Counter-extrapolation method for conjugate interfaces in computational heat and mass transfer

Off-lattice Boltzmann simulation of conjugate heat transfer for natural convection in two-dimensional cavities

This study addresses the inadequacy of isothermal wall conditions in predicting accurate flow features and thermal effects in multicomponent systems. A finite-difference characteristic-based off-lattice Boltzmann method (OLBM) with a source term-based conjugate heat transfer (CHT) model is utilized to analyze buoyancy-driven flows in two-dimensional enclosures. The source term-based CHT model [Karani and Huber, Phys. Rev. E 91, 023304 (2015)1539-375510.1103/PhysRevE.91.023304] is extended to handle curved conjugate boundaries. The proposed CHT-OLBM solver is verified using analytical solutions and reference data from the literature. The effects of wall conduction on conjugate natural convection (CNC) problems in square and horizontal annular cavities are systematically examined with a solid wall of a nondimensional thickness of 0.2. For the square cavity problem, the governing parameters considered are 10^{5}≤Gr≤10^{9} and χ=1,5,10, while for the horizontal annulus problem, the governing parameters are taken as 10^{5}≤Ra≤10^{7} and χ=1,5,10,100, where Gr is the Grashof number, Ra is the Rayleigh number, and χ is the thermal conductivity ratio. Qualitative analysis of the simulation results using isotherms and streamlines and quantitative analysis of the local fluid-solid interface temperature, solid wall temperature distribution, Nusselt number profiles, overall Nusselt number, and effective Grashof/Rayleigh number is conducted. The overall heat transfer reduction inside the cavities due to a solid wall is quantified, and correlations are obtained to represent the overall heat transfer inside both enclosures. The findings demonstrate the significance of CHT analysis, and the CHT-OLBM solver developed in this study can successfully investigate steady, unsteady, and chaotic CNC flows.

Oxygen transport across tank-treading red blood cell: Individual and joint roles of flow convection and oxygen-hemoglobin reaction

Gas, especially oxygen, transport in the microcirculation is a complex phenomenon, however, of critical importance for maintaining normal biological functions, and the cytoplasm fluid in red blood cells (RBCs) is the major vehicle for transporting oxygen from lungs to tissues via the circulatory system. Existing theoretical and numerical studies have neglected the cytoplasm convection effect by treating RBCs as rigid particles undergoing a constant translation velocity. As a consequence, the influence and mechanism of the cytoplasm flow on oxygen transport are still not clear in microcirculation research. In this study, we consider a tank-treading capsule in shear flow, which is generated with two parallel plates moving in opposite directions: the top plate of a higher oxygen pressure (P_O2) representing the RBC core in the central region of a microvessel and the bottom plate of a lower P_O2 representing the microvessel wall. Numerical simulations are conducted to investigate the individual and combined effects of cytoplasm convection and oxygen-hemoglobin (O₂-Hb) reaction on the oxygen transport efficiency across the tank-treading capsule, and different P_O2 situations and shear rates are also tested. Due to the lower oxygen diffusivity in cytoplasm, the presence of the capsule reduces the oxygen transfer flux across the gap by 7.34 % in the pure diffusion system where the flow convection and O₂-Hb reaction are both neglected. Including the flow convection or the O₂-Hb reaction has little influence on the oxygen flux; however, when they act together as in real microcirculation situations, the enhancement in oxygen transport could be significant, especially in the low P_O2 and high shear rate situations. In particular, with the respective P_O2 at 60 and 30 mmHg on the top and bottom plates and a 400 s^-1 shear rate, the oxygen flux reduction is only 0.02 %, suggesting that the cytoplasm convection can improve the oxygen transport across RBCs considerably. The simulation results are scrutinized to explore the underlying mechanism for the enhancement, and a new nondimensional parameter is introduced to characterize the importance of cytoplasm convection in oxygen transport. These simulation results, discussion and analysis could be helpful for a better understanding of the complex oxygen transport process and therefor valuable for relevant studies.

