1. A Numerical Simulation of the Vortex Ring Field Incurred by A Round Jet Rui Wang Advisor: Dr. Robin Shandas Department of Mechanical Engineering University of Colorado at Boulder Introduction to Research, 15,Oct. p.1/7

2. Introduction :  Early cardiac dysfunction detection is very important among cardiologists ;  When blood flows from the mitral valve into the ventricle, vortex rings exist ;  Flow spatial resolution affects shear conditions, stagnant regions and energy conversion in turn changing hemolysis, thrombus formation, cells damage etc;  Characterizing this time-resolved velocity field behavior will make early detection of cardiac dysfunction possible. Introduction to Research, 15,Oct. p.2/7

3. Objectives:  Obtaining Flow Field: the comprehensive velocity profile at various time steps;  Flow visualization: the trajectory and shape of the vortex ring at different time (t toff ) and different location;  Vorticity and Circulation calculations including shedding rate: numerically and analytically as well;  The pressure field associated with velocity distribution: by using vorticy equation additionally;  Comparing the results with existing data like slug model and Biot-Savart Law. Introduction to Research, 15,Oct. p.3/7

4. Approach:  Simulating ventricular filling with a suddenly starting round jet - Mitral valve annulus diameter D=2.51cm, ratio of stroke length (L) to orifice diameter (D) 4~13, Re. No.:3000-12000 match with mitral flow;  Using various waveforms to simulate the mitral flow velocity profile;  Creating computational domain: 10D x 10D,128X128 unstructured staggered grids;  Setting up B.C. and I.C.: Non-slip condition on the wall boundary, convective B.C. at outflow boundary, etc.  Problem solving: the Naiver-Stokes equations are solved using commercial code CFDRC and ĸ-ω 2- equation timing marching model (Wilcox, 1988). Introduction to Research, 15,Oct. p.4/7

5. Modeling: D L Introduction to Research, 15,Oct. p.5/7

6. Different Waveforms: U t U t U t Introduction to Research, 15,Oct. p.6/7

7. Computational domain: Introduction to Research, 15,Oct. p.7/7