Analysis of Bingham fluid radial flow in smooth fractures

Solutions for radial flow of a Bingham fluid are analyzed in this paper.It aims to eliminate confusions in the literature concerning the plug flow region in different solutions for analysis and design of grouting in rock fractures.The analyses based on the force balance equation reveal that the plug flow region in Bingham radial flow is independent of the fracture radius,and is not a growth function adapted from the solution of one-dimensional(1D)slit flow according to‘similarity’.Based on the shear stress distribution,we analytically proposed that a non-uniform plug flow region cannot exist.The Bingham fluid(grout)penetration and flowrate evolution as functions of grouting time are given using the correct expression for the plug flow region.The radius-independent plug flow region and the presented flowrate evolution equation are also verified numerically.For radial flow,the relative penetration length is equal to the relative width of plug flow region,which is the same as that for 1D channel flow.Discrepancies in analytical solutions for grout penetration and flowrate evolution were also illustrated.The clarification of the plug flow region and evaluation of discrepancies in analytical solutions presented in this work could simplify modeling and design of grouting in rock engineering applications.

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(2 D)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.

Discussion on “Analysis of Bingham fluid radial flow in smooth fractures”[J Rock Mech Geotech Eng 12(2020) 1112e1118]

Recently,Zou et al.(2020 a)published a theoretical analysis on the radial flow of a Bingham fluid,where they argued that the classical analysis by Dai and Bird(1981)violates the mass conservation.The present discussion aims to clarify this conflict between those two studies.It is noted that Zou et al.(2020 a)presumed the gap-wise mass flux is negligible in the mass conservation equation,while Dai and Bird(1981)did not require so in their model,and this is found to be the origin of the conflict.In fact,Dai and Bird(1981)’s model is shown to not violate the mass conservation.Therefore,those two models should be viewed as separate models derived from different perspectives.Details of the major difference between the two models are discussed.

Steady-State Radial Flow Modeling through the Production Well in the Confined Aquifer of Monzoungoudo,Benin

This study aims to develop a mathematical analysis for one-dimensional modeling of a radial flow through a production well drilled in a confined aquifer, in the case of steady-state flow conditions. An analytical solution has derived from that expression for estimation of drawdowns according to different flowrates. Through that process, the evaluation of static pressure, the calculation of hydraulic charge due to the waterflow through the well is evaluated, the drawdowns curves are drawn and at last, the obtained curves are analyzed. The curves obtained for the different flow rates have an asymptotic direction, the axis of the hydraulic charges. The variation of the hydraulic charge depends on the radial distance for different flow rates. The P point, is a common point of all curves obtained for different production flowrates in the well. This point is where the well production flowrate is optimum for the optimal hydraulic charge.

Investigation on a vertical radial flow adsorber designed by a novel parallel connection method

Due to the increasing global demand for industrial gas, the development of large-scale cryogenic air separation systems has attracted considerable attention in recent years. Increasing the height of the adsorption bed in a vertical radial flow adsorber used in cryogenic air separation systems may efficiently increase the treatment capacity of the air in the adsorber. However, uniformity of the flow distribution of the air inside the adsorber would be deteriorated using the height-increasing method. In order to reduce the non-uniformity of the flow distribution caused by the excessive height of adsorption bed in a vertical radial flow adsorber, a novel parallel connection method is proposed in the present work. The experimental apparatus is designed and constructed; the Computational Fluid Dynamics(CFD) technique is used to develop a CFD-based model, which is used to analyze the flow distribution, the static pressure drop and the radial velocity in the newly designed adsorber. In addition, the geometric parameters of annular flow channels and the adsorption bed thickness of the upper unit in the parallelconnected vertical radial flow adsorber are optimized, so that the upper and lower adsorption units could be penetrated by air simultaneously. Comparisons are made between the height-increasing method and the parallel connection method with the same adsorber height. It is shown that using the parallel connection method could reduce the difference between the maximum and minimum radial static pressure drop by 86.2% and improve the uniformity by 80% compared with those of using the height-increasing method. The optimal thickness ratio of the upper and lower adsorption units is obtained as 0.966, in which case the upper and lower adsorption units could be penetrated by air simultaneously, so that the adsorbents in adsorption space could be used more efficiently.

Hepatic reconstruction from fetal porcine liver cells using a radial flow bioreactor

AIM: To examine the efficacy of the radial flow bioreactor (RFB) as an extracorporeal bioartificial liver (BAL) and the reconstruction of liver organoids using embryonic pig liver cells. METHODS: We reconstructed the liver organoids using embryonic porcine liver cells in the RFB. We also determined the gestational time window for the optimum growth of embryonic porcine liver cells. Five weeks of gestation was designated as embryonic day (E) 35 and 8 wk of gestation was designated as E56. These cells were cultured for one week before morphological and functional examinations. Moreover, the efficacy of pulsed administration of a high concentration hepatocyte growth factor (HGF) was examined. RESULTS: Both cell growth and function were excellent after harvesting on E35. The pulsed administration of a high concentration of HGF promoted the differentiation and maturation of these fetal hepatic cells. Microscopic examination of organoids in the RFB revealed palisading and showed that bile duct-like structures were well developed, indicating that the organoids were mini livers. Transmission electron microscopy revealed microvilli on the luminal surfaces of bile duct-like structures and junctional complexes, which form the basis of the cytoskeleton of epithelial tissues. Furthermore, strong expression of connexin (Cx) 32, which is the main protein of hepatocyte gap junctions, was observed. With respect to liver function, ammonia detoxification and urea synthesis were shown to be performed effectively. CONCLUSION: Our system can potentially be applied in the fields of BAL and transplantation medicine.

