first proposed, based on six independent physical parameters: a Strouhal number, the mean flame angle with respect to the main flow direction, the vortical structures convection speed, a swirl intensity parameter, a time delay between acoustic and vortical perturbations, as well as a phase shift between bulk and local velocity signals. It is then shown how these parameters can be deduced from steady and unsteady simulations. The methodology is applied to a laboratory scale premixed swirl stabilized flame exhibiting features representative of real aero-engines. In this matter, cold and reactive flow Large Eddy Simulations are first validated by comparing results with reference data from experiments. The high fidelity simulations are seen to be able to capture the flame structure and velocity profiles at different locations while forced flame dynamics for the frequency range of interest also match the experimental data. From the same analytical transfer function model, three methodologies of increasing complexity are presented for the determination of the model parameters, depending on the available data or computational resources. A first estimation of the flame acoustic response is obtained by evaluating parameters from a single stationary flame simulation in conjunction with analytical estimations for the acoustic-convective time delay. Flame dynamics and swirl related parameters can then be determined from a series of robust treatments on pulsed simulations data to improve the model accuracy. It is shown that good qualitative agreement for the flame transfer function can be obtained from a single non-forced simulation while quantitative agreement over the frequency range of interest can be obtained using additional reactive or non-reactive pulsed simulations at one single forcing frequency corresponding to a local gain minimum. The method also naturally handles different perturbation levels.

Introduction Three-dimensional (3D) printing has evolved for medical applications as it can produce customized 3D models of devices and implants that can improve patient care. In this study, we aimed to validate the geometrical accuracy of the 3D models of intracranial aneurysms printed using Stereolithography 3D printing technology. Materials and methods To compare the unruptured intracranial aneurysm mesh between the five patients and 3D printed models, we opened the DICOM files in the Sim&Size® simulation software, selected the region of interest, and performed the threshold check. We juxtaposed the 3D reconstructions and manually rotated the images to get the same orientation when needed and measured deviations at different nodes of the patient and 3D printed model meshes. Results In the first patient, 80% of the nodes were separated by Conclusions 3D printed models of intracranial aneurysms are accurate, having surfaces that resemble that of patients’ angiographies with an 80% cumulative deviation below 0.21 mm.

Given the extensive and routine use of cardiovascular devices, a major limiting factor to their success is the thrombotic rate that occurs. This poses direct risk to the patient and requires counterbalancing with anticoagulation and other treatment strategies, contributing additional risks. Developing a better understanding of the mechanisms of device-induced thrombosis to aid in device design and medical management of patients is critical to advance the ubiquitous use and durability. Thus, mathematical and computational modeling of device-induced thrombosis has received significant attention recently, but challenges remain. Additional areas that need to be explored include microscopic/macroscopic approaches, reconciling physical and numerical timescales, immune/inflammatory responses, experimental validation, and incorporating pathologies and blood conditions. Addressing these areas will provide engineers and clinicians the tools to provide safe and effective cardiovascular devices.

Heart failure affects the heart’s ability to meet the oxygen needs of the organs. It concerns more than one million people in France. It can be defined by the reduced capacity of the heart to be fi...

Numerical simulations are used to compare the impact of the internal fluid viscosity and the membrane viscosity on an isolated tank-treading red blood cell. Both decrease the tank-treading frequency, with moderate changes in the deformation and inclination of the red blood cell. However, it is shown that tank-treading frequencies from existing experiments are only retrieved if membrane viscosity is accounted for, and with an apparent shear-thinning of the membrane.

Computational models of the coagulation cascade are used for a wide range of applications in bio-medical engineering such as drug and bio-medical device developments. However, a lack of robustness of numerical models has been highlighted when studying clinically relevant scenarios. In order to develop more robust models, numerical simulations need to be confronted with realistic situations relevant to clinical practice. In this work, two well-established numerical representations of the coagulation cascade initiated by the intrinsic and extrinsic systems, respectively, were compared with thrombin generation assays considering realistic pathological conditions. Proper modifications were needed to align the in vitro and in silico data, namely; adapting initial conditions to the thrombin assay system, omitting reactions irrelevant to our case study, and improving the fitting of some reaction rates. The modified models were able to capture the experimental trends of thrombin generation for a range of concentrations of factors XII, XI, and VIII for cases in which the coagulation cascade is triggered through the extrinsic and intrinsic systems. Our work emphasizes that when existing coagulation cascade models are extrapolated to experimental settings for which they were not calibrated, careful adjustments must be made. We show that the two coagulation models used in this work can predict physiological conditions, but when studying pathological conditions, proper modifications are needed to improve the numerical results.

