Amador M. Guzmán

Blood Flow Dynamics in Saccular Aneurysm Models of the Basilar Artery

Blood flow dynamics under physiologically realistic pulsatile conditions plays an important role in the growth, rupture, and surgical treatment of intracranial aneurysms. The temporal and spatial variations of wall pressure and wall shear stress in the aneurysm are hypothesized to be correlated with its continuous expansion and eventual rupture. In addition, the assessment of the velocity field in the aneurysm dome and neck is important for the correct placement of endovascular coils. This paper describes the flow dynamics in two representative models of a terminal aneurysm of the basilar artery under Newtonian and non-Newtonian fluid assumptions, and compares their hemodynamics with that of a healthy basilar artery. Virtual aneurysm models are investigated numerically, with geometric features defined by beta = 0 deg and beta = 23.2 deg, where beta is the tilt angle of the aneurysm dome with respect to the basilar artery. The intra-aneurysmal pulsatile flow shows complex ring vortex structures for beta = 0 deg and single recirculation regions for beta = 23.2 deg during both systole and diastole. The pressure and shear stress on the aneurysm wall exhibit large temporal and spatial variations for both models. When compared to a non-Newtonian fluid, the symmetric aneurysm model (beta = 0 deg) exhibits a more unstable Newtonian flow dynamics, although with a lower peak wall shear stress than the asymmetric model (beta = 23.2 deg). The non-Newtonian fluid assumption yields more stable flows than a Newtonian fluid, for the same inlet flow rate. Both fluid modeling assumptions, however, lead to asymmetric oscillatory flows inside the aneurysm dome.

Transition to chaos in converging-diverging channel flows : Ruelle-Takens-Newhouse scenario

Direct numerical simulations of the transition process from laminar to chaotic flow in converging–diverging channels are presented. The chaotic flow regime is reached after a sequence of successive supercritical Hopf bifurcations to periodic, quasiperiodic, and chaotic self‐sustained flow regimes. The numerical experiments reveal three distinct bifurcations as the Reynolds number is increased, each adding a new fundamental frequency to the velocity spectrum. In addition, frequency‐locked periodic solutions with independent but synchronized periodic functions are obtained. A scenario similar to the Ruelle–Takens–Newhouse scenario of the onset of chaos is verified in this forced convective open system flow. The results are illustrated for different Reynolds numbers using time‐velocity histories, Fourier power spectra, and phase space trajectories. The global structure of the self‐sustained oscillatory flow for a periodic regime is also discussed.

Dynamical flow characterization of transitional and chaotic regimes in converging–diverging channels

Numerical investigation of laminar, transitional and chaotic flows in converging-diverging channels are performed by direct numerical simulations in the Reynolds number range 10 < Re < 850. The temporal flow evolution and the onset of turbulence are investigated by combining classical fluid dynamics representations with dynamical system flow characterizations. Modern dynamical system techniques such as time-delay reconstructions of pseudophase spaces, autocorrelation functions, fractal dimensions and Eulerian Lyapunov exponents are used for the dynamical flow characterization of laminar, transitional and chaotic flow regimes. As a consequence of these flow characterizations, it is verified that the transitional flow evolves through intermediate states of periodicity, two-frequency quasi-periodicity, frequency-locking periodicity, and multiple-frequency quasi-periodicity before reaching a non-periodic unpredictable behaviour corresponding to low-dimensional deterministic chaos. Qualitative and quantitative differences in Eulerian dynamical flow parameters are identified to determine the predictability of transitional flows and to characterize chaotic, weak turbulent flows in converging-diverging channels. Autocorrelation functions, pseudophase space representations and Poincare maps are used for the qualitative identification of chaotic flows, assertion of their unpredictable nature, and recognition of the topological structure of the attractors for different flow regimes. The predictability of transitional flows is determined by analysing the autocorrelation functions and by representing their attractors in the reconstructed pseudophase spaces. The transitional flow behaviour is examined by the geometric visualization of the evolution of the attractors and Poincare maps until the appearance of a strange attractor at the onset of chaos. Eulerian Lyapunov exponents and fractal dimensions are quantitative parameters to establish the onset of chaos, the persistence of chaotic flow behaviour, and the long-term persistent unpredictability of chaotic Eulerian flow regimes. Lastly, three-dimensional simulations for converging-diverging channel flow are performed to determine the effect of the spanwise direction on the route of transition to chaos.

