Deviations of the results for the properties of a dense hard-sphere gas near the walls of a micro channel using the hybrid molecular dynamics—Monte Carlo simulation method

We study the deviations for the results of the properties of a hard-sphere gas near the walls of a micro/nano channel using the hybrid MD–MC simulation method compared to the pure MD and MC results. Our model for the micro channel consists of two parallel infinite plates situated at distance L apart from each other, and of gas molecules confined between these two walls. We study the dependence of the deviations for higher densities, considering different lengths of the different simulation domains in the hybrid MD–MC method. We find that when density is increased, the deviations in the pure MC results are increasing compared to pure MD results. The deviations in the hybrid simulation results are decreasing and are very small when increasing the width of the solid–gas interface. The deviations of the pure MC simulation results from the pure MD simulation results for the number density are found to be around 0.9%, when the reduced density η=0.1 and the width of the channel L=50λ, where λ is the mean free path. When the hybrid method is used, the deviations are decreasing with a factor from two to three, and are between 0.32%–0.42%. For more dense gas (η=0.2), the deviations of the MC simulation results for the number density are found to be 1.71%, and the deviations of the hybrid MD–MC simulation results between 0.246% and 0.6977%. We discuss how these deviations in case of a dense gas (η=0.2) depend on the width of the interface, and we study it for the case when the MD domain is 10% and MC domain is 90% from the simulation domain, and also for the case when the MD domain is 50% and MC domain 50% from the whole simulation domain. For more dilute gas, the MC, MD and hybrid MC–MD simulations are in very good agreement and the deviations are negligible.     

A hybrid discontinuous spectral element method and filtered mass density function solver for turbulent reacting flows

Abstract

We present a novel hybrid scheme for the large eddy simulation (LES) of turbulent reacting flows. The scheme couples the discontinuous spectral element method (DSEM) solver for the unsteady compressible Navier-Stokes equations with a Monte Carlo particle filtered mass density function (FMDF) solver for the transport of reacting species. The method is capable of high-order simulations on unstructured grids. Mean particle estimate construction mimics the DSEM numerical procedure and utilizes variable basis functions. The scheme is tested on non-reacting and reacting Taylor-Green vortex flows. Studies of varying polynomial order, different basis functions for constructing particle estimates, and varying particle quantities are conducted. We demonstrate that a tent kernel, in conjunction with high polynomial order, produces the most accurate results. The chemically reacting simulations validate the hybrid scheme and demonstrate its applicability across a range of reaction regimes. The hybrid scheme's computational cost is 2.1 times the DSEM-LES solver.     

A new two-dimensional hybrid grid generation method based on improved hole cutting

A new hybrid grid generation method for a two-dimensional computational domain is proposed in this paper. Based on the past research in this field, this new proposed method aims to generate high-quality hybrid mesh which is structured-grid (quadrilateral grid) dominated with unstructured grids (triangular grid) in a relatively small region. It is capable of preserving the advantageous features of both structured and unstructured grids and minimizing their shortcomings by improving several crucial aspects of previous algorithms. Through creating the structured part of the hybrid grids in a more flexible way and introducing some improvements to the vital procedure, so-called “hole cutting”, the present method could generate hybrid grids of desirable quality automatically and quickly without forming overlapped grids during the process. In this paper, the new method is described in detail and several grid generation examples are shown to evaluate the capability of this new method and illustrate its promising features.     

Hybrid central–WENO scheme for the large eddy simulation of turbulent flows with shocks

To provide an effective numerical method for the large eddy simulation (LES) of turbulent flows with shocks, a hybrid scheme is developed in a finite volume framework based on the fourth-order central scheme and the third-order weighted essentially non-oscillatory (WENO) scheme. A total of six easy-to-implement and promising switch functions (SFs) are examined in the hybrid central–WENO scheme for the LES of compressible turbulent flows. Both the dissipation and dispersion of the developed hybrid central–WENO scheme are theoretically confirmed using the Fourier technique. Then, the effectiveness and accuracy of this scheme and the SFs are numerically tested by three problems: decaying compressible isotropic turbulence, inviscid, and turbulent transonic flow over a bump. The numerical results show the developed hybrid scheme, coupled with the SF based on local velocity divergence and pressure gradient, has excellent capabilities of capturing shocks and resolving turbulence.     

