The Okubo-Weiss criterion in hydrodynamic flows:Geometric aspects and further extension

The Okubo [5]-Weiss [6] criterion has been extensively used as a diagnostic tool to divide a two-dimensional (2D) hydrodynamical flow field into hyperbolic and elliptic regions and to serve as a useful qualitative guide to the complex quantitative criteria. The Okubo-Weiss criterion is frequently validated on empirical grounds by the results ensuing its application. So, we will explore topological implications into the Okubo-Weiss criterion and show the Okubo-Weiss parameter is, to within a positive multiplicative factor, the negative of the Gaussian curvature of the underlying vorticity manifold. The Okubo-Weiss criterion is reformulated in polar coordinates, and is validated via several examples including the Lamb- Oseen vortex, and the Burgers vortex. These developments are then extended to 2D quasi- geostrophic (QG) flows. The Okubo-Weiss parameter is shown to remain robust under the -plane approximation to the Coriolis parameter. The Okubo-Weiss criterion is shown to be able to separate the 2D flow-field into coherent elliptic structures and hyperbolic flow configurations very well via numerical simulations of quasi-stationary vortices in QG flows. An Okubo-Weiss type criterion is formulated for 3D axisymmetric flows, and is validated via application to the round Landau-Squire Laminar jet flow.

The mathematical description of the bulk fluid flow and that of the content impurity dispersion, obtained by replacing integer order temporal derivatives with general temporal Caputo or general temporal Riemann-Liouville fractional order derivatives, are objective

In the field of fractional calculus applications, there is a tendency to admit that “integer-order derivatives cannot simply be replaced by fractional-order derivatives to develop fractional-order theories”. There are different arguments for that: initialization problem, inconsistency, use of nonsingular or singular kernels, loss of objectivity. In this paper it is shown that the mathematical description of the bulk fluid flow and that of the content impurity spread replacing integer order temporal derivatives with general temporal Caputo or general temporal Riemann-Liouville fractional order derivatives, are objective. More precisely, it is proven that, the mathematical description of the bulk fluid 2D flow and that of the content impurity spread, in a horizontal unconfined aquifer, obtained replacing integer order temporal derivatives with general temporal Caputo or general temporal Riemann-Liouville fractional order derivatives, are objective. It is also proven that, the mathematical description of a Newtonian, incompressible, viscous bulk fluid 3D flow and that of the contained impurity dispersion, obtained replacing integer order temporal derivatives with general temporal Caputo or general temporal Riemann-Liouville fractional order derivatives, are objective. The obtained results show the compatibility of the general temporal Caputo and general temporal Riemann-Liouville fractional order derivatives with the understanding of the “measured time” evolution. In the same time these results reveal that, the objectivity violation, when integer order temporal derivatives are replaced by classic temporal Caputo or classic temporal Riemann-Liouville fractional order derivatives, is originated in the incompatibility of the classic fractional order derivatives, with the understanding of the “measured time” evolution.

Peak flow measurements in patients with severe aortic stenosis: a prospective comparative study between cardiovascular magnetic resonance 2D and 4D flow and transthoracic echocardiography

Background Aortic valve stenosis (AS) is the most prevalent valvular disease in the developed countries. Four-dimensional (4D) flow cardiovascular magnetic resonance (CMR) is an emerging imaging technique, which has been suggested to improve the evaluation of AS severity compared to two-dimensional (2D) flow and transthoracic echocardiography (TTE). We investigated the reliability of CMR 2D flow and 4D flow techniques in measuring aortic transvalvular peak systolic flow in patients with severe AS. Methods We prospectively recruited 90 patients referred for aortic valve replacement due to severe AS (73.3 ± 11.3 years, aortic valve area 0.7 ± 0.1 cm2, and 54/36 tricuspid/bicuspid), and 10 non-valvular disease controls. All the patients underwent echocardiography and 2D flow and 4D flow CMR. Peak flow velocity measurements were compared using Wilcoxon signed rank sum test and Bland–Altman analysis. Results 4D flow underestimated peak flow velocity in the AS group when compared with TTE (bias − 1.1 m/s, limits of agreement ± 1.4 m/s) and 2D flow (bias − 1.2 m/s, limits of agreement ± 1.6 m/s). The differences between values obtained by TTE (median 4.3 m/s, range 2.7–6.1 m/s) and 2D flow (median 4.5 m/s, range 2.9–6.5 m/s) compared to 4D flow (median 3.1 m/s, range 1.7–5.1 m/s) were significant (p < 0.001). The difference between 2D flow and TTE were insignificant (bias 0.07 m/s, limits of agreement ± 1.5 m/s). In non-valvular disease controls, peak flow velocity was measured higher by 4D flow than 2D flow (1.4 m/s, 1.1–1.7 m/s and 1.3 m/s, 1.1–1.5 m/s, respectively; bias 0.2 m/s, limits of agreement ± 0.16 m/s). Conclusions CMR 4D flow significantly underestimates systolic peak flow velocity in patients with severe AS. 2D flow, in turn, estimated the AS velocity accurately, with measured peak flow velocities comparable to TTE.

