Material transport in the left ventricle with aortic valve regurgitation

This experimental in vitro work investigates material transport properties in a model left ventricle in the case of aortic regurgitation, a valvular disease characterized by a leaking aortic valve and consequently double-jet filling within the elastic left ventricular geometry. This study suggests that material transport phenomena are strongly determined by the motion of the counterrotating vortices driven by the regurgitant aortic and mitral jets. The overall particle residence time appears to be significantly longer with moderate aortic regurgitation, attributed to the dynamics resulting from the timing between the onset of the two jets. Increasing regurgitation severity is shown to be associated with higher frequencies in the time-frequency spectra of the velocity signals at various points in the flow, suggesting nonlaminar mixing past moderate regurgitation. Additionally, a large part of the regurgitant inflow is retained for at least one cardiac cycle. Such an increase in particle residence time accompanied by the occurrence and persistence of a number of attracting Lagrangian coherent structures presents favorable conditions and locations for activated platelets to agglomerate within the left ventricle, potentially posing an additional risk factor for patients with aortic regurgitation

P0006: Hearts on Fire

ABSTRACT: The left ventricle is the heart's powerhouse, responsible for pumping oxygen- and nutrient-rich blood to each and every tissue throughout the body. By consequence, diseases affecting this laborious chamber are not only more common but often more serious. The fluid dynamics in the healthy left ventricle is characterized by the impulsive formation of a vortex ring during its filling phase which facilitates the following ejection with very little energy loss. In the case of a leaking aortic valve however, the left ventricle will fill from two sides, resulting in the interaction between two pulsatile jets in a confined elastic vessel, marking a new and unique fluid dynamics problem. Here, we show the backward finite-time Lyapunov exponent in the healthy and diseased left ventricles, revealing the attracting Lagrangian coherent structures associated with the aortic (A) and mitral (M) inflows. The background shows the time-frequency spectra of velocity signals over one cardiac cycle taken at the entrance of the mitral (right) and aortic (left) inflows for the healthy (top) and diseased (bottom) cases. The overlay and perceptually-uniform colormap (thanks to Stéfan van der Walt and Nathaniel Smith) are such that the high frequency bursts (up to 200 Hz) occurring early in the filling phase give the appearance of fire

Towards the detection of moving separation in unsteady flows

In many engineering systems operating with a working fluid, the best efficiency is reached close to a condition of flow separation, which makes the prediction of this condition very important in industry. Provided that wall-based quantities can be measured, we know today how to obtain good predictions for two- and three-dimensional steady and periodic flows. In these flows, the separation is defined on a fixed line attached to a material surface. The last case to elucidate is the one where this line is no longer attached to the wall but on the contrary is contained within the flow. This moving separation is probably, however, the most common case of separation in natural flows and industrial applications. Since this case has received less attention during the past few years, we propose in this study to examine some properties of moving separation in two-dimensional, unsteady flows where the separation does not leave a signature on the wall. Since in this framework separation can be extracted by using a Lagrangian frame where the separation profile can be viewed as a hyperbolic unstable manifold, we propose a method to extract the separation point defined by the Lagrangian saddle point that belongs to this unstable manifold. In practice, the separation point and profile are initially extracted by detecting the most attracting Lagrangian coherent structure near the wall, and they can then be advected in time for subsequent instants. It is found that saddle points, which initially act as separation points in the viscous wall flow region, remarkably preserve their hyperbolicity even if they are ejected from the wall towards the inviscid region. Two test cases are studied: the creeping flow of a rotating and translating cylinder close to a wall, and the unsteady separation in the boundary layer generated by a planar jet impinging onto a plane wall.</jats:p

Experimental investigation of unsteady separation in the rotor-oscillator flow

Visualisations of various types of flow separation are presented in an experimental set-up that translates a rotating cylinder parallel to a wall. Particle image velocimetry is used to measure the two velocity components in a plane perpendicular to the cylinder where the flow is two-dimensional. To spatially resolve the flow close to the wall, a high-viscosity fluid is used. For a periodic translation, the fixed separation is compared to the theory of Haller (J. Fluid Mech., vol. 512, 2004, pp. 257–311), while for non-periodic translations, a method is proposed to extract the moving separation point captured by a Lagrangian saddle point, and its finite-time unstable direction (separation profiles). Intermediate cases are also presented where both types of separation, fixed and moving, are either present simultaneously or appear successively. Some results issued from numerical simulations of an impinging jet show that all the cases observed in the rotor-oscillator flow are not restricted to high-viscosity fluid motions but may also occur within any vortical flow.</jats:p

Exact theory of material spike formation in flow separation

We develop a frame-invariant theory of material spike formation during flow separation over a no-slip boundary in two-dimensional flows with arbitrary time dependence. Based on the exact curvature evolution of near-wall material lines, our theory identifies both fixed and moving flow separation, is effective also over short time intervals, and admits a rigorous instantaneous limit. As a byproduct, we derive explicit formulae for the evolution of material line curvature and the curvature rate for general compressible flows. The material backbone that we identify acts first as the precursor and later as the centrepiece of unsteady Lagrangian flow separation. We also discover a previously undetected spiking point where the backbone of separation connects to the boundary, and derive wall-based analytical formulae for its location. Finally, our theory explains the perception of off-wall separation in unsteady flows and provides conditions under which such a perception is justified. We illustrate our results on several analytical and experimental flows.</jats:p