Comparative investigation of a lattice Boltzmann boundary treatment of multiphase mass transport with heterogeneous chemical reactions

Multiphase reactive transport in porous media is an important component of many natural and engineering processes. In the present study, boundary schemes for the continuum species transport-lattice Boltzmann (CST-LB) mass transport model and the multicomponent pseudopotential model are proposed to simulate heterogeneous chemical reactions in a multiphase system. For the CST-LB model, a lattice-interface-tracking scheme for the heterogeneous chemical reaction boundary is provided. Meanwhile, a local-average virtual density boundary scheme for the multicomponent pseudopotential model is formulated based on the work of Li et al. [Li, Yu, and Luo, Phys. Rev. E 100, 053313 (2019)10.1103/PhysRevE.100.053313]. With these boundary treatments, a numerical implementation is put forward that couples the multiphase fluid flow, interfacial species transport, heterogeneous chemical reactions, and porous matrix structural evolution. A series of comparison benchmark cases are investigated to evaluate the numerical performance for different pseudopotential wetting boundary treatments, and an application case of multiphase dissolution in porous media is conducted to validate the present models' ability to solve complex problems. By applying the present LB models with reasonable boundary treatments, multiphase reactive transport in various natural or engineering scenarios can be simulated accurately.

Improved curved-boundary scheme for lattice Boltzmann simulation of microscale gas flow with second-order slip condition

An improved curved-boundary scheme with second-order velocity slip condition for multiple-relaxation-time-lattice Boltzmann (MRT-LB) simulation of microgas flow is proposed. The proposed interpolation bounce-back (IBB)-explicit counter-extrapolation (ECE) scheme adopts the IBB method to describe the curved boundary, while the ECE method is employed to predict the slip velocity on gas-solid interface. To incorporate the effect of second-order velocity slip term and the influence of boundary curvature, a slip velocity model is also derived, from which the gas slip velocity is captured by the ECE discretization method. The influence of fictitious slip velocity can be eliminated by adopting the present ECE method, and the influence of actual offset between the lattice node and the physical boundary can be well considered by the IBB method. The proposed IBB-ECE boundary scheme is then implemented with the MRT-LB model and tested by simulations of force-driven gas flow in horizontal (inclined) microchannel, gas flow around a micro-cylinder, and Couette flow between two micro-cylinders. Numerical results show that the proposed IBB-ECE scheme improves the computational accuracy of gas slip flow (0.001<Kn≤0.1) when compared with other boundary schemes reported in the literature, and provides a precise and easy implementing scheme for curved boundary with second-order slip condition.

Effects of Microscopic Properties on Macroscopic Thermal Conductivity for Convective Heat Transfer in Porous Materials

Porous materials are widely used in many heat transfer applications. Modeling porous materials at the microscopic level can accurately incorporate the detailed structure and substance parameters and thus provides valuable information for the complex heat transfer processes in such media. In this study, we use the generalized periodic boundary condition for pore-scale simulations of thermal flows in porous materials. A two-dimensional porous model consisting of circular solid domains is considered, and comprehensive simulations are performed to study the influences on macroscopic thermal conductivity from several microscopic system parameters, including the porosity, Reynolds number, and periodic unit aspect ratio and the thermal conductance at the solid–fluid interface. Our results show that, even at the same porosity and Reynolds number, the aspect ratio of the periodic unit and the interfacial thermal conductance can significantly affect the macroscopic thermal behaviors of porous materials. Qualitative analysis is also provided to relate the apparent thermal conductivity to the complex flow and temperature distributions in the microscopic porous structure. The method, findings and discussions presented in this paper could be useful for fundamental studies, material development, and engineering applications of porous thermal flow systems.

Consistent second-order boundary implementations for convection-diffusion lattice Boltzmann method

In this study, an alternative second-order boundary scheme is proposed under the framework of the convection-diffusion lattice Boltzmann (LB) method for both straight and curved geometries. With the proposed scheme, boundary implementations are developed for the Dirichlet, Neumann and linear Robin conditions in a consistent way. The Chapman-Enskog analysis and the Hermite polynomial expansion technique are first applied to derive the explicit expression for the general distribution function with second-order accuracy. Then, the macroscopic variables involved in the expression for the distribution function is determined by the prescribed macroscopic constraints and the known distribution functions after streaming [see the paragraph after Eq. (29) for the discussions of the "streaming step" in LB method]. After that, the unknown distribution functions are obtained from the derived macroscopic information at the boundary nodes. For straight boundaries, boundary nodes are directly placed at the physical boundary surface, and the present scheme is applied directly. When extending the present scheme to curved geometries, a local curvilinear coordinate system and first-order Taylor expansion are introduced to relate the macroscopic variables at the boundary nodes to the physical constraints at the curved boundary surface. In essence, the unknown distribution functions at the boundary node are derived from the known distribution functions at the same node in accordance with the macroscopic boundary conditions at the surface. Therefore, the advantages of the present boundary implementations are (i) the locality, i.e., no information from neighboring fluid nodes is required; (ii) the consistency, i.e., the physical boundary constraints are directly applied when determining the macroscopic variables at the boundary nodes, thus the three kinds of conditions are realized in a consistent way. It should be noted that the present focus is on two-dimensional cases, and theoretical derivations as well as the numerical validations are performed in the framework of the two-dimensional five-velocity lattice model.