The Construction Method for Solving Radial Flow Problem through the Homogeneous Reservoir

On the basis of similar structure of solutions of ordinary differential equation (ODE) boundary value problem, the similar construction method was put forward by solving problems of fluid flow in porous media through the homogeneous reservoir. It is indicate that the pressure distribution of dimensionless reservoir and bottom hole in Laplace space, which take on the radial flow, also shows similar structure, and the internal relationship between the above solutions were illustrated in detail.

Optimal operating conditions of radial flow moving-bed reactors for isobutane dehydrogenation

In this study, radial flow moving bed reactors for isobutane dehydrogenation have been modeled and simulated heterogeneously based on mass and energy conservation laws. The considered reaction networks in the model are isobutene dehydrogenation as main reaction, and hydrogenolysis, propane dehydrogenation as well as coke formation as side reactions that all occur on the catalyst surface. Then, the process condition has been optimized to produce more isobutene under steady state condition. To prove the accuracy of the considered mathematical model and assumptions, simulation results are compared with the plant data. As a powerful method in the global optimization, the genetic algorithm has been used to optimize the considered objective function. The isobutane conversion and isobutene selectivity under optimal conditions are about 40.1% and 91%, respectively.

Flow Field Simulation on Double-Ring Radial Flow Reactor

Compared with the traditional radial flow reactors(RFRs), the double-ring RFRs possess advantages including lower pressure drop, shorter flow path and greater flow area. According to the Ergun's equation and the continuity equation, a two-dimensional hydrodynamic model was established to describe the hydrodynamic behavior in the double-ring RFRs. The successive over-relaxation(SOR) method was applied to solve the two-dimensional hydrodynamic model. The flow assignment parameters(T_i) of mass flow in the inner channel to the outer catalyst bed and the inner catalyst bed were optimized by the Powell method. Simulations showed the trend of change in gas distribution uniformity along the axial direction and the weight hourly space velocity(WHSV) with the variation of reactor size. The model can be used to analyze the reasonability of dehydrogenation reactor design, and it can also provide quantitative reference for the design of new double-ring RFRs.

New P3D Hydraulic Fracturing Model Based on the Radial Flow

Pseudo three-dimension (P3D) hydraulic fracturing models often overpredict the fracture height for a poorly contained fracture. To solve this problem, a new method is presented in shaping the P3D fracture geometry on the basis of the fundamental theory and the original 1D fluid flow is replaced with a more representatively radial flow. The distribution of the fluid in the modified fluid field is analyzed and a sound explanation to the problem is given. Due to the consideration of the fluid flow in the vertical direction, the modified model can predict the fracture height much better. To validate the rationality of the radial fluid flow assumption, the distribution of the fluid in the modified fluid field is simulated with the plane potential flow by using finite element method. And the results agree effectively with those from the assumption. Through comparing with the full 3D model, the results show that this new P3D model can be used to aid the fracturing design and predict the fracture height under poorly contained situation.

Numerical Investigation into the Distributor Design in Radial Flow Adsorber

Air flow distribution in radial flow adsorber was numerically investigated using computational fluid dynamics(CFD)method,which was proved to be applicable to study the problem of non-uniform distribution in radial flow adsorber.Results showed that the degree of non-uniformity was more serious in desorption process than that is adsorption process.Therefore,it was considered that the non-uniform distribution of flow in a radial flow adsorber was mainly manifested in the desorption process.Optimum design of distributor parameters can improve the flow distribution in adsorber.Meanwhile,three different structures of distributor and the effect of breathing valve were analyzed.Results revealed that truncated cone is more effective than tubular and conical distributors in flow distribution.By inserting the truncated cone in central channel,desorption uniformity was increased by 6.56%and the breakthrough time of CO_(2)was extended from 564s to 1138s in the adsorption process.The“dead zone”problem at the top of adsorber during the desorption process was solved by opening breathing valve,which prolonged the working life of adsorber and was proved to have less effect on the uniform of airflow.

