H. T. Low

Dynamic motion of red blood cells in simple shear flow

A three-dimensional numerical model is proposed to simulate the dynamic motion of red blood cells (RBCs) in simple shear flow. The RBCs are approximated by ghost cells consisting of Newtonian liquid drops enclosed by Skalak membranes which take into account the membrane shear elasticity and the membrane area incompressibility. The RBCs have an initially biconcave discoid resting shape, and the internal liquid is assumed to have the same physical properties as the matrix fluid. The simulation is based on a hybrid method, in which the immersed boundary concept is introduced into the framework of the lattice Boltzmann method, and a finite element model is incorporated to obtain the forces acting on the nodes of the cell membrane which is discretized into flat triangular elements. The dynamic motion of RBCs is investigated in simple shear flow under a broad range of shear rates. At large shear rates, the cells are found to carry out a swinging motion, in which periodic inclination oscillation and shape deform...

Free Convection in a Porous Wavy Cavity Based on the Darcy-Brinkman-Forchheimer Extended Model

A numerical investigation is carried out for steady, free convection inside a cavity filled with a porous medium. The cavity has vertical wavy walls which are isothermal. The top and bottom horizontal straight walls are kept adiabatic. The numerical method is based on the finite-volume method with body-fitted and nonorthogonal grids. A generalized model, which includes a Brinkman term, a Forcheimmer term, and a nonlinear convective term, is used. Studies are carried out for a range of wave ratio λ = 0 − 1.8, aspect ratio A = 1–5, Darcy number Da = 10−1–10−6, and Darcy-Rayleigh number Ra* = 10–105. Results are presented in the form of streamlines, isotherms, and local and average Nusselt numbers. The generalized model which considers viscous, inertia, and convective effects enables results to be obtained for a wider range of Darcy and Rayleigh numbers.

A LATTICE BOLTZMANN STUDY ON THE LARGE DEFORMATION OF RED BLOOD CELLS IN SHEAR FLOW

The transient deformation of a liquid-filled elastic capsule, simulating a red blood cell, was studied in simple shear flow. The simulation is based on a hybrid method which introduces the immersed boundary concept in the framework of the multi-block lattice Boltzmann model. The method was validated by the study on deformation of an initially circular capsule with Hookes membrane. Also studied were capsules with Skalak membrane of initially elliptical and biconcave shapes, which are more representative of a red blood cell. Membrane tank treading motion is observed. As the ratio between membrane dilation modulus and shear modulus increases, the capsule shows asymptotic behavior. For an initially elliptical capsule, it is found that the steady shape is independent of initial inclination angle. For an initially biconcave capsule, the tank treading frequency from two-dimensional modeling is comparable to that of real cells. Another interesting finding is that the tank treading velocity has not attained steady state when the capsule shape becomes steady; and at this state there is the internal vortex pair. The treading velocity continues to decrease and reaches a steady value when the internal vortex pair has developed into a single vortex.

Characterization of flow behavior in an enclosed cylinder with a partially rotating end wall

The vortex breakdown phenomena in an enclosed cylindrical chamber with a rotating disk whose radius is smaller than that of the chamber were investigated by a numerical model based on the steady, axisymmetric Navier-Stokes equations. The flow behaviors were investigated over a wide range of parameters. The main recirculation region remains unchanged if the cylinder-to-disk ratio, the ratio of the chamber radius to the disk radius, is beyond the recirculation-invariance ratio. The recirculation-invariance ratio displays a generally linear relationship with the vertical ratio, the ratio of the chamber height to disk radius. The trends of the vortex breakdown boundary curves at different cylinder-to-disk ratios suggest that three regions, namely the quasi whole end-wall rotating region, the vortex-breakdown boundary invariance region, and the mixed region, can be used to characterize the occurrence of vortex breakdown. Depending on the specific conditions, the presence of the stationary end wall either serve...

An Efficient and Robust Numerical Scheme for the SIMPLER Algorithm on Non-Orthogonal Curvilinear Coordinates: CLEARER

In this article, an Improved SIMPLER (CLEARER) algorithm is formulated to solve the incompressible fluid flow and heat transfer on the nonstaggered, nonorthogonal curvilinear grid system. By virtue of a modified momentum interpolation method in calculating the interface contravariant velocity in both the predictor step and the corrector step, the coupling between pressure and velocity is fully guaranteed, and the conservation law is also satisfied. A second relaxation factor is introduced in the corrector step, of which the convergent solution is independent. By setting the second relaxation factor less than the underrelaxation factor for the velocity to some extent, both the convergence rate and robustness can be greatly enhanced. Meanwhile, the CLEARER algorithm can also overcome the severe grid nonorthogonality. With the simplified pressure-correction equation, the convergent solution can still be obtained even when the intersection angle among grid lines is as low as 1°, which may provide valuable guidance in studying the fluid flow in complex geometries.

