Lattice Boltzmann modeling of fluid flow and solute transport in karst aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Lattice boltzmann modeling of fluid flow to determine the permeability of a karst specimen

A limestone sample was scanned using computed tomography (CT) and the hydraulic conductivity of the 3D reconstructed sample was determined using Lattice- Boltzmann methods (LBM) at varying scales. Due to the shape and size of the original sample, it was challenging to obtain a consistent rectilinear test sample. Through visual inspection however, 91 mm and 76 mm samples were digitally cut from the original. The samples had porosities of 58% and 64% and produced hydraulic conductivity values of K= 13.5 m/s and K=34.5 m/s, respectively. Both of these samples were re-sampled to 1/8 and 1/64 of their original size to produce new virtual samples at lower resolutions of 0.542 mm/lu and 1.084 mm/lu, while still representing the same physical dimensions. The hydraulic conductivity tended to increase slightly as the resolution became coarser. In order to determine an REV, the 91 mm sample was also sub-sampled into blocks that were 1/8 and 1/64 the size of the original. The results were consistent with analytical expectations such as those produced by the Kozeny-Carman equation. A definitive REV size was not reached, however, indicating the need for a larger sample. The methods described here demonstrate the ability of LBM to test rock structures and sizes not normally attainable.

Lattice Boltzmann Modeling of Fluid Flow and Solute Transport in Karst Aquifers

A novel modeling approach is applied to karst hydrology. Long-standing problems in karst hydrology and solute transport are addressed using Lattice Boltzmann methods (LBMs). These methods contrast with other modeling approaches that have been applied to karst hydrology. The motivation of this dissertation is to develop new computational models for solving ground water hydraulics and transport problems in karst aquifers, which are widespread around the globe. This research tests the viability of the LBM as a robust alternative numerical technique for solving large-scale hydrological problems. The LB models applied in this research are briefly reviewed and there is a discussion of implementation issues. The dissertation focuses on testing the LB models. The LBM is tested for two different types of inlet boundary conditions for solute transport in finite and effectively semi-infinite domains. The LBM solutions are verified against analytical solutions. Zero-diffusion transport and Taylor dispersion in slits are also simulated and compared against analytical solutions. These results demonstrate the LBM’s flexibility as a solute transport solver. The LBM is applied to simulate solute transport and fluid flow in porous media traversed by larger conduits. A LBM-based macroscopic flow solver (Darcy’s law-based) is linked with an anisotropic dispersion solver. Spatial breakthrough curves in one and two dimensions are fitted against the available analytical solutions. This provides a steady flow model with capabilities routinely found in ground water flow and transport models (e.g., the combination of MODFLOW and MT3D). However the new LBM-based model retains the ability to solve inertial flows that are characteristic of karst aquifer conduits. Transient flows in a confined aquifer are solved using two different LBM approaches. The analogy between Fick’s second law (diffusion equation) and the transient ground water flow equation is used to solve the transient head distribution. An altered-velocity flow solver with source/sink term is applied to simulate a drawdown curve. Hydraulic parameters like transmissivity and storage coefficient are linked with LB parameters. These capabilities complete the LBM’s effective treatment of the types of processes that are simulated by standard ground water models. The LB model is verified against field data for drawdown in a confined aquifer.

Lattice Boltzmann method for flow and heat transfer in microgeometries

Recent technological developments have made it possible to design various microdevices where fluid flow and heat transfer are involved. For the proper design of such systems, the governing physics needs to be investigated. Due to the difficulty to study complex geometries in micro scales using experimental techniques, computational tools are developed to analyze and simulate flow and heat transfer in microgeometries. However, conventional numerical methods using the Navier-Stokes equations fail to predict some aspects of microflows such as nonlinear pressure distribution, increase mass flow rate, slip flow and temperature jump at the solid boundaries. This necessitates the development of new computational methods which depend on the kinetic theory that are both accurate and computationally efficient. In this study, lattice Boltzmann method (LBM) was used to investigate the flow and heat transfer in micro sized geometries. The LBM depends on the Boltzmann equation which is valid in the whole rarefaction regime that can be observed in micro flows. Results were obtained for isothermal channel flows at Knudsen numbers higher than 0.01 at different pressure ratios. LBM solutions for micro-Couette and micro-Poiseuille flow were found to be in good agreement with the analytical solutions valid in the slip flow regime (0.01 < Kn < 0.1) and direct simulation Monte Carlo solutions that are valid in the transition regime (0.1 < Kn < 10) for pressure distribution and velocity field. The isothermal LBM was further extended to simulate flows including heat transfer. The method was first validated for continuum channel flows with and without constrictions by comparing the thermal LBM results against accurate solutions obtained from analytical equations and finite element method. Finally, the capability of thermal LBM was improved by adding the effect of rarefaction and the method was used to analyze the behavior of gas flow in microchannels. The major finding of this research is that, the newly developed particle-based method described here can be used as an alternative numerical tool in order to study non-continuum effects observed in micro-electro-mechanical-systems (MEMS).

