Coanda Effect for Incompressible Flows in Moving Domains

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Coanda effect is a phenomenon that has been described in scientific literature as a tendency of a fluid jet to be attracted to a nearby surface. Recently, Coanda effect has been used in cardiology to describe the wall-hugging jets in mitral regurgitation: regurgitant blood flow through a leaky mitral valve sometimes hugs the wall of the left atrium which makes it difficult to assess the severity of mitral regurgitation using classical color Doppler imaging techniques. Despite the large cardiovascular and biomedical literature reporting on the Coanda effect in echocardiography, a connection with the fluid dynamics studies that could help identify and understand the main features of the corresponding flow conditions is lacking. This project makes this connection and explores the fluid dynamics properties leading to the Coanda effect in a novel environment: moving geometries and time periodic flow conditions, which will include those encountered in patients with mitral regurgitation. The corresponding fluid dynamics problem is associated with the behavior of flow through an orifice at Reynolds numbers below turbulence. Coanda effect corresponds to the breaking of symmetry (a bifurcation) in the solution of the Navier-Stokes equations at certain Reynolds numbers and for certain orifice shapes. While flows through orifices have been extensively studied (numerically and experimentally) in the context of fixed orifices and fixed fluid domains, there have been no results that shed light on the flow conditions leading to Coanda effect in moving orifices under time-periodic pressure loads. This project addresses this problem by combining sophisticated computational methodology and analytical techniques associated with fluid-structure interaction (FSI) between a viscous, incompressible fluid, and an elastic structure. The methodology is based on a monolithic, semi-implicit algorithm to solve an Arbitrary Lagrangian-Eulerian (ALE) formulation of the underlying FSI problem, and on the corresponding energy estimates. Experimental validation of the mathematical models and computer simulations will be performed with the medical collaborators at the DeBakey Heart and Vascular Center in Houston.Although over 50% of the US population has some degree of heart valve dysfunction, most cases do not require any medical treatment. In the cases when valve regurgitation is severe, failure of treatment can lead to arrhythmias, congestive heart failure and death. Doppler echocardiography is routinely used by physicians to diagnose and assess the severity of mitral valve regurgitation. The accurate assessment of valve regurgitation using echocardiography is, however, an ongoing challenge. In particular, regurgitant blood flow through a leaky mitral valve sometimes hugs the wall of the left atrium (known as the Coanda effect), which makes it difficult to see and measure the regurgitant volume. By using sophisticated mathematics, scientific computing, and experimental validation, the interdisciplinary team consisting of mathematicians and echocardiographic specialists, is investigating the blood flow conditions, and the shape of the regurgitant valves, that lead to the Coanda effect. This is a novel fluid-dynamics problem that has not been studied before due to the difficulties in resolving the interaction between blood flow and the moving regurgitant valve. By using a recently developed state-of-the-art computational algorithm that is capable of resolving this problem, and by developing novel mathematical techniques that will capture the bifurcation in the flow associated with Coanda effect, the results of this project will shed light on the complex intracardiac flow conditions associated with this phenomenon, and lead the way in designing novel protocols in echocardiographic assessment of mitral regurgitation. Students participate in all the aspects of this research. They are being trained in computer simulations, mathematical modeling, and in experimental validation of the mathematical models.