Coanda Effect for Incompressible Flows in Moving Domains

运动域中不可压缩流动的康达效应

• 批准号: 1109189
• 负责人: Suncica Canic
• 金额: $ 26.36万
• 依托单位: University of Houston
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-07-15 至 2015-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1109189&HistoricalAwards=false
• 关键词: Coanda; Effect; Incompressible; Flows; Moving

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.

柯恩达效应是在科学文献中描述为流体射流被吸引到附近表面的趋势的现象。 最近，柯恩达效应已被用于心脏病学来描述二尖瓣反流中的贴壁射流：通过泄漏的二尖瓣的反流血流有时会贴着左心房壁，这使得难以使用经典的彩色多普勒成像技术来评估二尖瓣反流的严重程度。 尽管大量的心血管和生物医学文献报道了超声心动图中的Coanda效应，但缺乏与流体动力学研究的联系，这些研究可以帮助识别和理解相应流动条件的主要特征。该项目建立了这种联系，并探索了在一个新的环境中导致柯恩达效应的流体动力学特性：移动的几何形状和时间周期性流动条件，其中包括二尖瓣返流患者遇到的情况。相应的流体动力学问题与雷诺数低于湍流时通过孔口的流动行为有关。柯恩达效应对应于在特定雷诺数和特定孔口形状下的Navier-Stokes方程解中的对称性破缺（分叉）。虽然已经在固定孔口和固定流体域的背景下对通过孔口的流动进行了广泛的研究（数值和实验），但是还没有结果阐明在时间周期性压力载荷下导致移动孔口中的柯恩达效应的流动条件。该项目通过结合与粘性不可压缩流体和弹性结构之间的流体-结构相互作用（FSI）相关的复杂计算方法和分析技术来解决这个问题。该方法是基于一个单片，半隐式算法来解决一个任意拉格朗日欧拉（ALE）制定的基本FSI问题，并在相应的能量估计。数学模型和计算机模拟的实验验证将与休斯顿DeBakey心脏和血管中心的医学合作者一起进行。尽管超过50%的美国人口有一定程度的心脏瓣膜功能障碍，但大多数病例不需要任何药物治疗。在瓣膜返流严重的情况下，治疗失败可导致心律失常、充血性心力衰竭和死亡。多普勒超声心动图通常被医生用于诊断和评估二尖瓣返流的严重程度。然而，使用超声心动图准确评估瓣膜返流是一个持续的挑战。特别是，通过渗漏的二尖瓣的血流有时会拥抱左心房的壁（称为柯恩达效应），这使得难以看到和测量血流体积。通过使用复杂的数学，科学计算和实验验证，由数学家和超声心动图专家组成的跨学科团队正在研究导致Coanda效应的血流条件和顺应性瓣膜的形状。这是一个新的流体动力学问题，以前没有研究过，由于在解决血液流动和移动的阻力阀之间的相互作用的困难。通过使用最近开发的最先进的计算算法，能够解决这个问题，并通过开发新的数学技术，将捕获与柯恩达效应相关的流动中的分叉，该项目的结果将揭示与这种现象相关的复杂的心内流动条件，并导致在设计新的协议，超声心动图评估二尖瓣返流的方式。学生参与了这项研究的各个方面。他们正在接受计算机模拟、数学建模和数学模型实验验证方面的培训。