Lagrangian chaos, Eulerian chaos, and mixing enhancement in converging–diverging channel flows

A study of Lagrangian chaos, Eulerian chaos, and mixing enhancement in converging–diverging channel flows, using spectral element direct numerical simulations, is presented. The time‐dependent, incompressible Navier–Stokes and continuity equations are solved for laminar, transitional, and chaotic flow regimes for 100≤Re≤850. Classical fluid dynamics representations and dynamical system techniques characterize Eulerian flows, whereas Lagrangian trajectories and finite‐time Lagrangian Lyapunov exponents identify Lagrangian chaotic flow regimes and quantify mixing enhancement. Classical representations demonstrate that the flow evolution to an aperiodic chaotic regime occurs through a sequence of instabilities, leading to three successive supercritical Hopf bifurcations. Poincare sections and Eulerian Lyapunov exponent evaluations verify the first Hopf bifurcation at 125<Re<150 and the onset of Eulerian chaos at Re≊550. Lagrangian trajectories and finite‐time Lagrangian Lyapunov exponents reveal the onset of...

Heat Transfer Enhancement Due to Frequency Doubling and Ruelle–Takens–Newhouse Transition Scenarios in Symmetric Wavy Channels

Heat transfer enhancement characteristics, through a transition scenario of flow bifurcations in symmetric wavy wall channels, are investigated by direct numerical simulations of the mass, momentum, and energy equations using spectral element methods. Flow bifurcations, transition scenarios, and heat transfer characteristics are determined by increasing the Reynolds numbers from a laminar to a transitional flow for the geometrical aspect ratios r =0.125 and r = 0.375. The numerical results demonstrate that the transition scenario to transitional flow regimes depends on the aspect ratio. For r =0.375, the transition scenario is characterized by one Hopf flow bifurcation in a frequency-doubling transition scenario, where further increases in the Reynolds number always lead to periodic flows; whereas, for r = 0.125, the transition scenario is characterized by a first Hopf flow bifurcation from a laminar to a time-dependent periodic flow and a second Hopf flow bifurcation from a periodic to a quasiperiodic flow. For r =0.125, the flow bifurcation scenario is similar to the Ruelle―Takens―Newhouse (RTN) transition scenario to Eulerian chaos observed in asymmetric wavy and grooved channels. The periodic and quasiperiodic flows are characterized by fundamental frequencies ω 1 , and ω 1 and ω 2 , respectively. For the aspect ratio r = 0.375, the Nusselt number increases slightly as the Reynolds number increases in the laminar regime until it reaches a critical Reynolds number of Re c ≈ 126. As the flow becomes periodic, and then quasiperiodic, the Nusselt number continuously increases with respect to the laminar regime, up to a factor of 4, which represents a significant heat transfer enhancement due to a better flow mixing.

Flow Mixing Enhancement from Balloon Pulsations in an Intravenous Oxygenator

Computational investigations of flow mixing and oxygen transfer characteristics in an intravenous membrane oxygenator (IMO) are performed by direct numerical simulations of the conservation of mass, momentum, and species equations. Three-dimensional computational models are developed to investigate flow-mixing and oxygen-transfer characteristics for stationary and pulsating balloons, using the spectral element method. For a stationary balloon, the effect of the fiber placement within the fiber bundle and the number of fiber rings is investigated. In a pulsating balloon, the flow mixing characteristics are determined and the oxygen transfer rate is evaluated. For a stationary balloon, numerical simulations show two well-defined flow patterns that depend on the region of the IMO device. Successive increases of the Reynolds number raise the longitudinal velocity without creating secondary flow. This characteristic is not affected by staggered or non-staggered fiber placement within the fiber bundle. For a pulsating balloon, the flow mixing is enhanced by generating a three-dimensional time-dependent flow characterized by oscillatory radial, pulsatile longitudinal, and both oscillatory and random tangential velocities. This three-dimensional flow increases the flow mixing due to an active time-dependent secondary flow, particularly around the fibers. Analytical models show the fiber bundle placement effect on the pressure gradient and flow pattern. The oxygen transport from the fiber surface to the mean flow is due to a dominant radial diffusion mechanism, for the stationary balloon. The oxygen transfer rate reaches an asymptotic behavior at relatively low Reynolds numbers. For a pulsating balloon, the time-dependent oxygen-concentration field resembles the oscillatory and wavy nature of the time-dependent flow. Sherwood number evaluations demonstrate that balloon pulsations enhance the oxygen transfer rate, even for smaller flow rates.

Methodology for predicting oxygen transport on an intravenous membrane oxygenator combining computational and analytical models.

