Scalar Transport Equation Research Articles

Numerical Investigation of Two-Phase Shock Waves in CO2 Flows Using a Modified Hertz–Knudsen Model

Abstract Understanding the complex behavior of two-phase shocks in CO2 flows is essential for a variety of applications, including carbon capture and storage () and transcritical refrigeration cycles. This study presents a comprehensive numerical investigation of two-phase shock waves using the multispecies user-defined real gas model in Ansys Fluent. The simulations are performed for de-Laval nozzles, exploring the two-phase shock features for three-dimensional (3D), two-dimensional (2D), and two-dimensional axisymmetric geometries. The nonequilibrium condensation, subsequent evaporation, and denucleation occurring across the shock are modeled through a set of user-defined scalar transport equations implemented within Ansys Fluent. The two-phase computational fluid dynamics (CFD) simulations are carried out in proximity to the critical point where real gas effects are relevant. The CO2 real gas properties are computed using an in-house Python code and integrated into the solver via user-defined functions as external look-up tables. This study provides valuable insights into the physical processes underlying two-phase shocks in CO2 flows and their sensitivity to geometric variations and thermodynamic conditions. The findings contribute to the development and modification of predictive models and optimized designs for systems involving two-phase CO2 flows. The results highlight the influence of geometry configurations and thermodynamic conditions on shock location and intensity, providing comparisons for shock waves occurring in two-phase flows and supercritical single-phase flows.

A modified model based on CFD simulation and experiments of chalcopyrite flotation

The increasing attention to enhancing flotation performance in strong turbulent environment has become a focal point in research and practical applications. To predict turbulent flotation process, Computational Fluid Dynamics (CFD) simulations and flotation experiments were investigated on pure chalcopyrite in both smooth and vortex generator (VG) mineralized tubes. These investigations aimed to analyze flotation kinetics and flotation rate constant under conditions of 0.4–0.7 m3/h slurry flow rate and 0–45 μm, 45–75 μm, 75–125 μm, 125–180 μm particle classes. In the simulation, the user-defined functions (UDFs) and user-defined scalar (UDS) transport equations were used to model the collision, attachment and detachment of bubble-particle, thereby predicting the flotation rate constant. The results showed that the existing flotation kinetic model exhibited unsatisfactory prediction at various particle class and slurry flow rate. It was attributed to the insufficient consideration of turbulence in attachment model. Finally, a modified attachment model adopting a back-calculated method was proposed. This model predicted the flotation rate constant and its trends with changes in slurry flow rate, and the average prediction error is within 26 %. External validation of the model using pure mineral cassiterite demonstrated a prediction error of only 12 %.

Effect of flow modifiers on the fluid flow characteristics in a slab caster tundish

ABSTRACT In a slab caster tundish, controlling liquid steel flow is of paramount importance for clean steel production. A conventional tundish design consists of a pouring box, a weir and a dam. To improve the overall performance of a 40 ton slab caster tundish, three different arrangements by incorporating additional flow modifiers have been examined. A three-dimensional steady state fluid flow model has been developed using a RANS (Reynolds-Averaged Navier-Stokes) approach. Subsequently, transient scalar-transport equations were solved to obtain the C-curve of the tundish. A different approach has been followed to evaluate the inlet boundary condition to mimic the process conditions more accurately. The CFD predictions were validated with the results of the water model. Mean residence time, dead volume fraction and flow structures have been considered for evaluating tundish performance. All the proposed configurations have shown improvements in comparison to the base case. The mean residence time of the fluid was found to be the highest for the case having two pairs of weir and dam. However, the insights derived from the flow structures specifically plug flow in zone 2 and near the tundish outlet region suggest that that having a single weir and two dams is the optimal choice.