Eulerian-Lagrangian two phase debris flow model

The main objective of this work is to develop a quasi three-dimensional numerical model to simulate stony debris flows, considering a continuum fluid phase, composed by water and fine sediments, and a non-continuum phase including large particles, such as pebbles and boulders. Large particles are treated in a Lagrangian frame of reference using the Discrete Element Method, the fluid phase is based on the Eulerian approach, using the Finite Element Method to solve the depth-averaged Navier-Stokes equations in two horizontal dimensions. The particle’s equations of motion are in three dimensions. The model simulates particle-particle collisions and wall-particle collisions, taking into account that particles are immersed in a fluid. Bingham and Cross rheological models are used for the continuum phase. Both formulations provide very stable results, even in the range of very low shear rates. Bingham formulation is better able to simulate the stopping stage of the fluid when applied shear stresses are low. Results of numerical simulations have been compared with data from laboratory experiments on a flume-fan prototype. Results show that the model is capable of simulating the motion of big particles moving in the fluid flow, handling dense particulate flows and avoiding overlap among particles. An application to simulate debris flow events that occurred in Northern Venezuela in 1999 shows that the model could replicate the main boulder accumulation areas that were surveyed by the USGS. Uniqueness of this research is the integration of mud flow and stony debris movement in a single modeling tool that can be used for planning and management of debris flow prone areas.

Lattice Boltzmann Method for Flow and Heat Transfer in Microgeometries

Recent technological developments have made it possible to design various microdevices where fluid flow and heat transfer are involved. For the proper design of such systems, the governing physics needs to be investigated. Due to the difficulty to study complex geometries in micro scales using experimental techniques, computational tools are developed to analyze and simulate flow and heat transfer in microgeometries. However, conventional numerical methods using the Navier-Stokes equations fail to predict some aspects of microflows such as nonlinear pressure distribution, increase mass flow rate, slip flow and temperature jump at the solid boundaries. This necessitates the development of new computational methods which depend on the kinetic theory that are both accurate and computationally efficient. In this study, lattice Boltzmann method (LBM) was used to investigate the flow and heat transfer in micro sized geometries. The LBM depends on the Boltzmann equation which is valid in the whole rarefaction regime that can be observed in micro flows. Results were obtained for isothermal channel flows at Knudsen numbers higher than 0.01 at different pressure ratios. LBM solutions for micro-Couette and micro-Poiseuille flow were found to be in good agreement with the analytical solutions valid in the slip flow regime (0.01 < Kn < 0.1) and direct simulation Monte Carlo solutions that are valid in the transition regime (0.1 < Kn < 10) for pressure distribution and velocity field. The isothermal LBM was further extended to simulate flows including heat transfer. The method was first validated for continuum channel flows with and without constrictions by comparing the thermal LBM results against accurate solutions obtained from analytical equations and finite element method. Finally, the capability of thermal LBM was improved by adding the effect of rarefaction and the method was used to analyze the behavior of gas flow in microchannels. The major finding of this research is that, the newly developed particle-based method described here can be used as an alternative numerical tool in order to study non-continuum effects observed in micro-electro-mechanical-systems (MEMS).

