Lattice Boltzmann method for interface capturing.

Accurately solving phase interface plays a great role in modeling an immiscible multiphase flow system. In this paper, we propose an accurate interface-capturing lattice Boltzmann method from the perspective of the modified Allen-Cahn equation (ACE). The modified ACE is built based on the commonly used conservative formulation via the relation between the signed-distance function and the order parameter also maintaining the mass-conserved characteristic. A suitable forcing term is carefully incorporated into the lattice Boltzmann equation for correctly recovering the target equation. We then test the proposed method by simulating some typical interface-tracking problems of Zalesaks disk rotation, single vortex, deformation field and demonstrate that the present model can be more numerically accurate than the existing lattice Boltzmann models for the conservative ACE, especially at a small interface-thickness scale.

Effect of Gap Length and Partition Thickness on Thermal Boundary Layer in Thermal Convection.

Two-dimensional direct numerical simulations of partitioned thermal convection are performed using the thermal lattice Boltzmann method for the Rayleigh number (Ra) of 109 and the Prandtl number (Pr) of 7.02 (water). The influence of the partition walls on the thermal boundary layer is mainly focused on. Moreover, to better describe the spatially nonuniform thermal boundary layer, the definition of the thermal boundary layer is extended. The numerical simulation results show that the gap length significantly affects the thermal boundary layer and Nusselt number (Nu). The gap length and partition wall thickness have a coupled effect on the thermal boundary layer and the heat flux. Based on the shape of the thermal boundary layer distribution, two different heat transfer models are identified at different gap lengths. This study provides a basis for improving the understanding of the effect of partitions on the thermal boundary layer in thermal convection.

Simulation of Cardiac Flow under the Septal Defect Based on Lattice Boltzmann Method.

In this paper, the lattice Boltzmann method was used to simulate the cardiac flow in children with aseptal defect. The inner wall model of the heart was reconstructed from 210 computed tomography scans. By simulating and comparing the cardiac flow field, the pressure field, the blood oxygen content, and the distribution of entropy generation before and after an operation, the effects of septal defect on pulmonary hypertension(PH), cyanosis, and heart load were analyzed in detail. It is found that the atrial septal defect(ASD) of the child we analyzed had a great influence on the blood oxygen content in the pulmonary artery, which leads to lower efficiency of oxygen binding in the lungs and increases the burden on the heart. At the same time, it also significantly enhanced the entropy generation rate of the cardiac flow, which also leads to a higher heart load. However, the main cause of PH is not ASD, but ventricular septal defect (VSD). Meanwhile, it significantly reduced the blood oxygen content in the brachiocephalic trunk, but rarely affects the blood oxygen contents in the downstream left common carotid artery, left subclavian artery, and descending aorta are not significantly affected by VSD. It causes severe cyanosis on the face and lips.

Small-scale fluctuation and scaling law of mixing in three-dimensional rotating turbulent Rayleigh-Taylor instability.

The effect of rotation on small-scale characteristics and scaling law in the mixing zone of the three-dimensional turbulent Rayleigh-Taylor instability (RTI) is investigated by the lattice Boltzmann method at small Atwood number. The mixing zone width h(t), the root mean square of small scale fluctuation, the spectra, and the structure functions are obtained to analyze the rotating effect. We mainly focus on the process of the development of plumes and discuss the physical mechanism in the mixing zone in rotating and nonrotating systems. The variation of kinetic energy spectra E_{u} and temperature energy spectra E_{θ} with the dimensionless rotation Ωτ demonstrate the suppression effect of rotation. Two scaling laws between the mixing layer width h(t) and dimensionless time t/τ are obtained at various Coriolis forces(sqrt[h(t)]≃t^{0.9} and sqrt[h(t)]≃t^{0.35}). The rotation increasingly suppresses the growth of the mixing layer width h(t). The velocity and temperature fluctuations are also suppressed by the rotation effect. The relation between the Nusselt number (Nu) and the Rayleigh number (Ra) indicates that the heat transfer is suppressed by the rotation effect in the rotating RT system. The width of the inertial subrange increasingly narrows with increasing Ωτ.

Temporal-Spatial Evolution of Kinetic and Thermal Energy Dissipation Rates in a Three-Dimensional Turbulent Rayleigh-Taylor Mixing Zone.