CFD Modeling of Aerosol Transport and Deposition Using a Drift-Flux Model

Aerosol transport and deposition are important processes in modeling of accident scenarios for a small modular reactor. An aerosol drift-flux model is attractive because it is computationally less expensive than Lagrangian particle tracking. It must be determined, however, how well it performs when implemented in a commercial computational fluid dynamics (CFD) code. This work presents results of modeling aerosol transport and deposition using a full Eulerian three-dimensional drift-flux model implemented in the commercial CFD code STAR-CCM+. The forces due to gravity and thermophoresis are included in the present drift-flux model along with Brownian motion and turbulent diffusion. The forces are added as a source term to a passive scalar transport equation. In addition, a drift velocity representing the forces is used in a built-in electrochemical species transport equation. The results of these two approaches are compared. An appropriate deposition velocity is used to calculate the aerosol concentration deposited on surfaces. The semiempirical relation proposed by Lai and Nazaroff (2000) is used to compute the deposition velocity due to gravitational settling, and the present results are compared with the experimental and numerical data obtained from the work of Chen et al. (2006). It was found that the concentration profile obtained from the present drift-flux model showed reasonable agreement with the literature data. A thermophoresis model showed good agreement when compared with the analytical solution of Nazaroff and Cass (1987). In addition to the particle concentration results, this work presents details of the drift-flux model implementation and the bulk flows. These extra details will enable comparisons by others developing similar models.

Reduction of Taylor dispersion in a capillary by spin-up flow—Theoretical insights

We have developed a theoretical framework to characterize the transport and mixing of a passive scalar in a capillary tube. In this configuration, a suspension of magnetic nanoparticles undergoes Poiseuille flow, while a rotating magnetic field is applied around the tube’s revolution axis, inducing a secondary flow in the azimuthal direction. This secondary flow facilitates the mitigation of concentration gradients and radial dispersion associated with the axial parabolic Poiseuille profile. The improvement in mixing is emphasized by a new dimensionless parameter, the mixing factor, which is incorporated into the scalar transport equation. Such a factor acts as a quantitative measure of the effect of the tangential motion induced by the spin-up flow on the overall mixing efficiency of the liquid and the observed reduction of the Taylor dispersion in the measured residence time distributions. Recognizing the mixing factor as a crucial parameter advances our understanding of the mechanisms governing scalar transport and provides a valuable tool for predicting and optimizing mixing in laminar capillary flows subjected to spin-up motion.

A finite element framework for fluid–structure interaction of turbulent cavitating flows with flexible structures

We present a finite element framework for the numerical prediction of cavitating turbulent flows interacting with flexible structures. The vapor–fluid phases are captured through a homogeneous mixture model, with a scalar transport equation governing the spatio-temporal evolution of cavitation dynamics. High-density gradients in the two-phase cavitating flow motivate the use of a positivity-preserving Petrov–Galerkin stabilization method in the variational framework. A mass transfer source term introduces local compressibility effects arising as a consequence of phase change. The turbulent fluid flow is modeled through a dynamic subgrid-scale method for large eddy simulations. The flexible structure is represented by a set of eigenmodes, obtained through a modal decomposition of the linear elasticity equations. While a partitioned iterative approach is adopted to couple the structural dynamics and cavitating fluid flow, the deforming flow domain is described by an arbitrary Lagrangian–Eulerian frame of reference. We establish the fidelity of the proposed framework by comparing it against experimental and numerical studies for both rigid and flexible hydrofoils in cavitating flows. Under unstable partial cavitating conditions, we identify specific vortical structures leading to cloud cavity collapse. We further explore features of cavitating flow past a rigid body such as re-entrant jet and turbulence-cavity interactions during cloud cavity collapse. Based on the validation study conducted over a flexible NACA66 rectangular hydrofoil, we elucidate the role of cavity and vortex shedding in governing the structural dynamics. Subsequently, we identify a broad spectrum frequency band whose central peak does not correlate to the frequency content of the cavitation dynamics or the natural frequencies of the structure, indicating the induction of unsteady flow patterns around the hydrofoil. Finally, we discuss the coupled fluid–structure dynamics during a cavitation cycle and the underlying mechanism associated with the promotion and mitigation of cavitation.

Bubble dynamics under the influence of the Marangoni force induced by a stratified field of contamination

The Marangoni effect assumes significance in bubbly flows when temperature or concentration gradients exist in the domain. This study investigated the hydrodynamics of single bubbles under the influence of the Marangoni force induced by stratified fields of dissolved sugar, providing a numerical framework for examining these phenomena. A laboratory-scale bubble column and high-speed imaging were utilized to analyze the bubble behavior. The OpenFOAM-based geometric volume of the fluid solver was extended by incorporating the solutocapillary Marangoni effect, and a passive scalar transport equation for the sugar concentration was solved. The results revealed that small bubbles entering regions with elevated sugar concentrations experienced deceleration, transitioning into linear paths, while those departing from regions with high sugar concentrations exhibited fluctuations and meandering. Furthermore, the concentration gradient leads larger bubbles to meander throughout the entire column, without a notable increase in their velocity. The intensity of these behaviors is governed by the magnitude of the Marangoni force. The findings provide a better understanding of single bubble hydrodynamics in complex environments.

