Numerical Study of Flow and Heat Transfer in Rotating Microchannels

Investigation of fluid flow and heat transfer in rotating microchannels is important for centrifugal microfluidics, which has emerged as an advanced technique in biomedical applications and chemical separations. The centrifugal force and the Coriolis force, arising as a consequence of the microchannel rotation, change the flow pattern significantly from the symmetric profile of a non-rotating channel. A successful design of a centrifugal microfluidic device depends on effectively regulating these forces in rotating microchannels. Although a large number of experimental studies have been performed in order to demonstrate the applications of centrifugal microfluidics in various fields, a systematic study on the effect of rotation, channel aspect ratio, and wall boundary conditions on the fluid flow and heat transfer phenomena in rotating microchannels has not yet been conducted. During the present study, pressure-based finite volume solvers in both staggered and collocated grids were developed to solve steady and unsteady, incompressible Navier-Stokes equations. The serial solver in collocated grid was parallelized using a Message Passing Interface (MPI) library. In order to accelerate the convergence of the collocated finite volume solver, a non-linear multi-grid method was developed. The parallel performances of the single and multi-grid solvers were tested on a two-dimensional lid driven cavity flow. High fidelity benchmark solution to a lid driven cavity flow problem in a 1024 x 1024 grid was presented for a range of Reynolds numbers. Parallel multigrid speedup as high as three orders of magnitude was achieved for low Reynolds number flows. In addition, the optimal multigrid efficiency was validated. The fluid flow in a rotating microchannel was modeled as a steady, laminar in compressible flow with no slip and slip boundary conditions. For no slip boundary condition, critical values of parameters that determine the extent of the centrifugal force and the Coriolis force were identified. The critical aspect ratio (=width/height) that causes the optimal mixing of two liquids was found to be 1.0. For liquid slip boundary condition, the effect of rotation on liquid slip flow in rotating microchannels with hydrophobic and superhydrophobic surfaces was studied. New correlations for friction relation (fRe) as a function of slip length (λ) and rotational Reynolds number (Reω) were proposed. It was also found that, the liquid slip can increase or decrease the heat transfer depending on the secondary flow effect and the aspect ratio of the microchannel. The microscale effects, such as surface tension and contact angle boundary condition, were included in the modeled problem. A level set method was applied to incorporate these microscale effects, which will enable us to investigate the unsteady nature of the liquid meniscus during two-phase flow simulations

Continuous, Semi-discrete, and Fully Discretized Navier-Stokes Equations

The Navier--Stokes equations are commonly used to model and to simulate flow phenomena. We introduce the basic equations and discuss the standard methods for the spatial and temporal discretization. We analyse the semi-discrete equations -- a semi-explicit nonlinear DAE -- in terms of the strangeness index and quantify the numerical difficulties in the fully discrete schemes, that are induced by the strangeness of the system. By analyzing the Kronecker index of the difference-algebraic equations, that represent commonly and successfully used time stepping schemes for the Navier--Stokes equations, we show that those time-integration schemes factually remove the strangeness. The theoretical considerations are backed and illustrated by numerical examples.Comment: 28 pages, 2 figure, code available under DOI: 10.5281/zenodo.998909, https://doi.org/10.5281/zenodo.99890

Study Of Low Speed Transitional Regime Gas Flows In Microchannels Using Information Preservation (Ip) Method

Proper design of thermal management solutions for future nano-scale electronics or photonics will require knowledge of flow and transport through micron-scale ducts. As in the macro-scale conventional counterparts, such micron-scale flow systems would require robust simulation tools for early-stage design iterations. It can be envisioned that an ideal Nanoscale thermal management (NSTM) solution will involve two-phase flow, liquid flow and gas flow. This study focuses on numerical simulation gas flow in microchannels as a fundamental thermal management technique in any future NSTM solution. A wellknown particle-based method, Direct Simulation Monte Carlo (DSMC) is selected as the simulation tool. Unlike continuum based equations which would fail at large Kn numbers, the DSMC method is valid in all Knudsen regimes. Due to its conceptual simplicity and flexibility, DSMC has a lot of potential and has already given satisfactory answers to a broad range of macroscopic problems. It has also a lot of potential in handling complex MEMS flow problems with ease. However, the high-level statistical noise in DSMC must be eliminated and pressure boundary conditions must be effectively implemented in order to utilize the DSMC under subsonic flow conditions. The statistical noise of classical DSMC can be eliminated trough the use of IP method. The method saves computational time by several orders of magnitude compared to a similar DSMC simulation. As in the regular DSMC procedures, the molecular velocity is used to determine the molecular positions and compute collisions. Separating the macroscopic velocity from the molecular velocity through the use of the IP method, however, eliminates the high-level of statistical noise as typical in DSMC calculations of low-speed flows. The conventional boundary conditions of the classical DSMC method, such as constant velocity free-stream and vacuum conditions are incorrect in subsonic flow conditions. There should be a substantial amount of backpressure allowing new molecules to enter from the outlet as well as inlet boundaries. Additionally, the application of pressure boundaries will facilitate comparison of numerical and experimental results more readily. Therefore, the main aim of this study is to build the unidirectional, non-isothermal IP algorithm method with periodic boundary conditions on the two dimensional classical DSMC algorithm. The IP algorithm is further modified to implement pressure boundary conditions using the method of characteristics. The applicability of the final algorithm in solving a real flow situation is verified on parallel plate Poiseuille and backward facing step flows in microchannels which are established benchmark problems in computational fluid dynamics studies. The backward facing step geometry is also of practical importance in a variety of engineering applications including Integrated Circuit (IC) design. Such an investigation in microchannels with sufficient accuracy may provide insight into the more complex flow and transport processes in any future Nanoscale thermal management (NSTM) solution. The flow and heat transfer mechanisms at different Knudsen numbers are investigated

