平行平板层流动力进口段问题的一种近似解法

本文用求解微分方程和积分方程相结合的方法求得了平行平板层流动力进口段在定常、不可压条件下的进口段长度、主流速度、排挤厚度、动量排挤厚度和壁面摩擦力等的理论解。     

An investigation of turbulent accelerated flow along smooth prismatic chutes

Turbulent chute flow was investigated experimentally and numerically for various flow conditions. The Navier‐Stokes equations are solved with the k ? ε turbulence model on a structured non‐orthogonal grid. A method based on water continuity was used to calculate the movement of the water surface. Using an adaptive grid in the vertical direction, the location of the water surface was recalculated from an initially horizontal profile. After several iterations a steady solution emerged. The velocity distribution in longitudinal and vertical directions and pressure distribution along the chute were calculated. The numerical model was calibrated and verified using experimental data model studies. Reasonable agreement was found between the experimental results and that from the numerical model. Multiple‐regression equation was developed for computing the water surface profile along chute.     

Wind tunnel velocity profiles generated by differentially-spaced flat plates

Production of linear shear with low turbulence level in a wind tunnel provides a convenient environment for testing the results of computational fluid dynamics simulations and equipment calibration. Boundary layer flow over a flat plate at zero incidence provides controlled deceleration of the approach flow according to plate length, with interacting boundary layers between adjoining flat plates merging to provide fully developed duct flow. In this way, an array of differentially-spaced flat plates can be used to modify a uniform wind tunnel velocity field to a specified velocity profile. A one-step iterative scheme is offered to determine plate spacings for simulation of weakly sheared flows, constrained by zero vertical pressure gradient in the downstream flow (representative of boundary layer conditions). The scheme is tested for realisation of uniform shear flow (maximum velocity variation ±10% of centreline velocity) by wind tunnel simulation, and produces reasonable results, at least comparable with previous studies.     

Boundary layer flow of nanofluids to analyse the heat absorption/generation over a stretching sheet with variable suction/injection in the presence of viscous dissipation

ABSTRACT

In this investigation, the heat and mass transfer characteristics in boundary layer flow about a stretching sheet in a porous medium filled with TiO₂ – water and Al₂O₃ – water-based nanofluids, in the presence of internal heat generation or absorption and viscous dissipation with variable suction or injection effects is numerically studied. The similarity transformations are used to transform the governing boundary layer equations for momentum, energy and species transfer into a set of non-linear ordinary differential equations which are solved numerically by Keller-box method. The obtained numerical results are validated against results computed by using MATLAB bvp4c routine, and excellent agreement is observed. The impact of various pertinent parameters on velocity, temperature and concentration as well as the friction factor coefficient, local heat and mass transfer rates are derived and discussed through graphs and tables for TiO₂ and Al₂O₃ water-based nanofluids. The present study reveals that an increase in Eckert number (Ec) and heat generation/absorption parameter (Q) significantly decreases local heat transfer rate.     

A numerical study on differences in using Navier–Stokes and Reynolds equations for modeling the fluid flow and particle transport in single rock fractures with shear

The study on fluid flow and transport processes of rock fractures in most practical applications involves two fundamental issues: the validity of Reynolds equation for fluid flow (as most often assumed) and the effects of shear displacements on the magnitudes and anisotropy of the fluid flow velocity field. The reason for such concerns is that the impact of the surface roughness of rock fractures is still an unresolved challenging issue. The later has been systematically investigated with results showing that shear displacement plays a dominant role on evolutions of fluid velocity fields, for both magnitudes and anisotropy, but the former has not received examinations in details due to the numerical complexities involving solution of the Navier–Stokes (NS) equations and the representations of fracture geometry during shear. The objective of this paper aims to solve this problem through a FEM modeling effort.Applying the COMSOL Multiphysics code (FEM) and assuming a 2D problem, we consider the coupled hydromechanical effect of fracture geometry change due to shear on fluid flow (velocity patterns) and particle transport (streamline/velocity dispersion), using measured topographical data of natural rock fracture surfaces. The fluid flow in the vertical 2D cross-sections of single rock fractures was simulated by solving both the Navier–Stokes and the Reynolds equation, and the particle transport was predicted by the streamline particle tracking method with calculated flow velocity fields (vectors) from the flow simulations, obtaining results such as flow velocity profiles, total flow rates, particle travel time, breakthrough curves and the Péclet number, Pe, respectively.The results obtained using NS and Reynolds equations were compared to illustrate the degree of the validity of the Reynolds equation for general applications in practice since the later is mush more computationally efficient for solving large-scale problems.The flow simulation results show that both the total flow rate and the flow velocity fields in a rough rock fracture predicted by the NS equation were quite different from those predicted by the Reynolds equation. The results show that a roughly 5–10% overestimation on the flow rate is produced when the Reynolds equation is used, and the ideal parabolic velocity profiles defined by the local cubic law, when Reynolds equation is used, is no longer valid, especially when the roughness feature of the fracture surfaces changes with shear. These deviations of flow rate and flow velocity profiles across the fracture aperture have a significant impact on the particle transport behavior and the associated properties, such as the travel time and Péclet number. The deviations increase with increasing flow velocity and become more significant when fracture aperture geometry changes with shear.     