Taylor–Couette flow and heat transfer in an elliptical enclosure with a rotating inner cylinder

We numerically investigate Taylor–Couette flows within a system consisting of an elliptical outer cylinder and a rotating inner circular cylinder, with particular emphasis on the behavior of Taylor cells. The three-dimensional unsteady Navier–Stokes equations are solved under the assumption of axial periodicity. Also, a scalar transport equation is solved for the heat transfer. Our methodology employs a Fourier-spectral meshless discretization technique, which interpolates variables at scattered points using polyharmonic splines and appended polynomials. A pressure-projection algorithm achieves the time advancement of the flow equations. We present findings for an elliptical enclosure with an aspect ratio of two, examining a range of Reynolds numbers (Re) from subcritical to 300. Our analysis includes streamlines, axial velocity contours, pressure, vorticity, and temperature profiles. The results indicate that the flow remains steady up to Re≈300 before transitioning to an unsteady state at Re≈350.

Hybrid large eddy simulation and Lagrangian simulation of a compressible turbulent planar jet with a chemical reaction

AbstractLarge eddy simulation (LES) coupled with Lagrangian particle simulation (LPS) is applied to investigate high‐speed turbulent reacting flows. Here, LES solves a velocity field while LPS solves scalar transport equations with notional particles. Although LPS does not require sub‐grid scale models for chemical source terms, molecular diffusion has to be modeled by a so‐called mixing model, for which a mixing volume model (MVM), that is originally proposed for an inert scalar in incompressible flow, is extended to reactive scalars in compressible flows. The extended model is based on a relaxation process toward the average of nearby notional particles and assumes a common mixing timescale for all species. LES/LPS with the MVM is applied to a temporally‐evolving compressible turbulent planar jet with an isothermal reaction and is tested by comparing the results with direct numerical simulation (DNS). The results show that LES/LPS well predicts the statistics of mass fractions. As the jet Mach number increases, the reaction progress delays due to the delayed jet development. This Mach number dependence is also well reproduced in LES/LPS. The mean molecular diffusion term of the product calculated as a function of its mass fraction also agrees well between LES/LPS and DNS. An important parameter for the MVM is the distance among particles, for which the requirement for accurate prediction is presented for the present test case. LES/LPS with the MVM is expected to be a promising method for investigating compressible turbulent reactive flows at a moderate computational cost.

CFD simulation of pollutant dispersion using anisotropic models: Application to an urban like environment under neutral and stable atmospheric conditions

Modeling the atmospheric dispersion of pollutants emitted from different types of sources under various atmospheric conditions is an essential prerequisite for risk assessment studies and emergency preparedness. In this study, we evaluate the performance of different turbulence models and velocity-scalar correlation models implemented in the Code_Saturne. The evaluation is done with observations of four trial cases of the Mock Urban Setting Test (MUST) campaign in an urban type environment and in neutral and stable atmospheric conditions. For all of the trials studied, the CFD model with a first-order closure model (k−ɛ) predicts 61.1% of the concentrations within a factor of two of the observations, which is higher than the percentage of predicted points (58.8%) when a second-order closure model (Rij−ɛ) is used. Overall, the CFD model underestimates observed concentrations, regardless of the turbulence model used. For the trial with slightly stable conditions, the results show that the k−ɛ model combined with an algebraic SGDH model predicts 75% concentrations within a factor of two of the observations. The performance of the k−ɛ model is compared to that of the Rij−ɛ model when used with the algebraic SGDH, GGDH models and with the scalar flux transport equation (DFM model). Under slightly stable atmospheric conditions, the DFM model predicts 69% of concentrations within a factor of two of observations, showing promise for modeling under these conditions, despite its relatively high computational cost.