A computational methodology for accurately predicting flow and oxygen-transport characteristics and performance of an intravenous membrane oxygenator (IMO) device is developed, tested, and validated. This methodology uses extensive numerical simulations of three-dimensional computational models to determine flow-mixing characteristics and oxygen-transfer performance, and analytical models to indirectly validate numerical predictions with experimental data, using both blood and water as working fluids. Direct numerical simulations for IMO stationary and pulsating balloons predict flow field and oxygen transport performance in response to changes in the device length, number of and balloon pulsation frequency. Multifiber models are used to investigate interfiber interference and length effects for a stationary balloon whereas a single fiber model is used to analyze the effect of balloon pulsations on velocity and oxygen concentration fields and to evaluate oxygen transfer rates. An analytical lumped model is developed and validated by comparing its numerical predictions with experimental data. Numerical results demonstrate that oxygen transfer rates for a stationary balloon regime decrease with increasing number of fibers, independent of the fluid type. The oxygen transfer rate ratio obtained with blood and water is approximately two. Balloon pulsations show an effective and enhanced flow mixing, with time-dependent recirculating flows around the fibers regions which induce higher oxygen transfer rates. The mass transfer rates increase approximately 100% and 80%, with water and blood, respectively, compared with stationary balloon operation. Calculations with combinations of frequency, number of fibers, fiber length and diameter, and inlet volumetric flow rates, agree well with the reported experimental results, and provide a solid comparative base for analysis, predictions, and comparisons with numerical and experimental data.

Flow and Oxygen Transfer Characteristics of an Intravenous Membrane Oxygenator: A Computational Study

Abstract Spectral element computational simulations of the conservation of mass, momentum and species equations are performed to investigate the flow and oxygen transfer characteristics of an Intravenous Membrane Oxygenator (IMO). The simulations consider a three-dimensional IMO computational model consisting of equally-spaced fibers, an elastic balloon with non-permeable walls positioned longitudinally within the vena cava, and a Newtonian and time-dependent incompressible flow. Flow characteristics and oxygen transfer parameters are determined for operating conditions of a stationary and a pulsating balloon. For the stationary balloon configuration the flow is two-dimensional, parallel, laminar and without secondary flows for the Reynolds number range of 5.7-455.2. Evaluations of the oxygen transfer characteristics for the stationary balloon indicate that the main transport mechanisms are diffusion and convection in the crosswise and streamwise directions, respectively. Additionally, evaluations of oxygen transfer rates and Sherwood numbers in this Reynolds number range indicate that the oxygen transfer rate reaches an asymptotic limit at relatively moderate Reynolds numbers. For the pulsating balloon, flow characteristic results demonstrate the existence of a strong secondary flow around the fiber, and between the balloon and the fiber. This secondary flow induces oscillatory crosswise and streamwise velocities and a seemingly random spanwise flow which enhances the flow mixing as well as the transport of oxygen from the fiber surface to the bulk flow.

Flow transitions and heat transfer in open block tandem channels

This work investigates the transition scenario and heat transfer characteristics in a channel with a block tandem, as the flow evolves from a laminar to a transitional regime, by two-dimensional direct numerical simulations (DNS) of the time dependent, incompressible continuity, Navier-Stokes and energy equations. This investigation uses an extended computational domain with 10 blocks to determine the existence of a fully developed flow and self-similar temperature profiles, and a reduced computational domain to investigate the heat transfer enhancement for laminar and transitional flow regimes. This investigation demonstrates that significant heat transfer enhancements can be obtained at supercritical transitional flow Reynolds numbers with a minimum of dissipation due to viscous stresses. This enhancement is obtained without the necessity of operating this channel to high volumetric flow rates associated to turbulent flow regimes, which demand high pumping powers. In this channel, the transitional flow regime is more efficient than a laminar flow regime as a method of cooling electronics.

Flow Characteristics of Rarified Gases in Micro-Grooved Channels by the Lattice-Boltzmann Method

The flow characteristics of a rarified gas have been investigated in microgrooved channels. The governing Boltzmann Transport Equation (BTE) is solved by the Lattice-Boltzmann method (LBM) for the Knudsen number range of 0.01–0.1. First, the compressibility and rarified effects are investigated in a plane channel by performing numerical simulations for different Knudsen numbers, pressure ratio and accommodation coefficients with the objective of validating the computational code used in this investigation and determining the transition characteristics from the macro to microscale. The numerical predictions are compared to existing analytical and numerical results. Then, numerical simulations are performed for microgrooved channels for the Knudsen numbers range of [0.01–0.1]. Different meshes are used for preserving numerical stabilities and obtaining accurate enough numerical results. For the microgrooved channel configuration, the fluid characteristics are determined in terms of pressure ratio and Knudsen numbers. The numerical results are compared to existing analytical predictions and numerical results obtained from plane channel and one cavity simulations.Copyright