Aydin Nabovati

On the lattice Boltzmann method for phonon transport

The lattice Boltzmann method is a discrete representation of the Boltzmann transport equation that has been employed for modeling transport of particles of different nature. In the present work, we describe the lattice Boltzmann methodology and implementation techniques for the phonon transport modeling in crystalline materials. We show that some phonon physical properties, e.g., mean free path and group velocity, should be corrected to their effective values for one- and two-dimensional simulations, if one uses the isotropic approximation. We find that use of the D2Q9 lattice for phonon transport leads to erroneous results in transient ballistic simulations, and the D2Q7 lattice should be employed for two-dimensional simulations. Furthermore, we show that at the ballistic regime, the effect of direction discretization becomes apparent in two dimensions, regardless of the lattice used. Numerical methodology, lattice structure, and implementation of initial and different boundary conditions for the D2Q7 lattice are discussed in detail.

Increasing angulation decreases measured aortic stent graft pullout forces

OBJECTIVE Experimentally measured pullout forces for stent grafts (SGs) are used in clinical discussions and as reference values in bench studies and computer simulations. Previous values of these forces are available from studies in which the SG was pulled out in the straight caudal direction. However, clinical and numerical studies have suggested that displacement forces acting on SGs are directed more anteriorly. The objective of this study was to measure pullout forces as a function of angulation and to test the hypothesis that pullout forces decrease with increasing angulation. METHODS Six different SGs (Bolton Treovance, Cook Zenith Flex, Cook Zenith LP, Medtronic Endurant, Medtronic Talent, and Vascutek Anaconda) were deployed in fresh bovine aortas, then pulled out by an electronic motor at 1 mm/s, while tension force was measured continuously with a digital load cell. The SG off-axis angulation was changed from 0 to 90 degrees in increments of 10 degrees. The test system was submerged in a custom-built temperature-controlled saline bath at 37°C. At least three tests were performed for each device at each angle (with the exception of the Cook Zenith Flex, which experienced plastic deformation of its barbs after a single test per device). Each aortic specimen was used only once and then discarded. Hand-sutured graft anastomoses were also tested at 0 degrees to provide a reference value. RESULTS A total of 374 pullout tests were performed for the SGs and anastomoses. Sixty-four tests were excluded because of failure of the aorta or apparatus before device pullout. The remaining 310 tests showed pullout forces that demonstrated a decrease in the average pullout force for all six devices from 0 to 90 degrees (Bolton Treovance from 39.3 N to 23.9 N; Cook Zenith Flex from 59.8 N to 48.9 N; Cook Zenith LP from 50.3 N to 41.8 N; Medtronic Endurant from 29.9 N to 25.8 N; Medtronic Talent from 6.0 N to 5.5 N; and Vascutek Anaconda from 37.0 N to 30.3 N). For reference, the mean pullout force for the hand-sutured anastomoses was 63 N. CONCLUSIONS This study reports for the first time the change in pullout force with angulation, showing a general pullout force decrease with increasing angle. With a larger number of samples than in previous studies, our results provide updated benchmark data that can be used for clinical discussions, computational and experimental studies, and future device design.

Hydrodynamic Boundary Condition at Open-Porous Interface: A Pore-Level Lattice Boltzmann Study

In this paper, we follow the pore-level simulation approach to investigate fluid flow over an open-porous interface using the lattice Boltzmann method. As this approach does not require any specific treatment for the interface, the predicted pore-level velocity field is averaged and used to evaluate the available macroscopic boundary conditions for the interface. Two most common interface boundary conditions are evaluated, and the unknown fitting parameters in them are calculated as a function of porosity of the porous region. Analytical solutions of the velocity profile in the close vicinity of the interface are used to validate the numerical methodology. It is shown that the predicted numerical results for penetration depth in the porous region, flow rate in open channel, and velocity profile in the open and porous regions are in excellent agreement with the predictions of the two available models, if the proposed values of their fitting parameters are used.

Assessment of the Holland model for silicon phonon-phonon relaxation times using lattice dynamics calculations

We assess the ability of the Holland model to accurately predict phonon-phonon relaxation times from bulk thermal conductivity values. First, lattice dynamics calculations are used to obtain phonon-phonon relaxation times and thermal conductivities for temperatures ranging from 10 K to 1000 K for Stillinger-Weber silicon. The Holland model is then fitted to these thermal conductivities and used to predict relaxation times, which are compared to the relaxation times obtained by lattice dynamics calculations. We find that fitting the Holland model to both total and mode-dependent thermal conductivities does not result in accurate mode-dependent phonon-phonon relaxation times. Introduction of Umklapp scattering for longitudinal modes resulted in improved prediction of mode-dependent relative contributions to thermal conductivity, especially at high temperatures. However, assumptions made by Holland regarding the frequency-dependence of phonon scattering mechanisms are found to be inconsistent with lattice dynamics data. Instead, we introduce a simple method based on using cumulative thermal conductivity functions to obtain better predictions of the frequency-dependence of relaxation times.We assess the ability of the Holland model to accurately predict phonon-phonon relaxation times from bulk thermal conductivity values. First, lattice dynamics calculations are used to obtain phonon-phonon relaxation times and thermal conductivities for temperatures ranging from 10 K to 1000 K for Stillinger-Weber silicon. The Holland model is then fitted to these thermal conductivities and used to predict relaxation times, which are compared to the relaxation times obtained by lattice dynamics calculations. We find that fitting the Holland model to both total and mode-dependent thermal conductivities does not result in accurate mode-dependent phonon-phonon relaxation times. Introduction of Umklapp scattering for longitudinal modes resulted in improved prediction of mode-dependent relative contributions to thermal conductivity, especially at high temperatures. However, assumptions made by Holland regarding the frequency-dependence of phonon scattering mechanisms are found to be inconsistent with lattice dy...