International audience; Thrombus formation is one of the main issues in the development of blood-contacting medical devices. This article focuses on the modeling of one aspect of thrombosis, the coagulation cascade, which is initiated by the contact activation at the device surface and forms thrombin. Models exist representing the coagulation cascade by a series of reactions, usually solved in quiescent plasma. However, large parameter uncertainty involved in the kinetic models can affect the predictive capabilities of this approach. In addition, the large number of reactions of the kinetic models prevents their use in the simulation of complex flow configurations encountered in medical devices. In the current work, both issues are addressed to improve the applicability and fidelity of kinetic models. A sensitivity analysis is performed by two different techniques to identify the most sensitive parameters of an existing detailed kinetic model of the coagulation cascade. The results are used to select the form of a novel reduced model of the coagulation cascade which relies on eight chemical reactors only. Then, once its parameters have been calibrated thanks to the Bayesian inference, this model shows good predictive capabilities for different initial conditions.

Intraventricular vector flow mapping (iVFM) is a technique for retrieving 2-D velocity vector fields of blood flow in the left ventricle. This method is based on conventional color Doppler imaging, which makes iVFM compatible with the clinical setting. We have generalized the iVFM for a three-dimensional reconstruction (3D-iVFM). 3D-iVFM is able to recover three-component velocity vector fields in a full intraventricular volume by using a clinical echocardiographic triplane mode. As with the 2-D version, the method is based on the mass conservation, and free-slip boundary conditions on the endocardial wall. These mechanical constraints were imposed in a least-squares minimization problem that was solved through the method of Lagrange multipliers. We validated 3D-iVFM in silico in a patient-specific CFD (computational fluid dynamics) model of cardiac flow, and tested its feasibility in vivo on volunteers. In both in silico and in vivo investigations, the dynamics of the intraventricular vortex that forms during diastole was deciphered by 3D-iVFM. Our results tend to indicate that 3D-iVFM could provide full-volume echocardiographic information on left intraventricular hemodynamics from the clinical modality of triplane color Doppler., Comment: original paper

A methodology to include flow–acoustic interactions in a Helmholtz solver is proposed and used to quantify their impact on the thermoacoustic modes of a real industrial combustor. This methodology ...

A numerical approach is presented to efficiently simulate time-resolved 3D phase-contrast Magnetic resonance Imaging (or 4D Flow MRI) acquisitions under realistic flow conditions. The Navier-Stokes and Bloch equations are simultaneously solved with an Eulerian-Lagrangian formalism. A semi-analytic solution for the Bloch equations as well as a periodic particle seeding strategy are developed to reduce the computational cost. The velocity reconstruction pipeline is first validated by considering a Poiseuille flow configuration. The 4D Flow MRI simulation procedure is then applied to the flow within an in vitro flow phantom typical of the cardiovascular system. The simulated MR velocity images compare favorably to both the flow computed by solving the Navier-Stokes equations and experimental 4D Flow MRI measurements. A practical application is finally presented in which the MRI simulation framework is used to identify the origins of the MRI measurement errors.

Numerical computations of hemodynamics inside intracranial aneurysms treated by endovascular braided devices such as flow-diverters contribute to understanding and improving such treatment procedures. Nevertheless, these simulations yield high computational and meshing costs due to the heterogeneity of length scales between the dense weave of the fine struts of the device and the arterial volume. Homogeneous strategies developed over the last decade to circumvent this issue substitute local dissipations due to the wires with a global effect in the form of a pressure-drop across the device surface. However, these methods cannot accurately reproduce the flow-patterns encountered near the struts, the latter strongly dictating the intra-saccular flow environment. In this work, a versatile theoretical framework which aims at correctly reproducing the local flow heterogeneities due to the wires while keeping memory consumption, meshing and computational times as low as possible is introduced. This model reproduces the drag forces exerted by the device struts onto the fluid, thus producing local and heterogeneous effects on the flow. Extensive validation for various flow and geometric configurations using an idealized device is performed. To further illustrate the method capabilities, a real patient-specific aneurysm endovascularly treated with a flow-diverter is used, enabling quantitative comparisons with classical approaches for both intra-saccular velocities and computational costs reduction. The proposed heterogeneous model endeavours to bridge the gap between CFD and clinical applications and ushers in a new era of numerical treatment planning with minimally costing computational tools. This article is protected by copyright. All rights reserved.