A lattice Boltzmann algorithm for fluid–solid conjugate heat transfer

A lattice Boltzmann algorithm for fluid–solid conjugate heat transfer is developed. A new generalized heat generation implement is presented and a “half lattice division” treatment for the fluid–solid interaction and energy transport is proposed, which insures the temperature and heat flux continuities at the interface. The new scheme agrees well with the classical CFD method for predictions of flow and heat transfer in a heated thick-wall microchannel with less mesh number and less computational costs.     

An edge-based smoothed point interpolation method (ES-PIM) for heat transfer analysis of rapid manufacturing system

This paper formulates an edge-based smoothed point interpolation method (ES-PIM) for analyzing 2D and 3D transient heat transfer problems with mixed boundary conditions and complicated geometries. In the ES-PIM, shape functions are constructed using the polynomial PIM with the Delta function property for easy treatment of essential boundary conditions. A generalized smoothing technique is used to reconstruct the temperature gradient field within the edge-based smoothing domains. The generalized smoothed Galerkin weak form is then used to establish the discretized system equations. Our results show that the ES-PIM can provide more close-to-exact stiffness compared with the “overly-stiff” finite element method (FEM) and the “overly-soft” node-based smoothed point interpolation method (NS-PIM). Owing to this important property, the present ES-PIM provides more accurate solutions than standard FEM using the same mesh. As an example, a practical cooling system of the rapid direct plasma deposition dieless manufacturing is studied in detail using the present ES-PIM, and a set of “optional” processing parameters of fluid velocity and temperature are found.     

A thermal immiscible multiphase flow simulation by lattice Boltzmann method

The lattice Boltzmann (LB) method, as a mesoscopic approach based on the kinetic theory, has been significantly developed and applied in a variety of fields in the recent decades. Among all the LB community members, the pseudopotential LB plays an increasingly important role in multiphase flow and phase change problems simulation. The thermal immiscible multiphase flow simulation using pseudopotential LB method is studied in this work. The results show that it is difficult to achieve multi-bubble/droplet coexistence due to the unphysical mass transfer phenomenon of “the big eat the small” – the small bubbles/droplets disappear and the big ones getting bigger before a physical coalescence when using an internal energy based temperature equation for single-component multiphase (SCMP) pseudopotential models. In addition, this unphysical effect can be effectively impeded by coupling an entropy-based temperature field, and the influence on density fields with different energy equations are discussed. The findings are identified and reported in this paper for the first time. This work gives a significant inspiration for solving the unphysical mass transfer problem, which determines whether the SCMP LB model can be used for multi-bubble/droplet systems.     

3D ALE Finite-Element Method for Two-Phase Flows With Phase Change

We seek to study numerically two-phase flow phenomena with phase change through the finite-element method (FEM) and the arbitrary Lagrangian–Eulerian (ALE) framework. This method is based on the so-called “one-fluid” formulation; thus, only one set of equations is used to describe the flow field at the vapor and liquid phases. The equations are discretized on an unstructured tetrahedron mesh and the interface between the phases is defined by a triangular surface, which is a subset of the three-dimensional mesh. The Navier–Stokes equation is used to model the fluid flow with the inclusion of a source term to compute the interfacial forces that arise from two-phase flows. The continuity and energy equations are slightly modified to take into account the heat and mass transport between the different phases. Such a methodology can be employed to study accurately many problems, such as oil extraction and refinement in the petroleum area, design of refrigeration systems, modeling of biological systems, and efficient cooling of electronics for computational purposes, which is the aim of this research. A comparison of the obtained numerical results to the classical literature is performed and presented in this paper, thus proving the capability of the proposed new methodology as a platform for the study of diabatic two-phase flows.     