Multiscale numerical modeling of a complete spray evolution including breakup of liquid jet injection in gaseous cross flow

A direct coupling of the Volume of Fluid method (VOF) and the Lagrangian Particle Tracking (LPT) technique within a Large Eddy Simulation (LES) framework is revisited and assessed by numerically investigating a liquid jet injection into a cross-flowing air (JICF). To close the subgrid scale (SGS) terms appropriate SGS models are considered. In particular, an interfacial SGS term is included into the VOF scalar transport equation in order to achieve a suitable LES and to describe properly the liquid column and the break-up processes (primary and secondary). The dilute spray region including the droplets resulting from the secondary breakup is solved using the LPT approach. Since the latter allows the cell size to be multiple times larger than the droplet diameter, this reduces the computational expenses significantly making it possible to handle the simulation of the whole spray evolution including the complete liquid atomization without complex tunable atomization models. For this purpose, two operating conditions of a JICF existing in the literature are considered. The achieved results are first presented in terms of mesh sensitivity, required computational costs and impact of the interfacial SGS term. Next, comparisons between pure VOF/LES and VOF/LPT/LES for both qualitative features and quantitative properties are provided and discussed. In overall, a good agreement with experiments for the quantitative properties is reported. It is especially found that both the Rosin–Rammler and Gaussian distributions offer nearly a more accurate fit to the particle size distribution except for the range from 0 to 10 μm. Together with the detailed characteristics of vortices evolving and an extended breakup regime map, the spray characteristics including the spray structure are well captured. Finally, even though the interfacial SGS term has an evident influence on the jet and atomization dynamics, its impact on quantitative properties is not so prominent under these operating conditions.

Tamed stability of finite difference schemes for the transport equation on the half-line

In this paper, we prove that, under precise spectral assumptions, some finite difference approximations of scalar leftgoing transport equations on the positive half-line with numerical boundary conditions are ℓ 1 \ell ^1 -stable but ℓ q \ell ^q -unstable for any q > 1 q>1 . The proof relies on the accurate description of the Green’s function for a particular family of finite rank perturbations of Toeplitz operators whose essential spectrum belongs to the closed unit disk and with a simple eigenvalue of modulus 1 1 embedded into the essential spectrum.

High-Fidelity Computational Assessment of Aero-Thermal Performance and the Reynolds’ Analogy for Additively Manufactured Anisotropic Surface Roughness

Abstract Direct numerical simulations of incompressible turbulent forced convection over irregular, anisotropic surface roughness in a pressure-driven plane channel flow have been performed. Heat transfer was simulated by solving the passive scalar transport equation with Prandtl number Pr = 0.7. The roughness topographies under investigation here are based on an X-ray computed tomography scan of an additively manufactured internal cooling passage, which had an irregular, multiscale and mildly non-Gaussian height distribution. Three different roughness topographies and three different friction Reynolds numbers (Reτ = 395, 590, 720) were considered, along with reference smooth-wall simulations at matched Reτ. By systematically varying the roughness topography and flow conditions, a direct computational assessment of aero-thermal performance (pressure losses and heat transfer) and the Reynolds analogy factor, i.e., 2Ch/Cf, where Ch is the heat-transfer coefficient (Stanton number) and Cf is the skin-friction coefficient, was conducted. The results highlight the profound impact that the roughness orientation (relative to the flow direction) has upon the aero-thermal performance of additively manufactured internal passages, with transverse-aligned roughness augmenting heat transfer by as much as 33%, relative to its streamwise-aligned counterpart. An interrogation of velocity and temperature statistics in the near-wall region was also performed, which underlined the growing dissimilarity between heat transfer and drag as fully rough conditions are approached.

Impact of external turbulence on film cooling designs using large eddy simulations

Large Eddy Simulations (LES) of film cooling flows were conducted to investigate the impact of high turbulence intensity in the main flow, representative of jet-engine combustor conditions. A comparison was made with LES simulations at zero turbulence at the main flow inlet boundary. The study investigated three different film cooling configurations, which involved cylindrical holes and two variations with holes embedded in trenches known as transverse and segmented trench. Different momentum ratios (I=3.5 and 8.3) relevant to combustor flows in jet-engines were applied. The LES simulations utilized OpenFOAM and solved the energy and passive scalar transport equations to determine film cooling efficiency (η), heat transfer coefficient (hf), and net heat flux reduction (NHFR). The numerical results were validated through comparison with experimental data. The mean and instantaneous results revealed that high turbulence intensity in the main flow significantly influenced film cooling performance. The film cooling efficiency was found to decrease with increased turbulence intensity, while for the ordinary film cooling design exhibiting jet lift-off, the increased mixing led to higher η. The heat transfer coefficient increased with turbulence intensity and momentum ratio, with turbulence intensity having a greater impact on ordinary designs and momentum ratio on trenched designs. Moreover, increasing turbulence intensity or momentum ratio resulted in lower NHFR for all designs. Hot spots were observed in the instantaneous results, with spatial variations depending on the film cooling design.