Reply to Discussion on “Analysis of Bingham fluid radial flow in smooth fractures”

Recently, Hoang et al. (2021) discussed our paper Zou et al. (2020). In our paper, we made a statement that Dai and Bird (1981)'s solution for two-dimensional (2D) radial Bingham fluid flow between parallel plates violates mass balance. Hoang et al. pointed out that Dai and Bird (1981)'s solution does not violate the mass balance because Dai and Bird (1981)'s solution and our analysis are based on different assumptions, i.e. with consideration of the vertical velocity component in the continuity equation or not, which leads to two different approximation models. In this sense, the mass balance of Dai and Bird (1981)'s solution should not be checked using our solution as a reference. In this reply, we add remarks on the two approximation models and their implication for rock grouting analysis. The discussion by Hoang et al. and this reply are helpful to thoroughly eliminate the existing confusion regarding the two solutions in the rock grouting research community.     

Influence of biofilm on the transport of fullerene (C60) nanoparticles in porous media

The significance of biofilm on fullerene C₆₀ nanoparticles transport and deposition were examined both in porous media and quartz crystal microbalance with dissipation (QCM-D) systems under a variety of environmentally relevant ionic strength (1-25 mM in NaCl and 0.1-5 mM in CaCl₂) and flow conditions (4-8 m day⁻¹). The magnitudes of deposition rate coefficients (k_d) were compared between porous media with and without biofilm extracellular polymeric substances (EPS) coating under equivalent fluid velocities and solution chemistries. The observed k_d were greater in porous media with biofilm EPS coating relative to those without biofilm EPS coating across the entire solution ionic strengths and fluid velocities examined, demonstrating that the enhancement of C₆₀ deposition by the biofilm EPS coating is relevant to a wide range of environmental conditions. This greater deposition was also observed on silica surfaces with biofilm EPS coating in QCM-D system. The results clearly showed that biofilm EPS have a great influence on C₆₀ deposition. Derjaguin-Landau-Verwey-Overbeek (DLVO) theory could not explain the enhanced C₆₀ deposition by biofilm EPS. Biochemical and physical characteristics of biofilm EPS were responsible for the increased C₆₀ deposition.     

基于透明土技术的多孔介质孔隙流动特性研究

土体作为一种特殊多孔介质,内部孔隙通道尺度与形态随机性强,导致土体渗流场中孔隙流速分布不均,即存在优势流现象。优势流是影响污染物运移、导致土体渗透变形的重要因素。基于透明土原理,利用聚丙烯酸钠交联聚合物颗粒和蒸馏水,配制成饱和透明多孔介质,并利用一种新的研究透明多孔介质内部流场的装置及方法,将绿色光源激光器、单反相机、十字滑台等组合成简易粒子图像测速(PIV)系统,采集不同水力梯度下透明多孔介质内部流场图像,结合粒子图像测速技术,将得到的流速数据进行统计分析,揭示孔隙液体的流动特性。研究表明,利用自制简易PIV系统进行流场测量,实测孔隙流动结果与宏观流速吻合程度高,能够实现对流场的多点、无扰、高精度测量。研究发现多孔介质内部纵断面上的孔隙面积与纵断面所在位置有关,而孔隙面积越大,断面上的孔隙流速也越大。多孔介质内部孔隙流速分布规律大致相同,优势流速随着断面流速的减小而减小,优势流速越小,其概率密度越高,优势流动现象越显著。     