Eulerian-Lagrangian Two Phase Debris Flow Model

The main objective of this work is to develop a quasi three-dimensional numerical model to simulate stony debris flows, considering a continuum fluid phase, composed by water and fine sediments, and a non-continuum phase including large particles, such as pebbles and boulders. Large particles are treated in a Lagrangian frame of reference using the Discrete Element Method, the fluid phase is based on the Eulerian approach, using the Finite Element Method to solve the depth-averaged Navier–Stokes equations in two horizontal dimensions. The particle’s equations of motion are in three dimensions. The model simulates particle-particle collisions and wall-particle collisions, taking into account that particles are immersed in a fluid. Bingham and Cross rheological models are used for the continuum phase. Both formulations provide very stable results, even in the range of very low shear rates. Bingham formulation is better able to simulate the stopping stage of the fluid when applied shear stresses are low. Results of numerical simulations have been compared with data from laboratory experiments on a flume-fan prototype. Results show that the model is capable of simulating the motion of big particles moving in the fluid flow, handling dense particulate flows and avoiding overlap among particles. An application to simulate debris flow events that occurred in Northern Venezuela in 1999 shows that the model could replicate the main boulder accumulation areas that were surveyed by the USGS. Uniqueness of this research is the integration of mud flow and stony debris movement in a single modeling tool that can be used for planning and management of debris flow prone areas.

Numerical Investigation of the Effect of Magnetic Field on Natural Convection in a Curved-Shape Enclosure

This investigation reports the magnetic field effect on natural convection heat transfer in a curved-shape enclosure. The numerical investigation is carried out using the control volume-based-finite element method (CVFEM). The numerical investigations are performed for various values of Hartmann number and Rayleigh number. The obtained results are depicted in terms of streamlines and isotherms which show the significant effects of Hartmann number on the fluid flow and temperature distribution inside the enclosure. Also, it was found that the Nusselt number decreases with an increase in the Hartmann number.

Tubular and sector heat pipes with interconnected branches for gas turbine and/or compressor cooling

Designing turbines for either aerospace or power production is a daunting task for any heat transfer scientist or engineer. Turbine designers are continuously pursuing better ways to convert the stored chemical energy in the fuel into useful work with maximum efficiency. Based on thermodynamic principles, one way to improve thermal efficiency is to increase the turbine inlet pressure and temperature. Generally, the inlet temperature may exceed the capabilities of standard materials for safe and long-life operation of the turbine. Next generation propulsion systems, whether for new supersonic transport or for improving existing aviation transport, will require more aggressive cooling system for many hot-gas-path components of the turbine. Heat pipe technology offers a possible cooling technique for the structures exposed to the high heat fluxes. Hence, the objective of this dissertation is to develop new radially rotating heat pipe systems that integrate multiple rotating miniature heat pipes with a common reservoir for a more effective and practical solution to turbine or compressor cooling. In this dissertation, two radially rotating miniature heat pipes and two sector heat pipes are analyzed and studied by utilizing suitable fluid flow and heat transfer modeling along with experimental tests. Analytical solutions for the film thickness and the lengthwise vapor temperature distribution for a single heat pipe are derived. Experimental tests on single radially rotating miniature heat pipes and sector heat pipes are undertaken with different important parameters and the manner in which these parameters affect heat pipe operation. Analytical and experimental studies have proven that the radially rotating miniature heat pipes have an incredibly high effective thermal conductance and an enormous heat transfer capability. Concurrently, the heat pipe has an uncomplicated structure and relatively low manufacturing costs. The heat pipe can also resist strong vibrations and is well suited for a high temperature environment. Hence, the heat pipes with a common reservoir make incorporation of heat pipes into turbo-machinery much more feasible and cost effective.

Tubular and Sector Heat Pipes with Interconnected Branches for Gas Turbine and/or Compressor Cooling

Designing turbines for either aerospace or power production is a daunting task for any heat transfer scientist or engineer. Turbine designers are continuously pursuing better ways to convert the stored chemical energy in the fuel into useful work with maximum efficiency. Based on thermodynamic principles, one way to improve thermal efficiency is to increase the turbine inlet pressure and temperature. Generally, the inlet temperature may exceed the capabilities of standard materials for safe and long-life operation of the turbine. Next generation propulsion systems, whether for new supersonic transport or for improving existing aviation transport, will require more aggressive cooling system for many hot-gas-path components of the turbine. Heat pipe technology offers a possible cooling technique for the structures exposed to the high heat fluxes. Hence, the objective of this dissertation is to develop new radially rotating heat pipe systems that integrate multiple rotating miniature heat pipes with a common reservoir for a more effective and practical solution to turbine or compressor cooling. In this dissertation, two radially rotating miniature heat pipes and two sector heat pipes are analyzed and studied by utilizing suitable fluid flow and heat transfer modeling along with experimental tests. Analytical solutions for the film thickness and the lengthwise vapor temperature distribution for a single heat pipe are derived. Experimental tests on single radially rotating miniature heat pipes and sector heat pipes are undertaken with different important parameters and the manner in which these parameters affect heat pipe operation. Analytical and experimental studies have proven that the radially rotating miniature heat pipes have an incredibly high effective thermal conductance and an enormous heat transfer capability. Concurrently, the heat pipe has an uncomplicated structure and relatively low manufacturing costs. The heat pipe can also resist strong vibrations and is well suited for a high temperature environment. Hence, the heat pipes with a common reservoir make incorporation of heat pipes into turbo-machinery much more feasible and cost effective.