Thermal fluctuations and boundary conditions in the lattice Boltzmann method

The lattice Boltzmann method is a popular approach for simulating hydrodynamic interactions in soft matter and complex fluids. The solvent is represented on a discrete lattice whose nodes are populated by particle distributions that propagate on the discrete links between the nodes and undergo local collisions. On large length and time scales, the microdynamics leads to a hydrodynamic flow field that satisfies the Navier-Stokes equation. In this thesis, several extensions to the lattice Boltzmann method are developed. In complex fluids, for example suspensions, Brownian motion of the solutes is of paramount importance. However, it can not be simulated with the original lattice Boltzmann method because the dynamics is completely deterministic. It is possible, though, to introduce thermal fluctuations in order to reproduce the equations of fluctuating hydrodynamics. In this work, a generalized lattice gas model is used to systematically derive the fluctuating lattice Boltzmann equation from statistical mechanics principles. The stochastic part of the dynamics is interpreted as a Monte Carlo process, which is then required to satisfy the condition of detailed balance. This leads to an expression for the thermal fluctuations which implies that it is essential to thermalize all degrees of freedom of the system, including the kinetic modes. The new formalism guarantees that the fluctuating lattice Boltzmann equation is simultaneously consistent with both fluctuating hydrodynamics and statistical mechanics. This establishes a foundation for future extensions, such as the treatment of multi-phase and thermal flows. An important range of applications for the lattice Boltzmann method is formed by microfluidics. Fostered by the “lab-on-a-chip” paradigm, there is an increasing need for computer simulations which are able to complement the achievements of theory and experiment. Microfluidic systems are characterized by a large surface-to-volume ratio and, therefore, boundary conditions are of special relevance. On the microscale, the standard no-slip boundary condition used in hydrodynamics has to be replaced by a slip boundary condition. In this work, a boundary condition for lattice Boltzmann is constructed that allows the slip length to be tuned by a single model parameter. Furthermore, a conceptually new approach for constructing boundary conditions is explored, where the reduced symmetry at the boundary is explicitly incorporated into the lattice model. The lattice Boltzmann method is systematically extended to the reduced symmetry model. In the case of a Poiseuille flow in a plane channel, it is shown that a special choice of the collision operator is required to reproduce the correct flow profile. This systematic approach sheds light on the consequences of the reduced symmetry at the boundary and leads to a deeper understanding of boundary conditions in the lattice Boltzmann method. This can help to develop improved boundary conditions that lead to more accurate simulation results

Catalytic flow with a coupled finite difference — Lattice Boltzmann scheme

Many catalyst devices employ flow through porous structures, which leads to a complex macroscopic mass and heat transport. To unravel the detailed dynamics of the reactive gas flow, we present an all-encompassing model, consisting of thermal lattice Boltzmann model by Kang et al., used to solve the heat and mass transport in the gas domain, coupled to a finite differences solver for the heat equation in the solid via thermal reactive boundary conditions for a consistent treatment of the reaction enthalpy. The chemical surface reactions are incorporated in a flexible fashion through flux boundary conditions at the gas–solid interface. We scrutinize the thermal FD-LBM by benchmarking the macroscopic transport in the gas domain as well as conservation of the enthalpy across the solid–gas interface. We exemplify the applicability of our model by simulating the reactive gas flow through a microporous material catalyzing the so-called water-gas-shift reaction

Investigation of volume diffusion hydrodynamics : application to tight porous media

Various engineering problems imply rarefied gas flows that rely in the transition and free molecular regimes, e.g., micro and nano devices. The recent expansion of shale gas production where rarefied conditions are found in reservoirs exposed another area of application with a major importance. Continuum based methods like standard Navier- Stokes equations break down in the transition regime and free molecular regime. In order to model such flows discrete methods are usually adopted. Boltzmann equation can theoretically be used to simulate rarefied gas flows. However, complexity of its collision integral limits its applications mostly to simple cases (i.e., one dimension problems). The direct simulation Monte Carlo method which mimics the Boltzmann equation is the dominant method for simulating rarefied gas flows. It has been tested in several engineering problems, ranging from nano scale flow to re-entry vehicles with very consistent results in comparison with experimental data and analytical solutions. Its computational cost is, however, enormous for complex cases. Observations from Crookes radiometer inspired extending the continuum methods so that they could capture non-equilibrium phenomena in small scales. In the present thesis two different hydrodynamic model are presented. The first one is based on the Korteweg expression and the second one is called “Bi-velocity”. Firstly, the two models are presented in their mathematical forms. The proposed models are then developed in open-source computational fluid dynamics solvers. The models are tested and benchmarked in different rarefied gas flows problems in the whole range of Knudsen number. We used problems that are found in micro and nano systems and tight porous media. Results from the hydrodynamic models are compared against experimental data where available and the direct simulation Monte Carlo method. The two extended hydrodynamic models show improved results in comparison with standard Navier-Stokes

Hybrid discretizations of the Boltzmann equation for the dilute gas flow regime

New hybrid numerical model allows large scale flow simulations in high-tech production equipmen