Entropic Lattice Boltzmann Simulation of the Flow Past Square Cylinder

Minimal Boltzmann kinetic models, such as lattice Boltzmann, are often used as an alternative to the discretization of the Navier-Stokes equations for hydrodynamic simulations. Recently, it was argued that modeling sub-grid scale phenomena at the kinetic level might provide an efficient tool for large scale simulations. Indeed, a particular variant of this approach, known as the entropic lattice Boltzmann method (ELBM), has shown that an efficient coarse-grained simulation of decaying turbulence is possible using these approaches. The present work investigates the efficiency of the entropic lattice Boltzmann in describing flows of engineering interest. In order to do so, we have chosen the flow past a square cylinder, which is a simple model of such flows. We will show that ELBM can quantitatively capture the variation of vortex shedding frequency as a function of Reynolds number in the low as well as the high Reynolds number regime, without any need for explicit sub-grid scale modeling. This extends the previous studies for this set-up, where experimental behavior ranging from $Re\sim O(10)$ to $Re\leq 1000$ were predicted by a single simulation algorithm.Comment: 12 pages, 5 figures, to appear in Int. J. Mod. Phys.

Energy distribution and spectral analysis of the turbulent flow downstream of stenotic and bioprosthetic aortic valves

Haemodynamic turbulence due to aortic stenoses or non-optimal bioprosthetic aortic valves (BAV) during peak flow may contribute to a variety of pathophysiological effects (Stein and Sabbah, 1976). We intend to characterise the energy carried by the turbulent fluctuations and the turbulent spectra for three valvular configurations using a direct numerical simulation of the incompressible flow downstream of a fixed-wall aortic stenosis (Corso et al., 2021) and 3D fluid-structure interaction simulations of BAV with moving leaflets (Nestola et al., 2019). The time-varying orifice shape of the BAV and the reduced orifice area of the stenosis is responsible for distinct large-scale anisotropic eddies. Despite a higher turbulence intensity in the stenotic case, the three-dimensional wavenumber spectra considered at one point (Frost and Moulden, 1977) in the ascending aorta and close to the sino-tubular junction display the typical inertial subrange in the three cases. By analysing the energy-bearing turbulent features and linking them to geometrical leaflet parameters, we shed light on an optimised leaflet design for improved valve performance

Toward an accurate estimation of wall shear stress from 4D flow magnetic resonance downstream of a severe stenosis

Purpose: First, to investigate the agreement between velocity, velocity gradient, and Reynolds stress obtained from four-dimensional flow magnetic resonance (4D flow MRI) measurements and direct numerical simulation (DNS). Second, to propose and optimize based on DNS, 2 alternative methods for the accurate estimation of wall shear stress (WSS) when the resolution of the flow measurements is limited. Thirdly, to validate the 2 methods based on 4D flow MRI data. Methods: In vitro 4D MRI has been conducted in a realistic rigid stenosed aorta model under a constant flow rate of 12 L/min. A DNS of transitional stenotic flow has been performed using the same geometry and boundary conditions. Results: Time-averaged velocity and Reynolds stresses are in good agreement between in vitro 4D MRI data and DNS (errors between 2% and 8% of the reference downsampled data). WSS estimation based on the 2 proposed methods applied to MRI data provide good agreement with DNS for slice-averaged values (maximum error is less than 15% of the mean reference WSS for the first method and 25% for the second method). The performance of both models is not strongly sensitive to spatial resolution up to 1.5 mm voxel size. While the performance of model 1 deteriorates appreciably at low signal-to-noise ratios, model 2 remains robust. Conclusions: The 2 methods for WSS magnitude give an overall better agreement than the standard approach used in the literature based on direct calculation of the velocity gradient close to the wall (relative error of 84%)