Joaquim Peiró

Pulse wave propagation in a model human arterial network: Assessment of 1-D visco-elastic simulations against in vitro measurements

The accuracy of the nonlinear one-dimensional (1-D) equations of pressure and flow wave propagation in Voigt-type visco-elastic arteries was tested against measurements in a well-defined experimental 1:1 replica of the 37 largest conduit arteries in the human systemic circulation. The parameters required by the numerical algorithm were directly measured in the in vitro setup and no data fitting was involved. The inclusion of wall visco-elasticity in the numerical model reduced the underdamped high-frequency oscillations obtained using a purely elastic tube law, especially in peripheral vessels, which was previously reported in this paper [Matthys et al., 2007. Pulse wave propagation in a model human arterial network: Assessment of 1-D numerical simulations against in vitro measurements. J. Biomech. 40, 3476–3486]. In comparison to the purely elastic model, visco-elasticity significantly reduced the average relative root-mean-square errors between numerical and experimental waveforms over the 70 locations measured in the in vitro model: from 3.0% to 2.5% (p<0.012) for pressure and from 15.7% to 10.8% (p<0.002) for the flow rate. In the frequency domain, average relative errors between numerical and experimental amplitudes from the 5th to the 20th harmonic decreased from 0.7% to 0.5% (p<0.107) for pressure and from 7.0% to 3.3% (p<10−6) for the flow rate. These results provide additional support for the use of 1-D reduced modelling to accurately simulate clinically relevant problems at a reasonable computational cost.

Adaptive remeshing for three-dimensional compressible flow computations

An adaptive mesh procedure for computing steady state solutions of the compressible Euler equations in three dimensions is presented. The method is an extension of previous work in two dimensions. The approach requires the coupling of a surface triangulator, an automatic tetrahedral mesh generator, a finite element flow solver and an error estimation procedure. An example involving flow at high Mach number is included to demonstrate the numerical performance of the proposed approach. The example shows that the use of this form of adaptivity in three dimensions offers the potential of even greater computational savings than those attained in the corresponding two-dimensional implementation.

The Influence of Out-of-Plane Geometry on the Flow Within a Distal End-to-Side Anastomosis

This paper describes a computational and experimental investigation of flow in a proto-type model geometry of a fully occluded 45 deg distal end-to-side anastomosis. Previous investigations have considered a similar configuration where the centerlines of the bypass and host vessels lie within a plane, thereby producing a plane of symmetry within the flow. We have extended these investigations by deforming the bypass vessel out of the plane of symmetry, thereby breaking the symmetry of the flow and producing a nonplanar geometry. Experimental data were obtained using magnetic resonance imaging of flow within perspex models and computational data were obtained from simulations using a high-order spectral/hp element method. We found that the nonplanar three-dimensional flow notably alters the distribution of wall shear stress at the bed of the anastomosis, reducing the peak wall shear stress peak by approximately 10 percent when compared with the planar model. Furthermore, an increase in the absolute flux of velocity into the occluded region, proximal to the anastomosis, of 80 percent was observed in the nonplanar geometry when compared with the planar geometry.

The computation of three-dimensional flows using unstructured grids

Abstract A general method is described for automatically discretising, into unstructured assemblies of tetrahedra, the three-dimensional solution domains of complex shape which are of interest in practical computational aerodynamics. An algorithm for the solution of the compressible Euler equations which can be implemented on such general unstructured tetrahedral grids is described. This is an explicit cell-vertex scheme which follows a general Taylor-Galerkin philosophy. The approach is employed to compute a transonic inviscid flow over a standard wing and the results are shown to compare favourably with experimental observations. As a more practical demonstration, the method is then applied to the analysis of inviscid flow over a complete modern fighter configuration. The effect of using mesh adaptivity is illustrated when the method is applied to the solution of high speed flow in an engine inlet.

Finite element multigrid solution of Euler flows past installed aero-engines

A finite element based procedure for the solution of the compressible Euler equations on unstructured tetrahedral grids is described. The spatial discretisation is accomplished by means of an approximate variational formulatin, with the explicit addition of a matrix form of artificial viscosity. The solution is advanced in time by means of an explicit multi-stage time stepping procedure. The method is implemented in terms of an edge based representation for the tetrahedral grid. The solution procedure is accelerated by use of a fully unstructured multigrid algorithm. The approach is applied to the simulation of the flow past an installed aero-engine nacelle, at three different free stream conditions. Comparison is made between the numerical predictions and experimental pressure observations.