Improvements in FFD Modeling by Using Different Numerical Schemes

Indoor environment design and air management in buildings requires fast simulation of air distribution. A fast fluid dynamics (FFD) model seems very promising. This work was to develop the FFD by improving its speed and accuracy. Enhancement of computing speed can be realized by modifying the time-splitting method. Improvements in accuracy were achieved by replacing the finite-difference scheme by the finite-volume method and by proposing a correction function for mass conservation. Using the new FFD model for several indoor air flows, the results show significant reduction in computing time and great improvements on accuracy.     

Visualisation of heat transfer in 3D unsteady flows

Heat transfer in fluid flows traditionally is examined in terms of temperature field and heat-transfer coefficients at non-adiabatic walls. However, heat transfer may alternatively be considered as the transport of thermal energy by the total convective–conductive heat flux in a way analogous to the transport of fluid by the flow field. The paths followed by the total heat flux are the thermal counterpart to fluid trajectories and facilitate heat-transfer visualisation in a similar manner as flow visualisation. This has great potential for applications in which insight into the heat fluxes throughout the entire configuration is essential (e.g. cooling systems, heat exchangers). To date this concept has been restricted to 2D steady flows. The present study proposes its generalisation to 3D unsteady flows by representing heat transfer as the 3D unsteady motion of a virtual fluid subject to continuity. This unified ansatz enables heat-transfer visualisation with well-known geometrical methods from laminar-mixing studies. These methods lean on the property that continuity “organises” fluid trajectories into sets of coherent structures (“flow topology”) that geometrically determine the fluid transport. Decomposition of the flow topology into its constituent coherent structures visualises the transport routes and affords insight into the transport properties. Thermal trajectories form a thermal topology of essentially equivalent composition that can be visualised by the same methodology. This thermal topology is defined in both flow and solid regions and thus describes the heat transfer throughout the entire domain of interest. The heat-transfer visualisation is provided with a physical framework and demonstrated by way of representative examples.     

A coupled volume of fluid and level set method based on analytic PLIC for unstructured quadrilateral grids

We develop a coupled volume of fluid and level set (VOSET) method for unstructured quadrilateral grids to simulate incompressible two-phase interfacial flows in irregular domains. In the method, an analytic piecewise linear interface calculation (PLIC) is first proposed and its solution speed is much faster (about five times) than that of Brent's iterative method; then an iterative geometric operation by which the level set function near interfaces can be calculated, is extended to unstructured quadrilateral grids; moreover, the volume fraction advection is solved by a Lagrangian-Eulerian advection scheme. Finally, the present method is validated by the single vortex flow problem, bubble rising problem and falling droplet problem. Our simulation results show good agreement with those in previous studies.     

An Improved Bubble Packing Method for Unstructured Grid Generation with Application to Computational Fluid Dynamics

An improved bubble packing method (BPM) is proposed to generate high-quality unstructured grids for prediction of the flow field in a domain with complex geometry. For a curved-boundary domain, bubble departure from the curved boundaries during the dynamic movement of bubbles can be avoided by using the mapping and the arc-length parameterization methods. Furthermore, the grid density of the whole region can be controlled effectively. Local mesh refinement is achieved by adding bubbles with different sizes to the real and artificial vertices of the domain, and vertex information is transferred to the inner nodes of the domain using the Shepard interpolation method. In order to validate the proposed BPM, a finite-volume solver on an unstructured collocated grid is developed to simulate both square and polar lid-driven cavity flows. The numerical simulation results agree well with the experimental data under different Reynolds numbers.     

Boundary conditions at the solid–liquid surface over the multiscale channel size from nanometer to micron