Color Doppler by transthoracic echocardiography creates two-dimensional fan-shaped maps of blood velocities in the cardiac cavities. It is a one-component velocimetric technique since it only returns the velocity components parallel to the ultrasound beams. Intraventricular vector flow mapping (iVFM) is a method to recover the blood velocity vectors from the Doppler scalar fields in an echocardiographic three-chamber view. We improved our iVFM numerical scheme by imposing physical constraints. The iVFM consisted in minimizing regularized Doppler residuals subject to the condition that two fluid-dynamics constraints were satisfied, namely planar mass conservation, and free-slip boundary conditions. The optimization problem was solved by using the Lagrange multiplier method. A finite-difference discretization of the optimization problem, written in the polar coordinate system centered on the cardiac ultrasound probe, led to a sparse linear system. The single regularization parameter was determined automatically for non-supervision considerations. The physics-constrained method was validated using realistic intracardiac flow data from a patient-specific computational fluid dynamics (CFD) model. The numerical evaluations showed that the iVFM-derived velocity vectors were in very good agreement with the CFD-based original velocities, with relative errors ranged between 0.3% and 12%. We calculated two macroscopic measures of flow in the cardiac region of interest, the mean vorticity and mean stream function, and observed an excellent concordance between physics-constrained iVFM and CFD. The capability of physics-constrained iVFM was finally tested with in vivo color Doppler data acquired in patients routinely examined in the echocardiographic laboratory. The vortex that forms during the rapid filling was deciphered. The physics-constrained iVFM algorithm is ready for pilot clinical studies and is expected to have a significant clinical impact on the assessment of diastolic function.

International audience; We generalized and improved our clinical technique of twodimensional intraventricular vector flow mapping (2D-iVFM) for a full-volume three-component analysis of the intraventricular blood flow (3D-iVFM). While 2D-iVFM uses three-chamber color Doppler images, 3D-iVFM is based on the clinical mode of triplane color Doppler echocardiography. As in the previous twodimensional version, 3D-iVFM relies on mass conservation and free-slip endocardial boundary conditions. For sake of robustness, the optimization problem was written as a constrained least-squares problem. We tested and validated 3D-iVFM in silico through a patient-specific heart-flow CFD (computational fluid dynamics) model, as well as in vivo in one healthy volunteer. The intraventricular vortex that forms during left ventricular filling was deciphered. After further validation, 3D-iVFM could offer clinically compatible 3-D echocardiographic insights into left intraventricular hemodynamics.

International audience; This paper uses machine learning to enrich magnetic resonance angiography and magnetic resonance imaging acquisitions. A convolutional neural network is built and trained over a synthetic database linking geometrical parameters and mechanical characteristics of the arteries to blood flow rates and pressures in an arterial network. Once properly trained, the resulting neural network can be used in order to predict blood pressure in cerebral arteries noninvasively in nearly real-time. One challenge here is that not all input variables present in the synthetic database are known from patient-specific medical data. To overcome this challenge, a learning technique, which we refer to as implicit manifold learning, is employed: in this view, the input and output data of the neural network are selected based on their availability from medical measurements rather than being defined from the mechanical description of the arterial system. The results show the potential of the method and that machine learning is an alternative to costly ensemble based inversion involving sophisticated fluid structure models

Gas turbine combustors are prone to undesirable combustion dynamics in the form of thermoacoustic oscillations. Analysis of the stability of thermoacoustic systems in the frequency domain leads to nonlinear eigenvalue problems (NLEVP); here, “nonlinear” refers to the fact that the eigenvalue, the complex oscillation frequency, appears in a nonlinear fashion. In this paper, we employ a noniterative strategy based on contour integration in the complex eigenvalue plane, which returns all eigenvalues inside the contour. An introduction to the technique is given, and is complemented with guidelines for the specific application to thermoacoustic problems. Two prototypical nonlinear eigenvalue problems are considered: a network model of the classical Rijke tube with an analytic flame response model and a finite element discretization of an annular model combustor with an experimental flame transfer function (FTF). Computation of all eigenvalues in a domain of interest is vital to assess stability of these systems. We demonstrate that this is generally challenging for iterative strategies. An eigenvalue solver based on contour integration, in contrast, provides a reliable, noniterative method to achieve this goal.