A lattice Boltzmann exploration of two-phase displacement in 2D porous media under various pressure boundary conditions

While experimental designs developed in recent decades have contributed to research on dynamic nonequilibrium effects in transient two-phase flow in porous media, this problem has been seldom investigated using direct numerical simulation (DNS). Only a few studies have sought to numerically solve Navier–Stokes equations with level-set (LS) or volume-of-fluid (VoF) methods, each of which has constraints in terms of meniscus dynamics for various flow velocities in the control volume (CV) domain. The Shan–Chen multiphase multicomponent lattice Boltzmann method (SC-LBM) has a fundamental mechanism to separate immiscible fluid phases in the density domain without these limitations. Therefore, this study applied it to explore two-phase displacement in a single representative elementary volume (REV) of two-dimensional (2D) porous media. As a continuation of a previous investigation into one-step inflow/outflow in 2D porous media, this work seeks to identify dynamic nonequilibrium effects on capillary pressure–saturation relationship (P_c–S) for quasi-steady-state flow and multistep inflow/outflow under various pressure boundary conditions. The simulation outcomes show that P_c, S and specific interfacial area (a_nw) had multistep-wise dynamic effects corresponding to the multistep-wise pressure boundary conditions. With finer adjustments to the increase in pressure over more steps, dynamic nonequilibrium effects were significantly alleviated and even finally disappeared to achieve quasi-steady-state inflow/outflow conditions. Furthermore, triangular wave-formed pressure boundary conditions were applied in different periods to investigate dynamic nonequilibrium effects for hysteretical P_c–S. The results showed overshoot and undershoot of P_c to S in loops of the nonequilibrium hysteresis. In addition, the flow regimes of multistep-wise dynamic effects were analyzed in terms of Reynolds and capillary numbers (Re and Ca). The analysis of REV-scale flow regimes showed higher Re (1 < Re < 10) for more significant dynamic nonequilibrium effects. This indicates that inertia is critical for transient two-phase flow in porous media under dynamic nonequilibrium conditions.     

光滑裂隙高流速非达西渗流运动规律的试验研究

 采用光滑平行板模拟岩体裂隙,研制可变裂隙开度、高水力梯度、自循环水流的单裂隙室内渗流模型试验装置。试验研究宽裂隙高水力梯度下的非达西渗流运动规律,建立流速与水力梯度的非线性关系曲线。将试验结果与Lomize紊流公式、速宝玉紊流半经验公式进行对比分析,发现三者在低水力梯度情况下结果较为一致,对于高水力梯度情况会出现较大的差异。最后探讨单裂隙高流速非达西渗流运动特点及判别准则等问题,建立非达西渗流流速与裂隙开度的关系曲线,以便于工程应用。     

岩石类材料压缩断裂路径的流体力学模拟

根据不可压缩粘性流体的模态速度场与平衡条件下弹性固体的位移场之间的对应性原理。推导了以流函数表示的弹性固体应力场公式，并证明了流线与主应力迹线之间的等效关系，利用茹柯夫斯基变换，给出了平板绕流问题的流函数解，并以此为基础，预测了岩石类材料压缩断裂路径的扩展规律，取得了与实验观察相一致的结果。     

A mixing‐length‐scale‐based analytical model for predicting velocity profiles of open‐channel flows with submerged rigid vegetation

In open‐channel flows with submerged vegetation, the vertical velocity profile can often be described by two layers: the vegetation layer in the lower region and the surface layer in the upper non‐vegetated region. In this paper, a new mixing‐length scale of eddy is proposed for predicting the vertical velocity profile of flow in an open‐channel with submerged rigid vegetation. The analytical model of velocity profile is based on the momentum equation of flow where the turbulent eddy viscosity is assumed to have a linear relationship with the local velocity. The proposed model was tested against different datasets from the literature. The 22 datasets used cover a range of submergence [flow depth (H)/vegetation height (h) = 1.25 ~ 3.38], different vegetation densities of ah = 0.11 ~ 1.85 (a defined as the frontal area of the vegetation per unit volume) and bed slopes (S_o = 1.8 × 10^?6 ~4.0 × 10^?3). This study showed that the proposed model can predict the velocity profiles well against all datasets, and that the mixing length scale of eddies (λ) is well related with both vegetation height (h) and flow depth of surface layer (i.e. the height of non‐vegetation layer, H–h). Close examination of λ in the proposed model showed that when λ = 0.03, the model predicts vertical velocity profiles well for all datasets used except for very shallow submergence (i.e. H/h < 1.5).     