The boundary condition at the solid surface is one of the important problems for the microfluidics. In this paper we study the effects of the channel sizes on the boundary conditions (BC), using the hybrid computation scheme adjoining the molecular dynamics (MD) simulations and the continuum fluid mechanics. We could reproduce the three types of boundary conditions (slip, no-slip and locking) over the multiscale channel sizes. The slip lengths are found to be mainly dependent on the interfacial parameters with the fixed apparent shear rate. The channel size has little effects on the slip lengths if the size is above a critical value within a couple of tens of molecular diameters. We explore the liquid particle distributions nearest the solid walls and found that the slip boundary condition always corresponds to the uniform liquid particle distributions parallel to the solid walls, while the no-slip or locking boundary conditions correspond to the ordered liquid structures close to the solid walls.The slip, no-slip and locking interfacial parameters yield the positive, zero and negative slip lengths respectively. The three types of boundary conditions existing in “microscale” still occur in “macroscale”. However, the slip lengths weakly dependent on the channel sizes yield the real shear rates and the slip velocity relative to the solid wall traveling speed approaching those with the no-slip boundary condition when the channel size is larger than thousands of liquid molecular diameters for all of the three types of interfacial parameters, leading to the quasi-no-slip boundary conditions.     

An iterative stabilized CNBS–CG scheme for incompressible non-isothermal non-Newtonian fluid flow

An iterative stabilized fractional step scheme abbreviated as I-CNBS–CG is developed, in which the Crank–Nicolson method based split (CNBS) scheme and the characteristic-Galerkin (CG) method are, respectively, used to discretize and solve the non-Newtonian momentum–mass conservation equations and the energy conservation equation in consideration of their convective character. Owing to introduction of an iterative procedure into the scheme the stability of the proposed scheme in time domain is greatly enhanced and much larger time step sizes are allowed to be used than those limited in existing explicit and semi-implicit ones. The proposed I-CNBS–CG scheme particularly suits to numerically model the non-isothermal non-Newtonian fluid flows with moderate or high viscosity and low thermal conductivity, such as molten polymer flow process in a mould cavity. Numerical experiments with the power-law fluid model demonstrate the improved performances of the proposed scheme.     

Simulation of Convective Heat Transfer of Gas–Liquid Bubble Train Flow in Wet Microtube

In this paper, a direct numerical simulation of a two‐phase incompressible gas–liquid flow for simulation of bubble motion and convective heat transfer in a microtube is presented. The microtube radius is 10 μm. The interface between the two phases is tracked by the volume of fluid method with the continuous surface force model. Newtonian flows are solved using a finite volume scheme based on the PISO algorithm. Numerical simulation is done on an axisymmetric domain with a periodic boundary condition for different values of pressure gradient, void fraction, and bubble period. Mean pressure gradient is fixed for each simulation. The superficial Reynolds numbers of gas and liquid phases studied are 0.3 to 7 and 5 to 210, respectively. Numerical results are coincident with the Serizawa regime map, and there is a linear relation between the void fraction and gas flow ratio. Simulation shows local Nusselt number increases in the presence of a gas bubble.     

A Hybrid Finite-Element/Finite-Difference Scheme for Solving the 3-D Energy Equation in Transient Nonisothermal Fluid Flow over a Staggered Tube Bank

This article presents a hybrid finite-element/finite-difference approach. The approach solves the 3-D unsteady energy equation in nonisothermal fluid flow over a staggered tube bank with five tubes in the flow direction. The investigation used Reynolds numbers of 100 and 300, Prandtl number of 0.7, and pitch-to-diameter ratio of 1.5. An equilateral triangle (ET) tube pattern is considered for the staggered tube bank. The proposed hybrid method employs a 2-D Taylor-Galerkin finite-element method, and the energy equation perpendicular to the tube axis is discretized. On the other hand, the finite-difference technique discretizes the derivatives toward the tube axis. Weighting the 3-D, transient, convection-diffusion equation for a cube verifies the numerical results. The L² norm of the error between numerical and exact solutions is also presented for three different hybrid meshes. A grid independence study for the energy equation preceded the final mesh. The outcome is found to be in acceptable concurrence with those from the previous studies. After the temperature field is attained, the local Nusselt number is computed for the tubes in the bundle at different times. The isotherms are also obtained at different times until a steady-state solution is reached. The numerical results converge to the exact results through refining the mesh. The implemented hybrid scheme requires less computation time compared with the conventional 3-D finite-element method, requiring less program coding.     