Ferrofluid Permeation into Three-Dimensional Random Porous Media: A Numerical Study Using the Lattice Boltzmann Method

Colloidal suspensions containing magnetic nanoparticles placed in appropriate carrier liquids present strong magnetic dipoles. These suspensions, in general, exhibit normal liquid behaviour coupled with super paramagnetic properties. This leads to the possibility of remotely controlling the flow of such liquids with a moderate-strength external magnetic field. In this study, we numerically investigate the viability of controlling and steering a base-fluid with magnetic-sensitive nanoparticles into randomly structured fibrous porous media. Three dimensional flow simulations are performed using the lattice Boltzmann method. The simulation results for the flow front are presented, and the effect of the magnetic field strength on the rate of ferrofluid penetration is discussed. It is shown that the porosity of the porous medium and the size of the fibres have a strong effect on the ferrofluid penetration rate.

Numerical Simulation of Thermomagnetic Convection in an Enclosure Using the Lattice Boltzmann Method

The application of the single relaxation time lattice Boltzmann method (LBM) is extended to the study of thermomagnetic convection in a differentially heated square cavity with an infinitely long third dimension. The magnetic field is created and controlled by placing a dipole at the bottom of the enclosure. The magnitude of the magnetic force acting on the ferrofluid is controlled by changing the electrical current through the dipole. In this study, the effects of combined natural convection and magnetic convection, which is commonly known as “thermomagnetic convection”, are analysed in what concerns the flow modes and heat transfer characteristics of a magnetic fluid (ferrofluid). This is a situation of considerable interest for cooling micro-electronic devices, when natural convection does not meet the cooling requirements, and forced convection is not viable due to the difficulties associated with pumping a ferrofluid.Copyright

A Transient Modified Fourier-Based Approach for Thermal Transport Modelling in Sub-Continuum Regime

The presence of sub-continuum effects in nano-scale systems, including size and boundary effects, causes the continuum-level relations (e.g., Fourier heat equation) to break down at such scales. The thermal sub-continuum effects are manifested as a temperature jump at the system boundaries and a reduced heat flux across the system. In this work, we reproduce transient and steady-state results of Gray lattice Boltzmann simulations by developing a one-dimensional, transient, modified Fourier-based approach. The proposed methodology introduces the following two modifications into the Fourier heat equation: (i) an increase in the sample length by a fixed length at the two ends, in order to capture the steady-state temperature jumps at the system boundaries, and (ii) a size-dependent effective thermal diffusivity, to recover the transient temperature profiles and heat flux values. The predicted temperature and heat flux values from the proposed modified Fourier approach are in good agreement with those predicted by the Gray lattice Boltzmann simulations.Copyright

Analysis of Fluid Flow in Porous Media Using the Lattice Boltzmann Method: Inertial Flow Regime

In this work, we use the lattice Boltzmann method to study inertial flow in three-dimensional random fibrous porous materials. In order to validate the methodology, inertial flow in two-dimensional hexagonal arrangements of circular cylinders is simulated, and the results are compared against those previously reported in the literature. The three-dimensional fibrous porous materials are then constructed by randomly placing straight cylindrical fibers inside the computational domain. Inertial effects are studied systematically for a wide range of pore Reynolds numbers in materials with porosities between 0.60 and 0.95. A previously proposed semi-empirical relation is modified to represent the inertial effects in three-dimensional fibrous materials. Three distinct regimes of constant, quadratic, and linear relations between the inverse of the permeability and pore Reynolds number are observed for both two- and three-dimensional simulations. The critical Reynolds number, beyond which the inertial effects are strong and this relation is linear, is shown to be smaller in three-dimensional simulations, when compared to the critical Reynolds number in two-dimensional simulations.© 2012 ASME

Assessment of the Hydrodynamic Boundary Condition at Open-Porous Interface Using Pore-Level Flow Simulations

In this paper, we follow the pore-level flow simulation approach to investigate fluid flow over an open-porous interface using the lattice Boltzmann method. As this approach does not require any specific treatment for the interface, its results can be used to evaluate the current macroscopic boundary conditions for the interface. The Beavers & Joseph boundary condition is evaluated and the value of slip coefficient is presented as a function of porosity of the porous region. Analytical solution of the velocity profile in the close vicinity of the interface is used to predict the penetration depth. The predicted numerical results for porous penetration depth are in excellent agreement with those predicted from the analytical solution.Copyright

Enhanced Thermal Map Prediction and Floor Plan Optimization in Electronic Devices Considering Sub-Continuum Thermal Effects

In current and next-generation semiconductor electronic devices, sub-continuum heat transfer effects and non-uniform power distribution across the die surface lead to large temperature gradients and localized hot spots on the die. These hot spots can adversely affect device performance and reliability. In this work, we propose an enhanced method for thermal map prediction that considers sub-continuum thermal transport effects and show their impact in floor plan optimization. Sub-continuum effects are expressed in terms of an effective thermal conductivity. We introduce and calibrate a 2D thermal model of the die for fast simulation of thermal effects under non-uniform power generation scenarios. The calibrated 2D model is then used to study the impact of the effective thermal conductivity on the thermal map prediction and floor plan optimization. Results show that sub-continuum effects radically change both the predicted thermal performance and the optimal floor plan configurations.Copyright