Numerical simulation of wind flow near a forest edge

This paper presents a computational fluid dynamics (CFD) model to simulate wind flow near a forest edge for the purpose of wind energy applications. The model uses a porous media analogy combined with a modified k–ε turbulence model to simulate momentum losses and turbulence generation within the forest. The momentum losses are represented by a drag coefficient and a leaf area density. Two directions were investigated: wind flow entering and wind flow leaving the forest. A fully developed solution with original boundary conditions was used as the inlet boundary condition in the two-dimensional CFD model for wind flow leaving the forest. Original boundary conditions were also proposed for the ground boundary within the forest. The model was solved using FLUENT 6.2 and validated against field measurements from three different authors. A sensitivity analysis was performed on two key parameters: drag coefficient and leaf area density. The results obtained using the proposed method show good agreement with the wind velocity and turbulence intensity measured experimentally.     

An analysis of a jet into a turbulent ambient fluid

A comparison of the results of an analysis for the mixing of a passive tracer in a uniform current with the results of two jet analyses, one based on the concept of entrainment, the other based on the concept of turbulent diffusion, suggests that the effect of mixing due to turbulence in the ambient fluid can be included in the jet analysis based on entrainment by adding a term to the integrated continuity equation. For a two-dimensional jet that is discharged parallel to the mean velocity of a turbulent ambient fluid, the local ratio of the effects of jet mixing to ambient mixing is given by 0·40 Eb•u•/•, where E is the entrainment coefficient, b• is a local measure of the jet width, u• is the local maximum excess jet velocity, and • is the local ambient turbulent diffusion coefficient. A numerical solution shows that an increase in the ambient turbulent diffusion coefficient causes a decrease in the maximum concentrations and an increase in the lateral spreading of the discharged fluid.     

Aggregation and transport of nano-TiO2 in saturated porous media: effects of pH, surfactants and flow velocity

Transport of manufactured nano-TiO₂ in saturated porous media was investigated as a function of morphology characteristics, pH of solutions, flow velocity, and the presence of anionic and non-ionic surfactants in different concentrations. Surfactants enhanced the transport of nano-TiO₂ in saturated porous media while a pH approaching the point of zero charge of nano-TiO₂ limited their transport. The deposition process, a retention mechanism of nano-TiO₂ in saturated porous media was impacted by surfactant and pH. In Dispersion 1 systems (pH 7), the size of the nano-TiO₂ aggregates was directly related to the presence of surfactants. The presence of non-ionic surfactant (Triton X-100) induced a size reduction of nano-TiO₂ aggregates that was dependent on the critical micelle concentration. In Dispersion 2 systems (pH 9), the stability provided by the pH had a significant effect on the size of nano-TiO₂ aggregates; the addition of surfactants did impact the size of the nano-TiO₂ aggregates but in less significance as compared to Dispersion 1 systems. The electrostatic and steric repulsion forces in connection with the size of nano-TiO₂ aggregates and flow velocity impacted the single-collector efficiency and attachment efficiency which dictated the maximum transport distance of nano-TiO₂ for the Dispersion 1 and Dispersion 2 systems. By doubling the flow velocity at pH 9, the No Surfactant, 50% CMC Triton X-100, 100% CMC Triton X-100 and 100% CMC SDBS dispersion systems allowed nano-TiO₂ to attain maximum transport distances of 0.898, 2.17, 2.29 and 1.12 m, respectively. Secondary energy minima played a critical role in the deposition mechanisms of nano-TiO₂. Nano-TiO₂ deposited in the secondary energy wells may be released because of changes in solution chemistry. The deposition of nano-TiO₂ in primary and secondary energy minima, the reversibility of their deposition should be characterized to analyze the transport of nanoparticles in porous media. This is necessary to assess the risk of nanoparticles to the environment and public health.     