Fluid dynamics and platelet deposition in a model arterial stenosis

The objective of this study was to gain further understanding and elucidation of the fluid dynamic factors and flow-induced mechanisms of the thrombogenic process of platelet deposition onto, and possible subsequent embolization from, the walls of an arterial stenosis. This has been accomplished by measurement of the axial dependence of platelet deposition within a modeled arterial stenosis for a transitional flow and a completely laminar flow field. The stenotic region of the model was collagen-coated to simulate a damaged endothelial lining of an artery. Fluid dynamics within a stenosis was studied using qualitative flow visualization, and was further compared to the in vitro platelet deposition studies. Normalized platelet density (NPD) measurements indicate decreased levels of NPD in the high shear throat region of the stenosis for a Reynolds number of 300 and a drastic increase in NPD at the throat for a Reynolds number of 175. This study provides further understanding of the flow dynamic effects on thrombus development within a stenosis. ^

Numerical investigation on the heat transfer enhancement using micro/nano phase-change particulate flow

The introduction of phase change material fluid and nanofluid in micro-channel heat sink design can significantly increase the cooling capacity of the heat sink because of the unique features of these two kinds of fluids. To better assist the design of a high performance micro-channel heat sink using phase change fluid and nanofluid, the heat transfer enhancement mechanism behind the flow with such fluids must be completely understood. ^ A detailed parametric study is conducted to further investigate the heat transfer enhancement of the phase change material particle suspension flow, by using the two-phase non-thermal-equilibrium model developed by Hao and Tao (2004). The parametric study is conducted under normal conditions with Reynolds numbers of Re = 90–600 and phase change material particle concentrations of ϵp ≤ 0.25, as well as extreme conditions of very low Reynolds numbers (Re < 50) and high phase change material particle concentration (ϵp = 50%–70%) slurry flow. By using the two newly-defined parameters, named effectiveness factor ϵeff and performance index PI, respectively, it is found that there exists an optimal relation between the channel design parameters L and D, particle volume fraction ϵp, Reynolds number Re, and the wall heat flux qw. The influence of the particle volume fraction ϵp, particle size dp, and the particle viscosity μ p, to the phase change material suspension flow, are investigated and discussed. The model was validated by available experimental data. The conclusions will assist designers in making their decisions that relate to the design or selection of a micro-pump suitable for micro or mini scale heat transfer devices. ^ To understand the heat transfer enhancement mechanism of the nanofluid flow from the particle level, the lattice Boltzmann method is used because of its mesoscopic feature and its many numerical advantages. By using a two-component lattice Boltzmann model, the heat transfer enhancement of the nanofluid is analyzed, through incorporating the different forces acting on the nanoparticles to the two-component lattice Boltzmann model. It is found that the nanofluid has better heat transfer enhancement at low Reynolds numbers, and the Brownian motion effect of the nanoparticles will be weakened by the increase of flow speed. ^

Movement Effects on the Flow Physics and Nutrient Delivery in Engineered Valvular Tissues

