Numerical comparison and calibration of geometrical multiscale models for the simulation of arterial flows

Arterial tree hemodynamics can be simulated by means of several models of different level of complexity, depending on the outputs of interest and the desired degree of accuracy. In this work, several numerical comparisons of geometrical multiscale models are presented with the aim of evaluating the benefits of such complex dimensionally-heterogeneous models compared to other simplified simulations. More precisely, we present flow rate and pressure wave form comparisons between three-dimensional patient-specific geometries implicitly coupled with one-dimensional arterial tree networks and (i) a full one-dimensional arterial tree model and (ii) stand-alone three-dimensional fluid-structure interaction models with boundary data taken from precomputed full one-dimensional network simulations. On a slightly different context, we also focus on the set up and calibration of cardiovascular simulations. In particular, we perform sensitivity analyses of the main quantities of interest (flow rate, pressure, and solid wall displacement) in respect to the parameters accounting for the elastic and viscoelastic responses of the tissues surrounding the external wall of the arteries. Finally, we also compare the results of geometrical multiscale models in which the boundary solid rings of the three-dimensional geometries are fixed, in respect to those where the boundary interfaces are scaled to enforce the continuity of the vessels size with the surrounding one-dimensional arteries.

Algorithms for the coupling of one-dimensional arterial networks with three-dimensional fluid-structure interaction problems

Simone Deparis, Adelmo Cristiano Innocenza Malossi

This work is focused on the development of a geometrical multiscale framework for modeling the human cardiovascular system. This approach is designed to deal with different geometrical and mathematical models at the same time, without any preliminary hypotheses on the layout of the general multiscale problem. This flexibility allows to set up a complete arterial tree model of the circulatory system, assembling first a network of one-dimensional models, described by non-linear hyperbolic equations, and then replacing some elements with more detailed (and expensive) three-dimensional models, where the Navier-Stokes equations are coupled with structural models through fluid-structure interaction algorithms. The coupling between models of different scale and type is addressed imposing the conservation equations in terms of averaged/integrated quantities (i.e., the flow rate and the normal component of the traction vector); in particular, three coupling strategies have been explored for the fluid problem. In all the cases, these strategies lead to small non-linear interface problems, which are solved using classical iterative algorithms.

2011

Part load flow in radial centrifugal pumps

Olivier Braun

Centrifugal pumps are required to sustain a stable operation of the system they support under all operating conditions. Minor modifications of the surfaces defining the pump's water passage can influence the tendency to unstable system operation significantly. The action of such modifications on the flow are yet not fully understood, leading to costly trial and error approaches in the solution of instability problems. The part-load flow in centrifugal pumps is inherently time-dependent due to the interaction of the rotating impeller with the stationary diffuser (Rotor-Stator Interaction, RSI). Furthermore, adverse pressure gradients in the pump diffuser may cause flow separation, potentially inducing symmetry-breaking non-uniformities, either spatially stationary or rotating and either steady or intermittent. Rotating stall, characterized by the presence of distinct cells of flow separation on the circumference, rotating at a fraction of the impeller revolution rate, has been observed in thermal and hydraulic turbomachines. Due to its complexity, the part-load flow in radial centrifugal pumps is a major challenge for numerical flow simulation methods. The present study investigates the part-load flow in radial centrifugal pumps and pump-turbines by experimental and numerical methods, the latter using a finite volume discretization of the Reynolds-averaged Navier-Stokes (RANS) equation. Physical phenomena of part load flow are evidenced based on three case studies, and the ability of numerical simulation methods to reproduce part-load flow in radial centrifugal pumps qualitatively and quantitatively is assessed. A numerical study of the flow in a high specific speed radial pump-turbine using steady approaches and the hypothesis of angular periodicity between neighboring blade channels evidences the relation of sudden flow topology changes with an increase of viscous losses, impacting on the energy-discharge characteristic, and thus increasing the risk of unstable operation. When the flow rate drops below a critical threshold, the straight through-flow with flow separation zones attached to the guide vanes changes to an asymmetrical flow. Energy is drawn off the mean flow and dissipated in a large vortex-like structure. Besides flow separation in some diffuser channels, time-dependent numerical simulations of the flow in a double suction pump evidence a flow rate imbalance between both impeller sides interacting with asymmetric flow separation in the diffuser. Viscous losses increase substantially as this imbalance occurs, the resulting segment of positive slope in the energy-discharge characteristic is found for a flow rate sensibly different from measurements. Different modes of rotating stall are identified by transient pressure measurements in a low-specific-speed pump-turbine, showing 3 to 5 zones of separated flow, rotating at 0.016 to 0.028 times impeller rotation rate, depending on discharge. For operating conditions where stall with 4 cells is most pronounced, velocity is measured by Laser-Doppler methods at locations of interest. The velocity field is reconstructed with respect to the passage of stall cells by definition of a stall phase obtained from simultaneous transient pressure measurements. Time-dependent numerical simulation predicting rotating stall with 4 cells shows velocity fields that are in reasonable agreement with the measured velocity fields, but occurring at a sensibly higher flow rate than found from experiments. In consideration of the quantitative shortcomings of the numerical simulation, a novel modelling approach is proposed: Replacing the costly 3-dimensional simulation of the major part of the impeller channels by a 1-dimensional model allows a significant economy in computational resources, allowing an improved modeling for the remainder of the domain at constant computational cost. The model is validated with the challenging cases of rotating stall and impeller side flow rate imbalance. The satisfying coherence of the results with the simulation including the entire impeller channels qualifies this approach for numerous turbomachinery applications. It could also provide improved, time-dependent boundary conditions for draft tube vortex rope simulations at reasonable computational cost. Parameter studies modifying deliberately some quantities of mean flow and turbulence at the modeled boundary surfaces can be implemented in the framework of the method.