In this work, the temporal-spatial evolution of kinetic and thermal energy dissipation rates in three-dimensional (3D) turbulent Rayleigh-Taylor (RT) mixing are investigated numerically by the lattice Boltzmann method. The temperature fields, kinetic and thermal energy dissipation rates with temporal-spatial evolution, the probability density functions, the fractal dimension of mixing interface, spatial scaling law of structure function for the kinetic and the thermal energy dissipation rates in 3D space are analysed in detail to provide an improved physical understanding of the temporal-spatial dissipation-rate characteristic in the 3D turbulent Rayleigh-Taylor mixing zone. Our numerical results indicate that the kinetic and thermal energy dissipation rates are concentrated in areas with large gradients of velocity and temperature with temporal evolution, respectively, which is consistent with the theoretical assumption. However, small scale thermal plumes initially at the section of half vertical height increasingly develop large scale plumes with time evolution. The probability density function tail of thermal energy dissipation gradually rises and approaches the stretched exponent function with temporal evolution. The slope of fractal dimension increases at an early time, however, the fractal dimension for the fluid interfaces is 2.4 at times t/τ ≥ 2, which demonstrates the self-similarity of the turbulent RT mixing zone in 3D space. It is further demonstrated that the second, fourth and sixth-order structure functions for velocity and temperature structure functions have a linear scaling within the inertial range.

Time Evolution Features of Entropy Generation Rate in Turbulent Rayleigh-Bénard Convection with Mixed Insulating and Conducting Boundary Conditions.

Time evolution features of kinetic and thermal entropy generation rates in turbulent Rayleigh-Bénard (RB) convection with mixed insulating and conducting boundary conditions at Ra = 109 are numerically investigated using the lattice Boltzmann method. The state of flow gradually develops from laminar flow to full turbulent thermal convection motion, and further evolves from full turbulent thermal convection to dissipation flow in the process of turbulent energy transfer. It was seen that the viscous, thermal, and total entropy generation rates gradually increase in wide range of t/τ < 32 with temporal evolution. However, the viscous, thermal, and total entropy generation rates evidently decrease at time t/τ = 64 compared to that of early time. The probability density function distributions, spatial-temporal features of the viscous, thermal, and total entropy generation rates in the closed system provide significant physical insight into the process of the energy injection, the kinetic energy, the kinetic energy transfer, the thermal energy transfer, the viscous dissipated flow and thermal dissipation.

Numerical Simulations of the Motion and Deformation of Three RBCs during Poiseuille Flow through a Constricted Vessel Using IB-LBM.

The immersed boundary-lattice Boltzmann method (IB-LBM) was used to examine the motion and deformation of three elastic red blood cells (RBCs) during Poiseuille flow through constricted microchannels. The objective was to determine the effects of the degree of constriction and the Reynolds (Re) number of the flow on the physical characteristics of the RBCs. It was found that, with decreasing constriction ratio, the RBCs experienced greater forced deformation as they squeezed through the constriction area compared to at other parts of the microchannel. It was also observed that a longer time was required for the RBCs to squeeze through a narrower constriction. The RBCs subsequently regained a stable shape and gradually migrated toward the centerline of the flow beyond the constriction area. However, a sick RBC was observed to be incapable of passing through a constricted vessel with a constriction ratio ≤1/3 for Re numbers below 0.40.

Numerical Study on Entropy Generation in Thermal Convection with Differentially Discrete Heat Boundary Conditions.

Entropy generation in thermal convection with differentially discrete heat boundary conditions at various Rayleigh numbers (Ra) are numerically investigated using the lattice Boltzmann method. We mainly focused on the effects of Ra and discrete heat boundary conditions on entropy generation in thermal convection according to the minimal entropy generation principle. The results showed that the presence of the discrete heat source at the bottom boundary promotes the transition to a substantial convection, and the viscous entropy generation rate (Su) generally increases in magnitude at the central region of the channel with increasing Ra. Total entropy generation rate (S) and thermal entropy generation rate (Sθ) are larger in magnitude in the region with the largest temperature gradient in the channel. Our results also indicated that the thermal entropy generation, viscous entropy generation, and total entropy generation increase exponentially with the increase of Rayleigh number. It is noted that lower percentage of single heat source area in the bottom boundary increases the intensities of viscous entropy generation, thermal entropy generation and total entropy generation. Comparing with the classical homogeneous thermal convection, the thermal entropy generation, viscous entropy generation, and total entropy generation are improved by the presence of discrete heat sources at the bottom boundary.

Statistics of Heat Transfer in Two-Dimensional Turbulent Rayleigh-Bénard Convection at Various Prandtl Number.