In Coulter counters, cells counting and volumetry are achieved by monitoring their electrical print when they flow through a sensing zone. However, the volume measurement may be impaired by the cell dynamics, which may be difficult to control. In this paper, numerical simulations of the dynamics and electrical signature of red blood cells in a Coulter counter are presented, accounting for the deformability of the cells. In particular, a specific numerical pipeline is developed to overcome the challenge of the multi-scale nature of the problem. It consists in segmenting the whole computation of the cell dynamics and electrical response in a series of dedicated computations, with a saving of one order of magnitude in computational time. This numerical pipeline is used with rigid spheres and deformable red blood cells in an industrial Coulter counter geometry, and compared with experimental measurements. The simulations not only reproduce electrical signatures typical of those measured experimentally, but also allow an analysis of the electrical signature in terms of the heterogeneity of the electrical field and dynamics of the particles in the measurement zone. This study provides a methodology for computing the sizing of rigid or deformable particles by Coulter counters, opening the way to a better understanding of cells signatures in such devices.

In the framework of wall-modeled large-eddy simulation (WMLES), the problem of combining sub-grid scale (SGS) models with the standard wall law is commonly acknowledged and expressed through multiple undesired near-wall behaviors. In this work, it is first observed that the static Smagorinsky model predicts efficiently the wall shear stress in a wall-modeled context, while more advanced static models like wall-adapting local eddy (WALE) viscosity or Sigma with proper cubic damping fail. It is, however, known that Smagorinsky is overall too dissipative in the bulk flow and in purely sheared flows, whereas the two other models are better suited for near-wall flows. The observed difficulty comes from the fact that the SGS model relies on the filtered velocity gradient tensor that necessarily comes with large errors in the near-wall region in the context of WMLES. Since the first off-wall node is usually located in the turbulent zone of the boundary layer, the turbulent structures within the first cell are neither resolved by the grid nor represented by the SGS model, which results in a lack of turbulent activity. In order to account for these subgrid turbulent structures, a stochastic forcing method derived from Reynolds-averaged Navier–Stokes (RANS) turbulence models is proposed and applied to the velocity gradients to better estimate the near-wall turbulent viscosity while providing the missing turbulent activity usually resulting from the WMLES approach. Based on such corrections, it is shown that the model significantly improves the wall shear stress prediction when used with the WALE and Sigma models.

We propose a regularized least-squares method for reconstructing 2D velocity vector fields within the left ventricular cavity from single-view color Doppler echocardiographic images. Vector flow mapping is formulated as a quadratic optimization problem based on an [Formula: see text]-norm minimization of a cost function composed of a Doppler data-fidelity term and a regularizer. The latter contains three physically interpretable expressions related to 2D mass conservation, Dirichlet boundary conditions, and smoothness. A finite difference discretization of the continuous problem was adopted in a polar coordinate system, leading to a sparse symmetric positive-definite system. The three regularization parameters were determined automatically by analyzing the L-hypersurface, a generalization of the L-curve. The performance of the proposed method was numerically evaluated using (1) a synthetic flow composed of a mixture of divergence-free and curl-free flow fields and (2) simulated flow data from a patient-specific CFD (computational fluid dynamics) model of a human left heart. The numerical evaluations showed that the vector flow fields reconstructed from the Doppler components were in good agreement with the original velocities, with a relative error less than 20%. It was also demonstrated that a perturbation of the domain contour has little effect on the rebuilt velocity fields. The capability of our intraventricular vector flow mapping (iVFM) algorithm was finally illustrated on in vivo echocardiographic color Doppler data acquired in patients. The vortex that forms during the rapid filling was clearly deciphered. This improved iVFM algorithm is expected to have a significant clinical impact in the assessment of diastolic function.