EPFL2009

Towards pre-dimensioning of natural gas networks on a web-platform

Massimiliano Capezzali, Gaëtan Cherix, Mathias Franz Pernet, Pablo Puerto

The MEU GIS-enabled web-platform has been developed in close collaboration with four Swiss cities: it enables detailed monitoring and planning for both energy demand and supply at individual building and neighborhood level (http://meu.epfl.ch). This web-platform gives access to entire cities comprising several thousands of buildings. In its actual configuration, this tool does not allow to pre-design networks depending on the energy demand of existing or futures infrastructures. Indeed, in MEU, gas networks or districts heating networks are handled in a simple steady-state way. This would in particular mean that, in scenarios, buildings can be arbitrary connected to energy networks without any territorial, power or technologic compatibility verification. Data about the amount of energy supplied by the gas or heat network in different parts of the studied cities are available but some data like the maximum power available, pipe’s diameters, parameters of pressure or heat loss and levels of temperatures, speed or flow rate are not known or reachable. In another hand, data about cooling and heating needs for a building are already known or estimated for each hour of the year by some modules of the platform. The precision already exist and we will use it to simulate the behavior of a gas network, and calculate all the flow rates, injections and consumptions for an urban zone. The idea is to create a new module allowing to test different pre-designed scenarios, to simulate the behavior of each scenario in order to calculate and display dynamics data for the considered network. We are targeting to create new functionalities for city energy manager in order to help them to design new network and expand present network or for system diagnostic purpose. Our aim is to allow users to create new buildings, add or delete nodes and pipes, modify installed heating power for an existing building and add feed-in of biogas. The resulting new network will be then tested and its behavior simulated to see if the means of production matches the demand and if the pressure is adequate in reducing stations to pipe the gas to consumers. The network tool will be useful to determine if a new district can be connected to the existent network or if the actual network need to be densified. It will also help to estimate the effect of a missing pipe due to road maintenance. The first step for the creation of those new functionalities consists in developing an operational module prototype for gas network management. The first phase of a test for a new scenario is the creation of the new state for the considered network. The user will be able to create his gas network based on the actual installation, pipes and structures. Then come the simulation phase. The user can choose the step, the duration and the period of the simulation. The simulation is based on a perfect and compressible gas model. The composition of the gas is considered as pure methane. The model include linear pressure loss equation and is built on a conservation of the molar flow rate through each node. Heating power are calculated for each building using a MEU module building physics software which simulates the energy demand by correlating real annual data from utilities and hourly simulated data. Feed-in gas flow rates are so determined. The studied system is limited to medium pressure (< 5bar) and low pressure networks (< 0.050 bar). Distribution pipelines between 40 bar and 50 bar are not include in the model. The simulation calculates pressure, molar flow rate and density of gas for every node of the network. The resolution of the equations system for each node of the network is made by a MATLAB® function (fsolve) using the Levenberg-Marquardt algorithm. The raw results of the simulation are then exploited and converted to graphics. The user can choose nodes and the associate variable (pressure, speed, flow rate, etc…) that catch his attention and require to be added to graphics. We are currently testing the model using a comparison between the simulation of our model results and the results of a NEPLAN® simulation for the same neighborhood.