Reduced models of the cardiovascular system

Due to the large number of vessels involved and the multitude of different length scales required to accurately represent the flow in the various regions of the cardiovascular system, simulations of the flow of blood in the system based on full 3D models (see Chapters 2 and 3) are beyond the capability of current computers and they will be for years to come. Moreover, the huge amount of data that would be generated by such simulations is costly to process and of difficult clinical interpretation.

Vortical Flow Structure Identification and Flow Transport in Arteries

Our interest in vortices arises for two reasons. Firstly, at moderate to large Reynolds numbers (at least 100) which characterise flow in larger arteries, vortices are quite persistent. The presence of vortices in a flow may exert a strong influence on its behaviour, although tracking vortices may be difficult as they can evolve rapidly. The effects of vortices or vortical structures are particularly evident when considering both flow stability, and the processes of mixing and transport by the flow. The object of this paper is to examine the dynamics both of vortex motion and of particle transport in arteries, and to relate these to parameters such as geometry and unsteadiness. The Lagrangian particle tracking and the vortex dynamic techniques which are described should help in understanding arterial fluid dynamics and suggest new approaches to modelling.

An Experimental and Numerical Assessment of Airfoil Polars for Use in Darrieus Wind Turbines—Part I: Flow Curvature Effects

A better comprehension of the aerodynamic behavior of rotating airfoils in Darrieus Vertical-axis wind turbines (VAWTs) is crucial both for the further development of these machines and for improvement of conventional design tools based on zero or one-dimensional models (e.g. BEM models).When smaller rotors are designed with high chord-to-radius (c/R) ratios so as not to limit the blade Reynolds number, the performance of turbine blades has been suggested to be heavily impacted by a virtual camber effect imparted on the blades by the curvilinear flow they experience.To assess the impact of this virtual camber effect on blade and turbine performance, a standard NACA0018 airfoil and a NACA0018 conformally transformed such that the airfoil’s chord line follows the arc of a circle, where the ratio of the airfoil’s chord to the circle’s radius is 0.25 were considered. For both airfoils, wind tunnel tests were carried out to assess their aerodynamic lift and drag coefficients for Reynolds numbers of interest for Darrieus VAWTs.Unsteady CFD calculations have been then carried out to obtain curvilinear flow performance data for the same airfoils mounted on a Darrieus rotor with a c/R of 0.25. The blade incidence and lift and drag forces were extracted from the CFD output using a novel incidence angle deduction technique.According to virtual camber theory, the transformed airfoil in this curvilinear flow should be equivalent to the NACA0018 in rectilinear flow, while the NACA0018 should be equivalent to the inverted transformed airfoil in rectilinear flow.Comparisons were made between these airfoil pairings using the CFD output and the rectilinear performance data obtained from the wind tunnel tests and XFoil output in the form of pressure distributions and lift and drag polars.Blade torque coefficients and turbine power coefficient are also presented for the CFD VAWT using both blade profiles.Copyright

A Reparameterisation Based Approach to Geodesic Constrained Solvers for Curve Matching

We present a numerical algorithm for a new matching approach for parameterisation independent diffeomorphic registration of curves in the plane, targeted at robust registration between curves that require large deformations. This condition is particularly useful for the geodesic constrained approach in which the matching functional is minimised subject to the constraint that the evolving diffeomorphism satisfies the Hamiltonian equations of motion; this means that each iteration of the nonlinear optimisation algorithm produces a geodesic (up to numerical discretisation). We ensure that the computed solutions correspond to geodesics in the shape space by enforcing the horizontality condition (conjugate momentum is normal to the curve). Explicitly introducing and solving for a reparameterisation variable allows the use of a point-to-point matching condition. The equations are discretised using the variational particle-mesh method. We provide comprehensive numerical convergence tests and benchmark the algorithm in the context of large deformations, to show that it is a viable, efficient and accurate method for obtaining geodesics between curves.

A Guide to the Implementation of Boundary Conditions in Compact High-Order Methods for Compressible Aerodynamics

The nature of boundary conditions, and how they are implemented, can have a significant impact on the stability and accuracy of a Computational Fluid Dynamics (CFD) solver. The objective of this paper is to assess how different boundary conditions impact the performance of compact discontinuous high-order spectral element methods (such as the discontinuous Galerkin method and the Flux Reconstruction approach), when these schemes are used to solve the Euler and compressible Navier-Stokes equations on unstructured grids. Specifically, the paper will investigate inflow/outflow and wall boundary conditions. In all studies the boundary conditions were enforced by modifying the boundary flux. For Riemann invariant (characteristic), slip and no-slip conditions we have considered a direct and an indirect enforcement of the boundary conditions, the first obtained by calculating the flux using the known solution at the given boundary while the second achieved by using a ghost state and by solving a Riemann problem. All computations were performed using the open-source software Nektar++ (www.nektar.info).