Incorporating Unresolved Stresses in Blood Damage Modeling: Energy Dissipation More Accurate Than Reynolds Stress Formulation

Objective: Reynolds Averaged Navier Stokes (RANS) models are often used as the basis for modeling blood damage in turbulent flows. To predict blood damage by turbulence stresses that are not resolved in RANS, a stress formulation that represents the corresponding scales is required. Here, we compare two commonly employed stress formulations: a scalar stress representation that uses Reynolds stresses as a surrogate for unresolved fluid stresses, and an effective stress formulation based on energy dissipation. Methods: We conducted unsteady RANS simulations of the CentriMag blood pump with three different closure models and a Large Eddy Simulation (LES) for reference. We implemented both stress representations in all models and compared the resulting total stress distributions in Eulerian and Lagrangian frameworks. Results: The Reynolds-stress-based approach overestimated the contribution of unresolved stresses in RANS, with differences between closure models of up to several orders of magnitude. With the dissipation-based approach, the total stresses predicted with RANS deviated by about 50% from the LES reference, which was more accurate than only considering resolved stresses. Conclusion: The Reynolds-stress-based formulation proved unreliable for estimating scalar stresses in our RANS simulations, while the dissipation-based approach provided an accuracy improvement over simply neglecting unresolved stresses. Significance: Our results suggest that dissipation-based inclusion of unresolved stresses should be the preferred choice for blood damage modeling in RANS.