Numerical Analysis of Periodically Developed Fluid Flow and Heat Transfer Characteristics in the Triangular Wavy Fin-and-Tube Heat Exchanger Based on Field Synergy Principle

In this article the three-dimensional periodically developed incompressible flow in the triangular wavy fin-and-tube heat exchanger is numerically simulated. A novel CLEARER algorithm is adopted to guarantee the coupling between the pressure and velocity, and it can also overcome the severe grid non-orthogonality in the complex wavy fin-and-tube heat exchanger. The influence of wavy angle, fin pitch, tube diameter, and wavy density on pressure drop and heat transfer characteristics is provided under different Reynolds numbers. The numerical results show that with the increase of wavy angle, tube diameter, or wavy density both the friction factor and Colburn factor will increase, while the increase rate of friction factor is higher than that of the Colburn factor. Opposite to the wavy fin-and-tube heat exchanger with uniform inlet velocity distribution, the wavy fin-and-tube heat exchanger with periodically developed flow owns a higher Colburn factor at larger fin pitch. The influence of wavy angle, fin pitch, tube diameter, and wavy density on the heat transfer performance can all be explained well from the viewpoint of the field synergy principle, and it means that the higher Colburn factor can be attributed to the better synergy between the velocity field and temperature field. Those results may provide an insight into the heat transfer enhancement in the wavy fin-and-tube heat exchanger.

Numerical studies of physiological pulsatile flow through constricted tube

A detailed analysis on the characteristics of laminar flow over a bell‐shaped stenosis for a physiological pulsatile flow is presented in this study. In order to have a good understanding of the physiological pulsatile flow, a comparison of the numerical solutions to three types of pulsatile flows, including a physiological flow, an equivalent pulsatile flow and a pure sinusoidal flow, are made in this work. The comparison shows that the flow behavior cannot be properly estimated if the equivalent or simple pulsatile inlet flow is used in the study of flow fields through stenosed arteries instead of actual physiological one. Then the physiological pulsatile flow is further studied by considering the effect of constriction ratio of stenosis, Womersley number and Reynolds number on the flow behavior through stenosed arteries. The analysis shows that the variation of these flow parameters puts significant impacts on the pulsatile flow field for the physiological flow.

Forced Convection Over a Backward-Facing Step with a Porous Floor Segment

Forced convection after a backward-facing step, with a porous floor segment, is investigated numerically using the SIMPEC method. The Brinkman-Forcheimmer extended model is used to govern the flow in the porous-medium region. At the interface, the flow boundary condition imposed is a shear stress jump, which includes the inertial effect, together with a continuity of normal stress. The thermal interfacial condition is continuities of temperature and heat flux. Results are presented for Reynolds number up to 800 and Darcy number up to 10−1. Also varied are the length and depth of the porous segment. Compared with the case with no porous floor, the local heat transfer is augmented after the porous floor. Within the porous floor, the heat transfer is reduced, but this may be offset by using a porous medium of higher conductivity than the fluid. To obtain good heat enhancement after the porous segment, it should approximately match the length of the recirculation region. The porous segment should have large permeability (Darcy number around 10−1), but it is not necessary that it be of great depth. The interfacial stress jump coefficients β and β 1 are varied from − 5 to + 5, and some effects are observed on the local Nusselt numbers, velocity profile, and temperature distribution.

Pressure/flow behaviour in collapsible tube subjected to forced downstream pressure fluctuations

An experimental investigation has been made into the pressure/flow behaviour of a collapsible tube subjected to downstream pressure fluctuations. These downstream pressure waves are observed to be transmitted upstream beyond the point of collapse. The mean flow rate is not significantly affected by the amplitude or frequency of pressure fluctuations. However, the oscillatory flow amplitude is reduced at the higher frequency. The mean flow rate also remains independent of the mean driving pressure.

Dynamics of simultaneously impinging drops on a dry surface: Role of impact velocity and air inertia.

Three dimensional simulations are performed to investigate the interaction dynamics between two drops impinging simultaneously on a dry surface. Of particular interest in this study is to understand the effects of impact velocity and surrounding gas density on droplet interactions. To simulate the droplet dynamics and morphologies, a computational framework based on the phase-field lattice Boltzmann formulation is employed for the two-phase flow computations involving high density ratio. Two different coalescence modes are identified when the impinging droplets have different impact speeds. When one of the droplet has a tangential impact velocity component, asymmetric ridge formation is observed. Influence of droplet impact angle on the interaction dynamics of the central ridge is further investigated. Traces of different fluid particles are seeded to analyse internal flow dynamics in oblique impact scenarios. Greater overlapping between the fluid particles is observed with increase in the impact angle. Finally, the present simulations indicate that the ambient gas density has a significant influence to determine the final outcome of the droplet interactions.