Fourth-order analysis of a diffusive lattice Boltzmann method for barrier coatings

We examine the applicability of diffusive lattice Boltzmann methods to simulate the fluid transport through barrier coatings, finding excellent agreement between simulations and analytical predictions for standard parameter choices. To examine more interesting non-Fickian behavior and multiple layers of different coatings, it becomes necessary to explore a wider range of parameters. However, such a range of parameters exposes deficiencies in such an implementation. To investigate these discrepancies, we examine the form of higher-order terms in the hydrodynamic limit of our lattice Boltzmann method. We identify these corrections to fourth order and validate these predictions with high accuracy. However, it is observed that the validated correction terms do not fully explain the bulk of observed error. This error was instead caused by the standard finite boundary conditions for the contact of the coating with the imposed environment. We identify a self-consistent form of these boundary conditions for which these errors are dramatically reduced. The instantaneous switching used as a boundary condition for the barrier problem proves demanding enough that any higher-order corrections meaningfully contribute for a small range of parameters. There is a large parameter space where the agreement between simulations and analytical predictions even in the second-order form are below 0.1%, making further improvements to the algorithm unnecessary for such an application.

Fluctuating lattice Boltzmann method for the diffusion equation

We derive a fluctuating lattice Boltzmann method for the diffusion equation. The derivation removes several shortcomings of previous derivations for fluctuating lattice Boltzmann methods for hydrodynamic systems. The comparative simplicity of this diffusive system highlights the basic features of this first exact derivation of a fluctuating lattice Boltzmann method.

Conjugate heat transfer with the entropic lattice Boltzmann method

A conjugate heat-transfer model is presented based on the two-population entropic lattice Boltzmann method. The present approach relies on the extension of Grad's boundary conditions to the two-population model for thermal flows, as well as on the appropriate exact conjugate heat-transfer condition imposed at the fluid-solid interface. The simplicity and efficiency of the lattice Boltzmann method (LBM), and in particular of the entropic multirelaxation LBM, are retained in the present approach, thus enabling simulations of turbulent high Reynolds number flows and complex wall boundaries. The model is validated by means of two-dimensional parametric studies of various setups, including pure solid conduction, conjugate heat transfer with a backward-facing step flow, and conjugate heat transfer with the flow past a circular heated cylinder. Further validations are performed in three dimensions for the case of a turbulent flow around a heated mounted cube.

Lattice Boltzmann method for convection-diffusion equations with general interfacial conditions

In this work, we propose an interfacial scheme accompanying the lattice Boltzmann method for convection-diffusion equations with general interfacial conditions, including conjugate conditions with or without jumps in heat and mass transfer, continuity of macroscopic variables and normal fluxes in ion diffusion in porous media with different porosity, and the Kapitza resistance in heat transfer. The construction of this scheme is based on our boundary schemes [Huang and Yong, J. Comput. Phys. 300, 70 (2015)JCTPAH0021-999110.1016/j.jcp.2015.07.045] for Robin boundary conditions on straight or curved boundaries. It gives second-order accuracy for straight interfaces and first-order accuracy for curved ones. In addition, the new scheme inherits the advantage of the boundary schemes in which only the current lattice nodes are involved. Such an interfacial scheme is highly desirable for problems with complex geometries or in porous media. The interfacial scheme is numerically validated with several examples. The results show the utility of the constructed scheme and very well support our theoretical predications.

Full Eulerian lattice Boltzmann model for conjugate heat transfer

In this paper a full Eulerian lattice Boltzmann model is proposed for conjugate heat transfer. A unified governing equation with a source term for the temperature field is derived. By introducing the source term, we prove that the continuity of temperature and its normal flux at the interface is satisfied automatically. The curved interface is assumed to be zigzag lines. All physical quantities are recorded and updated on a Cartesian grid. As a result, any complicated treatment near the interface is avoided, which makes the proposed model suitable to simulate the conjugate heat transfer with complex interfaces efficiently. The present conjugate interface treatment is validated by several steady and unsteady numerical tests, including pure heat conduction, forced convection, and natural convection problems. Both flat and curved interfaces are also involved. The obtained results show good agreement with the analytical and/or finite volume results.