Experimental analysis of the air velocity and contaminant dispersion of human exhalation flows

Human exhalation flow is a potential source of pathogens that can constitute a cross‐infection risk to people in indoor environments. Thus, it is important to investigate the characteristics of this flow, its development, area of influence, and the diffusion of the exhaled contaminants. This paper uses phase‐averaged particle image velocimetry together with a tracer gas (CO₂) to study two different exhalation flows over time: the exhalation of an average male (test M) and an average female (test F), using a life‐sized thermal manikin in a supine position. The exhalation jets generated for both tests are similar in terms of symmetrical geometry, vorticity values, jet opening angles, and velocity and concentration decays. However, there is a difference in the penetration length of the two flows throughout the whole exhalation process. There is also a time difference in reaching maximum velocity between the two tests. It is also possible to see that the tracer gas dispersion depends on the momentum of the jet so the test with the highest velocity decay shows the lowest concentration decay. All these results are of interest to better understand cross‐infection risk.     

Performance of radiator by using SiO2 nano fluids

ABSTRACT

This article reports a study on heat transfer and flow characteristics of nano fluid consisting of water and ethylene glycol as base fluid with different concentrations of SiO₂as nanoparticles (0.1% and 0.15%) are flowing in a shell and tube exchanger. The SiO₂ nanoparticles of about 15 nm diameter are used in this study. The results showed that the heat transfer coefficient of nano fluid was slightly higher than that of the base fluid at the same inlet temperature and at the same mass flow rate. It was observed that heat transfer coefficient of nano fluid was increased with an increased mass flow rate. Heat transfer coefficient was noticed to increase with the increase of the volumetric concentration of the SiO₂. But increasing the volume concentration caused the increase in the viscosity of the nano fluid resulted in an increase in friction factor.     

砂土渗流过程的细观数值模拟

基于散体介质理论,利用PFC2D内置FISH语言定义的流固之间的作用力方程和压力梯度方程,求解不可压缩流体中两相介质的连续方程和Navier-Stoke方程。并尝试用该理论模拟不同水压下渗流引起砂土特性变化的全过程,数值试验得到了流速、渗透系数、孔隙率和砂的流失量等参量的定性变化规律,表明水土相互作用贯穿于渗流的全过程。模拟结果与试验结果相符,且流速与压力梯度满足达西定律,表明应用该理论来模拟复杂的水土相互作用是可行的,它具有一定的理论意义,为进一步研究多孔介质中考虑流固耦合的渗透破坏研究如流土、管涌等奠定了一定的理论基础。     

Backflow air and pressure analysis in emptying a pipeline containing an entrapped air pocket

ABSTRACT

The prediction of the pressure inside the air pocket in water pipelines has been the topic for a lot of research works. Several aspects in this field have been discussed, such as the filling and the emptying procedures. The emptying process can affect the safety and the efficiency of water systems. Current research presents an analysis of the emptying process using experimental and computational results. The phenomenon is simulated using the two-dimensional computational fluid dynamics (2D CFD) and the one-dimensional mathematical (1D) models. A backflow air analysis is also provided based on CFD simulations. The developed models show good ability in the prediction of the sub-atmospheric pressure and the flow velocity in the system. In most of the cases, the 1D and 2D CFD models show similar performance in the prediction of the pressure and the velocity results. The backflow air development can be accurately explained using the CFD model.     

CFD simulation analysis of two-dimensional convergent-divergent nozzle

ABSTRACT

Computational fluid dynamics is one of the parts of fluid mechanics and calculating numerical methods are solving the various flows of fluid. Two-dimensional models, which is to solve the flow rate of supersonic flow and analyzed the mathematical operations, which has solved the energy equations. This iteration process has analyzed and shown better results of temperature and static pressure, velocity, static temperature. The investigating results showing better temperature and velocity flows. The 2D nozzle line diagram is done in Ansys 14.5 geometry modular and calculated iteration process can be done in fluid flow. The nozzle is done and meshes using automatic method and sizing of different value of the meshing process. In the order to analyzed the Ansys fluent software and solved the flow process of the convergent-divergent iteration nozzle. Standard nozzle equation manually calculated and compared with analyzing the results.