Flow Structures Identification through Proper Orthogonal Decomposition: The Flow around Two Distinct Cylinders

Numerical simulations of fluid flows can produce a huge amount of data and inadvertently important flow structures can be ignored, if a thorough analysis is not performed. The identification of these flow structures, mainly in transient situations, is a complex task, since such structures change in time and can move along the domain. With the decomposition of the entire data set into smaller sets, important structures present in the main flow and structures with periodic behaviour, like vortices, can be identified. Therefore, through the analysis of the frequency of each of these components and using a smaller number of components, we show that the Proper Orthogonal Decomposition can be used not only to reduce the amount of significant data, but also to obtain a better and global understanding of the flow (through the analysis of specific modes). In this work, the von Kármán vortex street is decomposed into a generator base and analysed through the Proper Orthogonal Decomposition for the 2D flow around a cylinder and the 2D flow around two cylinders with different radii. We consider a Newtonian fluid and two non-Newtonian power-law fluids, with n=0.7 and n=1.3. Grouping specific modes, a reconstruction is made, allowing the identification of complex structures that otherwise would be impossible to identify using simple post-processing of the fluid flow.

Numerical Study of Vortex Shedding behind a NACA 0009 Hydrofoil

This paper addresses the propeller singing mitigation strategy of implementing an anti-singing edge so that the vortex shedding mechanism causing the excitation at the trailing edge of the propeller blade can be reduced. A Reynolds-Averaged Navier Stokes model with a k-ε turbulence formulation in 2D-flow was used to investigate the problem numerically. Simulations on a NACA 0009 hydrofoil with varying inflow velocity, angle of attack, and bevel angle were done. The content in this paper is a summary of the work done by the author during his MSc Individual Project at University College London (Johannessen, MSc thesis, 2020).

Coronary Flow Assessment Using Accelerated 4D Flow MRI With Respiratory Motion Correction

Magnetic resonance imaging (MRI) can potentially be used for non-invasive screening of patients with stable angina pectoris to identify probable obstructive coronary artery disease. MRI-based coronary blood flow quantification has to date only been performed in a 2D fashion, limiting its clinical applicability. In this study, we propose a framework for coronary blood flow quantification using accelerated 4D flow MRI with respiratory motion correction and compressed sensing image reconstruction. We investigate its feasibility and repeatability in healthy subjects at rest. Fourteen healthy subjects received 8 times-accelerated 4D flow MRI covering the left coronary artery (LCA) with an isotropic spatial resolution of 1.0 mm3. Respiratory motion correction was performed based on 1) lung-liver navigator signal, 2) real-time monitoring of foot-head motion of the liver and LCA by a separate acquisition, and 3) rigid image registration to correct for anterior-posterior motion. Time-averaged diastolic LCA flow was determined, as well as time-averaged diastolic maximal velocity (VMAX) and diastolic peak velocity (VPEAK). 2D flow MRI scans of the LCA were acquired for reference. Scan-rescan repeatability and agreement between 4D flow MRI and 2D flow MRI were assessed in terms of concordance correlation coefficient (CCC) and coefficient of variation (CV). The protocol resulted in good visibility of the LCA in 11 out of 14 subjects (six female, five male, aged 28 ± 4 years). The other 3 subjects were excluded from analysis. Time-averaged diastolic LCA flow measured by 4D flow MRI was 1.30 ± 0.39 ml/s and demonstrated good scan-rescan repeatability (CCC/CV = 0.79/20.4%). Time-averaged diastolic VMAX (17.2 ± 3.0 cm/s) and diastolic VPEAK (24.4 ± 6.5 cm/s) demonstrated moderate repeatability (CCC/CV = 0.52/19.0% and 0.68/23.0%, respectively). 4D flow- and 2D flow-based diastolic LCA flow agreed well (CCC/CV = 0.75/20.1%). Agreement between 4D flow MRI and 2D flow MRI was moderate for both diastolic VMAX and VPEAK (CCC/CV = 0.68/20.3% and 0.53/27.0%, respectively). In conclusion, the proposed framework of accelerated 4D flow MRI equipped with respiratory motion correction and compressed sensing image reconstruction enables repeatable diastolic LCA flow quantification that agrees well with 2D flow MRI.

Bayesian Inference of Experimental Data for Axial Compressor Performance Assessment

As the next generation of turbomachinery components becomes more sensitive to instrumentation intrusiveness, a reduction of the number of measurement devices required for the evaluation of performance is a possible and cost-effective way to mitigate the arising of non-mastered experimental errors. A first approach to a data assimilation methodology based on Bayesian inference is developed with the aim of reducing the instrumentation effort. A numerical model is employed to provide an initial belief of the flow, that is then updated based on experimental observations, using an ensemble Kalman filter algorithm for inverse problems. Validation of the algorithm is achieved with the usage of experimental measurements not used in the data assimilation process. The methodology is tested for a low aspect ratio axial compressor stage, showing a good prediction of the corrected compressor map, as well as a promising prediction of the inter-row radial pressure distribution and 2D flow field.