Statistical Behaviour and Modelling of Variances of Reaction Progress Variable and Temperature During Flame-Wall Interaction of Premixed Flames Within Turbulent Boundary Layers

The statistical behaviour of the transport of reaction progress variable variance, c″2~,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{{c^{^{\\prime\\prime}2} }},$$\\end{document} and non-dimensional temperature variance, T″2~,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{{T^{^{\\prime\\prime}2} }},$$\\end{document} have been analysed using three-dimensional Direct Numerical Simulation (DNS) data of turbulent premixed flame-wall interaction with isothermal inert walls within turbulent boundary layers for (i) an unsteady head-on quenching of a statistically planar flame propagating across the boundary layer, and (ii) a statistically stationary oblique wall quenching of a V-flame. It has been found that the reaction rate contribution acts as a leading order source term to the transport of both reaction progress variable variance, c″2~,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{{c^{^{\\prime\\prime}2} }},$$\\end{document} and non-dimensional temperature variance, T″2~,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{{T^{^{\\prime\\prime}2} }},$$\\end{document} whereas the molecular dissipation term remains the leading order sink term for both configurations analysed here. With the progress of flame wall interaction, the magnitude of all the source terms for the transport equations of both reaction progress variable and non-dimensional temperature variances vanish in the near-wall region with the onset of flame quenching. However, the molecular dissipation term continues to act as a sink term. The performances of the existing models for turbulent scalar flux, reaction rate and scalar dissipation rate contributions have been assessed for both flame-wall interaction configurations based on a priori DNS analysis. The existing available models for scalar dissipation rate for temperature and the reaction rate contribution in the variance transport equations even with the previously proposed wall corrections do not adequately predict the behaviour in the near-wall region. Modifications have been suggested to the existing closure models for the scalar dissipation rate and the reaction rate contribution to the scalar variance transport equations to improve the predictions in the near-wall region. Furthermore, the recommended closures for the unclosed terms of both reaction progress variable variance, c″2~,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{{c^{^{\\prime\\prime}2} }},$$\\end{document} and non-dimensional temperature variance, T″2~,\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\widetilde{{T^{^{\\prime\\prime}2} }},$$\\end{document} are shown to accurately capture the corresponding variations obtained from DNS data for both near to and away from the wall.

A Lattice-Boltzmann-based modelling chain for traffic-related atmospheric pollutant dispersion at the local urban scale

Urban traffic-related air pollution is a major source of environmental and health damage and is difficult to quantify due to its inherent physical complexity. We construct a CFD-based simulation framework coupling an efficient numerical method for turbulent fluid flows with a microscopic traffic model and an emissions model to simulate road transport pollutant dispersion at the urban microscale. We improve the open-source Lattice-Boltzmann based CFD software OpenLB to overcome its original stability deficiencies for high Reynolds number flows. A stable recursive regularization procedure with a double distribution function approach is proposed to solve an advection diffusion equation for passive scalar transport at high Reynolds number. The code is successfully validated on three reference cases of increasing complexity and the traffic model SUMO along with a physical engine emissions model are coupled with OpenLB to simulate traffic-induced pollution from a road network in a realistic complex geometry. Transient flow features are analysed and the time-averaged concentration levels in different neighbourhoods of the considered geometry are evaluated: high concentration levels are observed close to the streets but also inside specific building infrastructures due to complex wind dynamics. Analyses of altitudinal concentration variations show that flow recirculations located close to traffic lights can drive pollutant over the buildings and increase concentration levels inside inner courtyards. Time-averaged concentration maps are constructed using both spatially uniform and non-uniform line sources and it is shown that using uniform sources leads to up to 20% local concentration overestimations inside the urban canopy.

A novel well‐balanced numerical model for water‐solute mixture underflows coupled with ambient water

AbstractThis study considers a water‐solute mixture underflow coupled with ambient water. Such physical phenomenons are modelled by a two‐layer stratified Saint‐Venant system with a scalar transport equation in this paper. The governing system is first relaxed to a hyperbolic system discretized by a path‐conservative algorithm. In such framework, a novel discrete formula of nonconservative and source terms, is proposed to be able to guarantee the well‐balanced property for the hydrodynamic model and preserve the uniform concentration in underflows, especially at wet‐dry fronts. The performances of the developed numerical schemes are verified by several tests.