Mechanical conditioning has been shown to promote tissue formation in a wide variety of tissue engineering efforts. However the underlying mechanisms by which external mechanical stimuli regulate cells and tissues are not known. This is particularly relevant in the area of heart valve tissue engineering (HVTE) owing to the intense hemodynamic environments that surround native valves. Some studies suggest that oscillatory shear stress (OSS) caused by steady flow and scaffold flexure play a critical role in engineered tissue formation derived from bone marrow derived stem cells (BMSCs). In addition, scaffold flexure may enhance nutrient (e.g. oxygen, glucose) transport. In this study, we computationally quantified the i) magnitude of fluid-induced shear stresses; ii) the extent of temporal fluid oscillations in the flow field using the oscillatory shear index (OSI) parameter, and iii) glucose and oxygen mass transport profiles. Noting that sample cyclic flexure induces a high degree of oscillatory shear stress (OSS), we incorporated moving boundary computational fluid dynamic simulations of samples housed within a bioreactor to consider the effects of: 1) no flow, no flexure (control group), 2) steady flow-alone, 3) cyclic flexure-alone and 4) combined steady flow and cyclic flexure environments. We also coupled a diffusion and convention mass transport equation to the simulated system. We found that the coexistence of both OSS and appreciable shear stress magnitudes, described by the newly introduced parameter OSI-t , explained the high levels of engineered collagen previously observed from combining cyclic flexure and steady flow states. On the other hand, each of these metrics on its own showed no association. This finding suggests that cyclic flexure and steady flow synergistically promote engineered heart valve tissue production via OSS, so long as the oscillations are accompanied by a critical magnitude of shear stress. In addition, our simulations showed that mass transport of glucose and oxygen is enhanced by sample movement at low sample porosities, but did not play a role in highly porous scaffolds. Preliminary in-house in vitro experiments showed that cell proliferation and phenotype is enhanced in OSI-t environments.

Numerical Investigation on the Heat Transfer Enhancement Using Micro/Nano Phase-Change Particulate Flow

The introduction of phase change material fluid and nanofluid in micro-channel heat sink design can significantly increase the cooling capacity of the heat sink because of the unique features of these two kinds of fluids. To better assist the design of a high performance micro-channel heat sink using phase change fluid and nanofluid, the heat transfer enhancement mechanism behind the flow with such fluids must be completely understood. A detailed parametric study is conducted to further investigate the heat transfer enhancement of the phase change material particle suspension flow, by using the two-phase non-thermal-equilibrium model developed by Hao and Tao (2004). The parametric study is conducted under normal conditions with Reynolds numbers of Re=600-900 and phase change material particle concentrations ¡Ü0.25 , as well as extreme conditions of very low Reynolds numbers (Re < 50) and high phase change material particle concentration (0.5-0.7) slurry flow. By using the two newly-defined parameters, named effectiveness factor and performance index, respectively, it is found that there exists an optimal relation between the channel design parameters, particle volume fraction, Reynolds number, and the wall heat flux. The influence of the particle volume fraction, particle size, and the particle viscosity, to the phase change material suspension flow, are investigated and discussed. The model was validated by available experimental data. The conclusions will assist designers in making their decisions that relate to the design or selection of a micro-pump suitable for micro or mini scale heat transfer devices. To understand the heat transfer enhancement mechanism of the nanofluid flow from the particle level, the lattice Boltzmann method is used because of its mesoscopic feature and its many numerical advantages. By using a two-component lattice Boltzmann model, the heat transfer enhancement of the nanofluid is analyzed, through incorporating the different forces acting on the nanoparticles to the two-component lattice Boltzmann model. It is found that the nanofluid has better heat transfer enhancement at low Reynolds numbers, and the Brownian motion effect of the nanoparticles will be weakened by the increase of flow speed.

Design Optimization of Nozzle Shapes for Maximum Uniformity of Exit Flow

The objective of this study is to identify the optimal designs of converging-diverging supersonic and hypersonic nozzles that perform at maximum uniformity of thermodynamic and flow-field properties with respect to their average values at the nozzle exit. Since this is a multi-objective design optimization problem, the design variables used are parameters defining the shape of the nozzle. This work presents how variation of such parameters can influence the nozzle exit flow non-uniformities. A Computational Fluid Dynamics (CFD) software package, ANSYS FLUENT, was used to simulate the compressible, viscous gas flow-field in forty nozzle shapes, including the heat transfer analysis. The results of two turbulence models, k-e and k-ω, were computed and compared. With the analysis results obtained, the Response Surface Methodology (RSM) was applied for the purpose of performing a multi-objective optimization. The optimization was performed with ModeFrontier software package using Kriging and Radial Basis Functions (RBF) response surfaces. Final Pareto optimal nozzle shapes were then analyzed with ANSYS FLUENT to confirm the accuracy of the optimization process.