The NASA rotor 37 is investigated accounting for as many as 9 simultaneous operational and geometrical uncertainties. The combined influence of uncertainties on input quantities such as the total inlet pressure, static outlet pressure, tip gap or leading and trailing edge angles on output quantities is studied. These simulations provide results which go far beyond the standard deterministic simulation. A probabilistic collocation method in combination with a sparse grid quadrature is introduced into the software suite FINE™ propagating combined operational and geometrical uncertainties in complex 3D CFD simulations. The modification of the parameterized geometry and the consequent re-meshing is provided by a fully automatic tool, which also couples with the flow solver and provides post-treatment routines. It is this automation, which makes this kind of study feasible. A manual modification of geometry, manual meshing and simulation set-up accounting for a multitude of simultaneous uncertainties is simply unfeasible for as many as hundreds of complex 3D turbo-machinery simulations. This work represents thus a break-through in the uncertainty management towards the application of uncertainty propagation in the daily engineering practice.
BackgroundIt is a known fact that blood flow pattern and more specifically the pulsatile time variation of shear stress on the vascular wall play a key role in atherogenesis. The paper presents the conception, the building and the control of a new in vitro test bench that mimics the pulsatile flows behavior based on in vivo measurements.MethodsAn in vitro cardiovascular simulator is alimented with in vivo constraints upstream and provided with further post-processing analysis downstream in order to mimic the pulsatile in vivo blood flow quantities. This real-time controlled system is designed to perform real pulsatile in vivo blood flow signals to study endothelial cells’ behavior under near physiological environment. The system is based on an internal model controller and a proportional-integral controller that controls a linear motor with customized piston pump, two proportional-integral controllers that control the mean flow rate and temperature of the medium. This configuration enables to mimic any resulting blood flow rate patterns between 40 and 700 ml/min. In order to feed the system with reliable periodic flow quantities in vivo measurements were performed. Data from five patients (1 female, 4 males; ages 44–63) were filtered and post-processed using the Newtonian Womersley’s solution. These resulting flow signals were compared with 2D axisymmetric, numerical simulation using a Carreau non-Newtonian model to validate the approximation of a Newtonian behavior.ResultsThis in vitro test bench reproduces the measured flow rate time evolution and the complexity of in vivo hemodynamic signals within the accuracy of the relative error below 5%.ConclusionsThis post-processing method is compatible with any real complex in vivo signal and demonstrates the heterogeneity of pulsatile patterns in coronary arteries among of different patients. The comparison between analytical and numerical solution demonstrate the fair quality of the Newtonian Womersley’s approximation. Therefore, Womersley’s solution was used to calculate input flow rate for the in vitro test bench.
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