Performance Study of a Circumferential Overlap Trisection Helical Baffle Heat Exchanger at the Shell Side

Using the three-dimensional (3D) modeling software Gambit, a mathematical model of a circumferential overlap trisection helical baffle shell-and-tube heat exchanger (cothSTHX) was developed with 34 tubes and three pulling rods with an equilateral triangle tube layout and a baffle incline angle of 20°. The numerical simulation of flow and thermal performances was performed with the analysis software Fluent. The temperature, pressure, and velocity nephograms are shown for different slices, including spiral, concentric hexagon longitudinal, meridian, eccentric longitudinal, and transverse slices. The nephograms of temperature, pressure, and velocity with superimposed velocity vectors vividly display the important parameters of the cothSTHX. The “Dean vortex secondary flow” is a key mechanism to enhance the heat transfer in heat exchangers, which is clearly depicted to show that the spiral fluid flows outward under the centrifugal force, then flows back to the axis under the radial differential pressure, forming a single vortex in each helix cycle. The structure of circumferential overlap baffles restricts the shortcut leakage flow, and the flow pattern in the cothSTHX is very close to “plug flow” on the unfolded hexagon slices.     

SENSITIVITY ANALYSIS AND OPTIMIZATION FOR JOULE HEATING WITH TEMPERATURE-DEPENDENT CONDUCTIVITIES

The physical phenomenon of interest in this study relates to the joule heating of solids with temperature-dependent thermal/electrical conductivities and coupled field equations. The sensitivity analysis (SA) expressions of a general integral functional with respect to material and “loading” functions in the thermal-electric field are derived by using the adjoint variable method. The SA expressions are generally used in the mathematical programming solution methods of the so-called inverse problems, such as optimization and identification problems. In particular, a two-dimensional example optimization problem is studied numerically by discretizing the primary and adjoint field equations by the finite-element method, while minimizing the objective function of optimization by nonlinear programming routines. The parametric studies performed with various mesh topologies and (finite) decision vectors indicate the feasibility and efficiency of the proposed numerical scheme.     

Comparative Analysis of Thermal Models in the Lattice Boltzmann Method for the Simulation of Natural Convection in a Square Cavity

In this article, a comparative analysis of thermal models in the lattice Boltzmann method for the simulation of natural convection in a square cavity is presented. A hybrid method, in which the thermal equation is solved by the Navier-Stokes equation method while the mass and momentum equations are solved by the lattice Boltzmann method (LBM), is introduced and its merits are explained. All the governing equations are discretized on a cell-centered, nonuniform grid using the finite-volume method. The convection terms are treated by a second-order central-difference scheme with a deferred-correction method to ensure accuracy of solutions. The resulting algebraic equations are solved by a strongly implicit procedure. The hybrid method is applied to the simulation of natural convection in a square cavity and the predicted results are compared with the benchmark solutions given in the literatures. The predicted results are also compared with those by the double-population LBM and by the Navier-Stokes equation method. In general, the present hybrid method is as accurate as the Navier-Stokes equation method and the double-population LBM. The hybrid method shows better convergence and stability than the double-population LBM. These observations indicate that this hybrid method is an efficient and economic method for the simulation of incompressible fluid flow and heat transfer problems involving complex geometries.     

A study of numerical hazard prediction method of gas explosion

A 3-dimensional computational fluid dynamics (CFD) simulation of a premixed hydrogen/air explosion in a large-scale domain is performed. The main feature of the numerical model is the solution of a transport equation for the reaction progress variable using a function for turbulent burning velocity that characterizes the turbulent regime of propagation of free flames derived by introducing the fractal theory. The model enables the calculation of premixed gaseous explosion without using fine mesh of the order of micrometer, which would be necessary to resolve the details of all instability mechanisms. The value of the empirical constant contained in the function for turbulent burning velocity is evaluated by analyzing the experimental data of hydrogen/air premixed explosion. The comparison of flame behavior between the experimental result and numerical simulation shows good agreement. The effect of mesh size on simulated flame propagation velocity is also tested, showing that the numerical result agrees reasonably well with experiment when the mesh size is less than about 20 cm.