Practical implications of the erroneous treatment of exposure time in the Eulerian hemolysis power law model.

Eulerian and Lagrangian power-law formulations are both widely used for computational fluid dynamics (CFD) to predict flow-induced hemolysis in blood-contacting medical devices. Both are based on the same empirical power-law correlation between hemolysis and the shear stress and exposure time. In the Lagrangian approach, blood damage is predicted by tracking both the stress and exposure time along a finite number of pathlines in the domain. In the Eulerian approach, a scalar transport equation is solved for a time-linearized damage index within the entire domain. Previous analytical work has demonstrated that there is a fundamental problem with the treatment of exposure time in the Eulerian model formulation such that the only condition under which the model correctly represents the true exposure time is in a flow field with no streamwise velocity variation. However, the practical implications of this limitation have yet to be thoroughly investigated. In this study, we demonstrate the inaccuracy of Eulerian hemolysis power-law model predictions due to the erroneous treatment of exposure time by systematically considering four benchmark test cases with increasing degrees of flow acceleration: Poiseuille flow through a straight tube, inclined Couette flow, and flow through a converging tube with two different convergence ratios. Compared with Lagrangian predictions, we show that, as flow acceleration becomes more pronounced, the resultant inaccuracy in the Eulerian predictions increases. For the inclined Couette flow case, there is a small degree of flow acceleration that yields a discrepancy in the range of 10% between Lagrangian and Eulerian predictions. For flows with a larger degree of acceleration, as occurs in the converging tube flow cases, the discrepancy is considerably larger (up to 257%). The inaccuracy of hemolysis predictions due to the erroneous treatment of exposure time in the Eulerian power-law model can be significant when there is streamwise velocity variation in the flow field. These results may partially explain the extremely large variability in CFD hemolysis predictions reported in the literature between Lagrangian and Eulerian models.

Investigation of Inlet Conditions in The Mixing Process of Nanoparticles and Blood in a T-Shaped Microfluidic Reactor with Small Rectangular Cavities.

During the metastasis of cancer cells, circulating tumor cells (CTCs) are released from the primary tumor, reach the bloodstream, and colonize new organs. A potential reduction of metastasis may be accomplished through the use of nanoparticles in micromixers in order to capture the CTCs that circulates in blood. In the present study, the effective mixing of nanoparticles and the blood that carries the CTCs are investigated. The mixing procedure was studied under various inlet velocity ratios and several T-shaped micromixer geometries with rectangular cavities by using computational fluid dynamics techniques. The Navier-Stokes equations were solved for the blood flow; the discrete motion of particles is evaluated by a Lagrangian method while the diffusion of blood substances is studied by using a scalar transport equation. Results showed that as the velocity ratio between the inlet streams increases, the mixing rate of nanoparticles with the blood flow is increased. Moreover, nanoparticles are uniformly distributed across the mixing channel while their concentration is decreased along the channel. Furthermore, the evolution in time of the blood substances in the mixing channel increases with the increase of the velocity ratio between the two streams. On the other hand, the concentration of both the blood substances and the nanoparticles is decreased in the mixing channel as the velocity ratio increases. Finally, the differences in the dimensions of the rectangular cavities seems to have an insignificant effect both in the evolution in time of the blood substances and the concentration of nanoparticles in the mixing channel.

A low-dissipative and accurate method of simulating the unsteady mixing process

Micro/milli-reactors have been widely used because of their advantages, e.g., intrinsic safety, fast heat transfer and exquisite control of the reaction conditions. However, the mixing efficiency in microreactors is often limited by slow molecular diffusion in steady laminar flow. The mixing efficiency is higher in the unsteady state, but the lack of an accurate simulation method for unsteady mixing limits the development of highly efficient mixers. Thus, this work establishes a new method to precisely simulate the unsteady mixing process, without being affected by numerical diffusion, based on the Lagrangian scalar transport equation. The method is validated by experimental results. Sensitivity analyses are conducted to confirm the simulation results. The accurate simulation of the mixing process will reduce the number of experiments, hence accelerating the development of highly efficient mixers.