| We developped a finite element method to predict hemolysis in flows. It uses a discontinuous Galerkin formulation to solve the hemolysis prediction model. The latter is a hyperbolic advection-reaction equation. Solving such equations is not a trivial task. The task becomes even more complicated when the reaction term (source term) is complex and discontinuous, and the flow contains recirculation zones. To overcome these difficulties, we developped a solution algorithm that includes adaptive remeshing driven by error estimates for both the velocity and hemolysis fields. To our knowledge we present the first such error estimator for hemolysis. Code verification using the method of manufactured solutions shows that the finite element method delivers the theoretical convergence rate. Lower convergence rates were observed for more complex, realistic flows in cannulae and sudden axisymmetric contractions. Hemolysis predictions in cannulae allowed us to assess the usability of our tool and its capability to produce realistic predictions in this particular case. We then measured in vitro the hemolysis in blood circulating through sudden and gradual contractions. The flow Reynold's number for experiments and simulations was set to 1200, based on contraction's inlet diameter and average velocity, and blood's viscosity at infinite shear rate (mu infinity) for a shear-thinning fluid. Detailed experimental procedures were put together to ensure accurate and consistent hemolysis measurements in the laboratory. In particular, a lot of energy was spent on the precise measurement of blood's muinfinity viscosity. Due to the presence of red cells, detrimental effects such as slip or end effects are often observed when measuring blood viscosity. We finally found out that those effects could be neglected due probably to the low hematocrit levels (28 and 31%) measured in our bovine blood samples. Comparisons between hemolysis predictions and experimental measurements lead us conclude that the threshold value of the mechanical stress to produce hemolysis (set to 250 Pa in the prediction model and based on the literature) is probably too low for this type of flow. |