Gas turbine combustors are prone to undesirable combustion dynamics in the form of thermoacoustic oscillations. Analysis of the stability of thermoacoustic systems in the frequency domain leads to nonlinear eigenvalue problems; here, ‘nonlinear’ refers to the fact that the eigenvalue, the complex oscillation frequency, appears in a nonlinear fashion. In this paper, we employ a non-iterative strategy based on contour integration in the complex eigenvalue plane, which returns all eigenvalues inside the contour. An introduction to the technique is given, and is complemented with guidelines for the specific application to thermoacoustic problems. Two prototypical nonlinear eigenvalue problems are considered: a network model of the classical Rijke tube with an analytic flame response model and a finite element discretization of an annular model combustor with an experimental flame transfer function. Computation of all eigenvalues in a domain of interest is vital to assess stability of these systems. We demonstrate that this is generally challenging for iterative strategies. An eigenvalue solver based on contour integration, in contrast, provides a reliable, non-iterative method to achieve this goal.

International audience; An Uncertainty Quantification analysis of a swirled stabilized combustor experiment is performed. Theobjective is to estimate the modal risk factor of the system, i.e. the probability of a thermoacoustic mode tobe unstable, which may facilitate the development and optimization of suitable control methods. Topropagate uncertainties, a Monte Carlo method is initially used based on 4000 Helmholtz-basedthermoacoustic simulations with random perturbations on the flame input parameters. The analysis of theMonte Carlo database suggests that a reduced two-step Uncertainty Quantification strategy may beefficient to deal with thermoacoustic systems. First, three bilinear surrogate models are tuned from amoderate number of Helmholtz solutions (a few tens). Then, these algebraic models are used to perform aMonte Carlo analysis at reduced cost and approximate the risk factor of the mode. Good agreements areobtained when comparing the risk factor from the full Monte Carlo database and the risk factor fromsurrogate models.

International audience; While the computational power is still increasing, thus arousing theinterest for high-fidelity simulations, the need of low-order models is also feltto both predict and understand combustion instabilities at low costs. Historicallyapplied to simple systems like longitudinal Rijke tubes to unveil the driven mechanismsleading to instability, they have recently been adapted to more complexconfigurations such as annular combustors. A network model is presented here topredict thermo-acoustic modes in an annular combustion chamber fed by burnersconnected to an annular plenum, typical of modern combustor designs. Explicitexpressions of the growth rate are derived in several cases showing key parameterscontrolling the stability. In more general situations, no explicit solution canbe obtained. Nevertheless, such an analytical model can be solved numerically atlow-cost compared with 3D acoustic tools and high-fidelity simulations. In thisframework, efficient sensitivity techniques and UQ methods can be developed totackle the UQ problem: “How can we assess the risk of instability in industrialcombustors at the predesign stage?”.

International audience; A low-order model is proposed to predict the temperature of a multi-perforated plate from an unresolved adiabatic computation. Its development relies on the analysis of both an adiabatic and a conjugate heat transfer wall resolved large eddy simulation of an academic multi-perforated liner representative of the cooling systems used in combustion chambers of actual aero-engines. These two simulations show that the time averaged velocity field is marginally modified by the coupling with the heat diffusion in the perforated plate when compared to the adiabatic case. This gives rise to a methodology to assess the wall temperature from an unresolved adiabatic computation. It relies on heat transfer coefficients from refer-enced correlations as well as a mixing temperature relevant to the flow in the injection region where the cold micro-jets mix with the hot outer flow. In this approach, a coarse mesh simulation using an homogeneous adiabatic model for the aerodynamics of the flow with effusion is post-processed to provide a low cost alternative to conjugate heat transfer computations based on hole resolved meshes. The model is validated on an academic test case and successfully applied to a real industrial combustion chamber.

International audience; In aero-engines, mutiperforation cooling systems are often used to shield the combustor wall and ensure durability of the engine. Fresh air coming from the casing goes through thousands of angled perforations and forms a film which protects the liner. When performing Large Eddy Simulations (LES) of a real engine, the number of sub-millimetric holes is far too large to allow a complete and accurate description of each aperture. Homogeneous models allow to simulate multiperforated plates with a mesh size bigger than the hole but fail in representing the jet penetration and mixing. A heterogeneous approach is proposed in this study, where the apertures are thickened if necessary so that the jet-crossflow interaction is properly represented. Simulations using homogeneous and thickened-hole models are compared to a fully resolved computation for various grid resolutions in order to illustrate the potential of the method.