Statistics of heat transfer in two-dimensional (2D) turbulent Rayleigh-Bénard (RB) convection for Pr=6,20,100 and 106 are investigated using the lattice Boltzmann method (LBM). Our results reveal that the large scale circulation is gradually broken up into small scale structures plumes with the increase of Pr, the large scale circulation disappears with increasing Pr, and a great deal of smaller thermal plumes vertically rise and fall from the bottom to top walls. It is further indicated that vertical motion of various plumes gradually plays main role with increasing Pr. In addition, our analysis also shows that the thermal dissipation is distributed mainly in the position of high temperature gradient, the thermal dissipation rate εθ already increasingly plays a dominant position in the thermal transport, εu can have no effect with increase of Pr. The kinematic viscosity dissipation rate and the thermal dissipation rate gradually decrease with increasing Pr. The energy spectrum significantly decreases with the increase of Pr. A scope of linear scaling arises in the second order velocity structure functions, the temperature structure function and mixed structure function(temperature-velocity). The value of linear scaling and the 2nd-order velocity decrease with increasing Pr, which is qualitatively consistent with the theoretical predictions.

Study on Bifurcation and Dual Solutions in Natural Convection in a Horizontal Annulus with Rotating Inner Cylinder Using Thermal Immersed Boundary-Lattice Boltzmann Method.

A numerical investigation has been carried out to understand the mechanism of the rotation effect on bifurcation and dual solutions in natural convection within a horizontal annulus. A thermal immersed boundary-lattice Boltzmann method was used to resolve the annular flow domain covered by a Cartesian mesh. The Rayleigh number based on the gap width is fixed at 104. The rotation effect on the natural convection is analyzed by streamlines, isotherms, phase portrait and bifurcation diagram. Our results manifest the existence of three convection patterns in a horizontal annulus with rotating inner cylinder which affect the heat transfer in different ways, and the linear speed ( U i * ) determines the proportion of each convection. Comparison of average Nusselt number versus linear speed for the inner cylinder indicates the existence of the three different mechanisms which drive the convection in a rotation system. The convection pattern caused by rotation reduces the heat transfer efficiency. Our results in phase portraits also reveal the differences among different convection patterns.

Entropy Generation Rates in Two-Dimensional Rayleigh-Taylor Turbulence Mixing.

Entropy generation rates in two-dimensional Rayleigh-Taylor (RT) turbulence mixing are investigated by numerical calculation. We mainly focus on the behavior of thermal entropy generation and viscous entropy generation of global quantities with time evolution in Rayleigh-Taylor turbulence mixing. Our results mainly indicate that, with time evolution, the intense viscous entropy generation rate s u and the intense thermal entropy generation rate S θ occur in the large gradient of velocity and interfaces between hot and cold fluids in the RT mixing process. Furthermore, it is also noted that the mixed changing gradient of two quantities from the center of the region to both sides decrease as time evolves, and that the viscous entropy generation rate 〈 S u 〉 V and thermal entropy generation rate 〈 S θ 〉 V constantly increase with time evolution; the thermal entropy generation rate 〈 S θ 〉 V with time evolution always dominates in the entropy generation of the RT mixing region. It is further found that a "smooth" function 〈 S u 〉 V ∼ t 1 / 2 and a linear function 〈 S θ 〉 V ∼ t are achieved in the spatial averaging entropy generation of RT mixing process, respectively.

Numerical Investigation of Flow Characteristics in the Obstructed Realistic Human Upper Airway.

The flow characteristics in the realistic human upper airway (HUA) with obstruction that resulted from pharyngeal collapse were numerically investigated. The 3D anatomically accurate HUA model was reconstructed from CT-scan images of a Chinese male patient (38 years, BMI 25.7). The computational fluid dynamics (CFD) with the large eddy simulation (LES) method was applied to simulate the airflow dynamics within the HUA model in both inspiration and expiration processes. The laser Doppler anemometry (LDA) technique was simultaneously adopted to measure the airflow fields in the HUA model for the purpose of testifying the reliability of LES approach. In the simulations, the representative respiration intensities of 16.8 L/min (slight breathing), 30 L/min (moderate breathing), and 60 L/min (severe breathing) were conducted under continuous inspiration and expiration conditions. The airflow velocity field and static pressure field were obtained and discussed in detail. The results indicated the airflow experiences unsteady transitional/turbulent flow in the HUA model under low Reynolds number. The airflow fields cause occurrence of forceful injection phenomenon due to the narrowing of pharynx caused by the respiratory illness in inspiration and expiration. There also exist strong flow separation and back flow inside obstructed HUA owing to the vigorous jet flow effect in the pharynx. The present results would provide theoretical guidance for the treatment of obstructive respiratory disease.