This work introduces a novel method to represent the topological complexity of liners and boundaries in Low Order Models for thermoacoustic instabilities, under the assumption of zero-Mach number flow. In typical industrial combustion devices, the difficulty to model these elements is twofold: (1) they are characterized by complex-valued Rayleigh conductivities or acoustic impedances, and (2) they consist of large, curved panels whose geometries have first-order effect on the combustor thermoacoustic stability. To deal with the first point, the present approach makes use of a frame modal expansion recently introduced by Laurent et al. (2019)[41], which is a generalization of the classical rigid-wall Galerkin expansion, intended to deal with non-trivial boundary conditions. The core of this work lies in the second difficulty: complex-shaped liners and boundaries are modeled as two-dimensional manifolds, for which a specific set of curvilinear governing equations is derived. The inclusion of acoustic impedance or Rayleigh conductivity into these equations enforces the proper conservation equations at the frontiers of the adjacent volumes. Surface modal projections are then introduced to expand acoustic variables onto an orthogonal basis of modes solutions of a curvilinear Helmholtz eigenproblem. The resulting dynamical system is embedded into a state-space framework to build acoustic networks. A first non-reacting canonical test case, consisting of a multi-perforated liner in a cylindrical geometry is studied to assess the convergence and precision of the method. The ability of the approach to deal with realistic reacting cases is then illustrated by modeling the partially reflecting outlet of a multi-sector annular combustor typical of industrial gas turbines. This methodology enables the inclusion of liners and other boundaries of arbitrary geometrical complexity in modal projection-based thermoacoustic Low Order Models.

Since its introduction in the late 19th century, symmetry breaking has been found to play a crucial role in physics. In particular, it appears as one key phenomenon controlling hydrodynamic and acoustic instabilities in problems with rotational symmetries. A previous paper investigated its desired potential application to the control of circumferential thermoacoustic modes in one annular cavity coupled with multiple flames (Bauerheim et al., J. Fluid Mech., vol. 760, 2014, pp. 431–465). The present paper focuses on a similar problem when symmetry breaking appears unintentionally, for example when uncertainties due to tolerances are taken into account. It yields a large uncertainty quantification (UQ) problem containing numerous uncertain parameters. To tackle this well-known ‘curse of dimensionality’, a novel UQ methodology is used. It relies on the active subspace approach to construct a reduced set of input variables. This strategy is applied on two annular cavities coupled by 19 flames to determine its modal risk factor, i.e. the probability of an azimuthal acoustic mode being unstable. Since each flame is modelled by two uncertain parameters, it leads to a large UQ problem involving 38 parameters. An acoustic network model is then derived, which yields a nonlinear dispersion relation for azimuthal modes. This nonlinear problem, subject to bifurcations, is solved quasi-analytically. Results show that the dimension of the probabilistic problem can be drastically reduced, from 38 uncertain parameters to only 3. Moreover, it is found that the three active variables are related to physical quantities, which unveils underlying phenomena controlling the stability of the two coupled cavities. The first active variable is associated with a coupling strength controlling the bifurcation of the system, while the two others correspond to a symmetry-breaking effect induced by the uncertainties. Thus, an additional destabilization effect appear caused by the non-uniform pattern of the uncertainty distribution, which breaks the initial rotating symmetry of the annular cavities. Finally, the active subspace is exploited by fitting the response surface with polynomials (linear, quadratic and cubic). By comparing accuracy and cost, results prove that 5 % error can be achieved with only 30 simulations on the reduced space, whereas 2000 are required on the complete initial space. It exemplifies that this novel UQ technique can accurately predict the risk factor of an annular configuration at low cost as well as unveil key parameters controlling the stability.

The present chapter investigates an uncertainty quantification (UQ) approach for the simulations of combustion instabilities (CI). They stem from the interaction between acoustic waves and heat release fluctuations. CI are harmful to gas turbines engines if they are not mastered at the design level. The targeted test case within the UMRIDA project is a realistic full annular helicopter combustor from Safran Helicopter Engines. This combustor is equipped with several burners and flames, each of them described by two uncertain input parameters. Therefore, we are facing a “curse of dimensionality” as around 10–20 independent uncertain parameters are generally involved in real combustors. In order to break the curse, active subspace methods (Constantine et al, J Sci Comput, 2013) and efficient surrogate techniques are used to assess the risk factor of the system, i.e., the probability of an acoustic mode to be unstable. For such high-dimensional complex systems, active subspace methods based on gradient correlations are known to provide dimension reduction of the necessary input parameters. Efficiency of the proposed method was shown effective on practical examples (Bauerheim et al. Combust Flame 161(5):1374–1389, 2014). In the scope of our overall approach, an Analytical Tool to Analyze and Control Azimuthal Mode in Annular Chambers named ATACAMAC (Bauerheim et al. Combust Flame 161(5):1374–1389, 2014) is used to deal with the complexity of the combustor features. Besides, it is hardly conceivable having recourse to 3D LES or even 3D Helmholtz solvers to deal with uncertainties in the high-dimensional spaces within a reasonable computational timeframe. To avoid expensive Helmholtz simulations, the quasi-analytical tool ATACAMAC is first applied to generate a reference Monte Carlo database to obtain the statistical benchmark database for the risk factor of the acoustic mode. Thereafter, the dimension of the system is drastically reduced to much less than 20–40 parameters using the active subspace methodology. Linear and quadratic surrogate models are introduced based on moderate active variables previously determined. Such models proved satisfactory in cheaply and accurately estimating the risk factor of the mode (Ndiaye et al, ASME Turbo Expo, 2015). The surrogate models are then fitted with the thousands of ATACAMAC simulations performed within the Monte Carlo analysis. These low-order models are then reused 100 000 times to determine the PDF of the growth rate of the acoustic disturbances, a necessary quantity to estimate the risk factor of the mode. A discussion ensued to evaluate the uncertainty quantification approach adopted.

A recent study of red blood cells (RBCs) in shear flow [Lanotte et al., Proc. Natl. Acad. Sci. U.S.A. 113, 13289 (2016)PNASA60027-842410.1073/pnas.1608074113] has demonstrated that RBCs first tumble, then roll, transit to a rolling and tumbling stomatocyte, and finally attain polylobed shapes with increasing shear rate, when the viscosity contrast between cytosol and blood plasma is large enough. Using two different simulation techniques, we construct a state diagram of RBC shapes and dynamics in shear flow as a function of shear rate and viscosity contrast, which is also supported by microfluidic experiments. Furthermore, we illustrate the importance of RBC shear elasticity for its dynamics in flow and show that two different kinds of membrane buckling trigger the transition between subsequent RBC states.

International audience; Several well-resolved 4D Flow MRI acquisitions of an idealized rigid flow phantom featuring an aneurysm, a curved channel as well as a bifurcation were performed under pulsatile regime. The resulting hemodynamics were processed to remove MRI artifacts. Subsequently, they were compared with CFD predictions computed on the same flow domain, using an in-house high-order low dissipative flow solver. Results show that reaching a good agreement is not straightforward but requires proper treatments of both techniques. Several sources of discrepancies are highlighted and their impact on the final correlation evaluated. While a very poor correlation ($r^2$ = 0.63) is found in the entire domain between raw MRI and CFD data, correlation as high as $r^2$ = 0.97 is found when artifacts are removed by post-processing the MR data and down sampling the CFD results to match the MRI spatial and temporal resolutions. This work demonstrates that, in a well-controlled environment, both PC-MRI and CFD might bring reliable and correlated flow quantities when a proper methodology to reduce the errors is followed.

International audience; Using a previously developed inversion platform for functional cerebral medical imaging with ensemble Kalman filters, this work analyzes the sensitivity of the results with respect to different parameters entering the physical model and inversion procedure, such as the inlet flow rate from the heart, the choice of the boundary conditions, and the nonsymmetry in the network terminations. It also proposes an alternative low complexity construction for the covariance matrix of the hemodynamic parameters of a network of arteries including the circle of Willis. The platform takes as input patient-specific blood flow rates extracted from magnetic resonance angiography and magnetic resonance imaging (dicom files) and is applied to several available patients data. The paper presents full analysis of the results for one of these patients, including a sensitivity study with respect to the proximal and distal boundary conditions. The results notably show that the uncertainties on the inlet flow rate led to uncertainties of the same order of magnitude in the estimated parameters (blood pressure and elastic parameters) and that three-lumped parameters boundary conditions are necessary for a correct retrieval of the target signals.