Effect of Radial Resistance Gap on the Pressure Drop of a Compact Annular-Radial-Orifice Flow Magnetorheological Valve

A compact annular-radial-orifice flow magnetorheological(MR)valve was developed to investigate the effects of radial resistance gap on pressure drop.The fluid flow paths of this proposed MR valve consist of a single annular flow channel,a single radial flow channel and an orifice flow channel through structure design.The finite element modelling and simulation analysis of the MR valve was carried out using ANSYS/Emag software to investigate the changes of the magnetic flux density and yield stress along the fluid flow paths under the four different radial resistance gaps.Moreover,the experimental tests were also conducted to evaluate the pressure drop,showing that the proposed MR valve has significantly improved its pressure drop at 0.5 mm width of the radial resistance gap when the annular resistance gap is fixed at 1 mm.

Rotating instability in the vaneless diffuser of a radial flow pump

纸在操作条件的部分流动指光线的流动泵更弥漫的翼更少的行为。一些试验性的数据用 2D/2C PIV 和在内的不稳定的压力大小被获得了更弥漫，处于各种各样的操作条件。以更低的流动率的试验性的结果与二维的数字计算相比。

Radial profile of sap flow velocity in mature Xinjiang poplar(Populus alba L. var. pyramidalis) in Northwest China

Estimation of the transpiration rate for a tree is generally based on sap flow measurements within the hydro-active stem xylem. In this study, radial variation of sap flow velocity(Js) was investigated at five depths of the xylem(1, 2, 3, 5 and 8 cm under the cambium) in three mature Xinjiang poplar(Populus alba L. var. pyramidalis) trees grown at the Gansu Minqin National Studies Station for Desert Steppe Ecosystem from May to October 2011. Thermal dissipation probes of various lengths manufactured according to the Granier's design were installed into each tree for simultaneous observation of the radial patterns of Js through the xylem. The radial patterns were found to fit the four-parameter GaussAmp equation. The peak Js was about 27.02±0.95 kg/(dm2?d) at approximately 3 to 5 cm deep from the cambium of the three trees,and the lowest Js appeared at 1 cm deep in most of the time. Approximately 50% of the total sap flow in Xinjiang poplar occurred within one-third of the xylem from its outer radius, whereas 90% of the total sap flow occurred within two-fifth of the xylem. In addition, the innermost point of the xylem(at 8-cm depth), which appeared as the penultimate sap flow in most cases during the study period, was hydro-active with Js,8 of 7.55±3.83 kg/(dm2?d). The radial pattern of Js was found to be steeper in midday than in other time of the day, and steeper diurnal fluctuations were recorded in June, July and August(the mid-growing season). Maximum differences between the lowest Js(Js,1 or Js,8) and the highest Js(Js,3 or Js,5) from May through October were 12.41, 17.35, 16.30, 18.52, 12.60 and 16.04 g/(cm2?h), respectively. The time-dependent changes of Js along the radial profile(except at 1-cm depth) were strongly related to the reference evapotranspiration(ET0). Due to significant radial variability of Js, the mean daily sap flow at the whole-tree level could be over-estimated by up to 29.69% when only a single probe at depth of 2 cm was used. However, the accuracy of the estimation of sap flow in Xinjiang poplar could be significantly improved using a correction coefficient of 0.885.

Convective heat and mass transfer in MHD mixed convection flow of Jeffrey nanofluid over a radially stretching surface with thermal radiation

Mixed convection flow of magnetohydrodynamic(MHD) Jeffrey nanofluid over a radially stretching surface with radiative surface is studied. Radial sheet is considered to be convectively heated. Convective boundary conditions through heat and mass are employed. The governing boundary layer equations are transformed into ordinary differential equations. Convergent series solutions of the resulting problems are derived. Emphasis has been focused on studying the effects of mixed convection, thermal radiation, magnetic field and nanoparticles on the velocity, temperature and concentration fields. Numerical values of the physical parameters involved in the problem are computed for the local Nusselt and Sherwood numbers are computed.

Dufour and Soret effects on MHD flow of viscous fluid between radially stretching sheets in porous medium

The aim of this paper is to examine the Dufour and Soret effects on the two-dimensional magnetohydrodynamic (MHD) steady flow of an electrically conducting viscous fluid bounded by infinite sheets. An incompressible viscous fluid fills the porous space. The mathematical analysis is performed in the presence of viscous dissipation, Joule heating, and a first-order chemical reaction. With suitable transformations, the governing partial differential equations through momentum, energy, and concentration laws are transformed into ordinary differential equations. The resulting equations are solved by the homotopy analysis method (HAM). The convergence of the series solutions is ensured. The effects of the emerging parameters, the skin friction coefficient, the Nusselt number, and the Sherwood number are analyzed on the dimensionless velocities, temperature, and concentration fields.

Design and Numerical Simulation on Coupled Flow Field of Radial Turbine with Air-Inlet Volute

As one of the core components of turbocharger or micro-turbine, radial turbine has the features of small size and high rotation speed. In order to explore the design method and flow mechanism of the turbine with a volute, a centimeter-scale radial turbine with a vaneless air-inlet volute was designed and simulated numerically to investigate the characteristics of the coupled flow field. The results show that the wheel efficiency of single passage computation without the volute is 80.1%. After accounting for the factors of the loss caused by the volute and the interaction between each passage, the performance is more accurate according to the whole flow passage computation with the volute. High load region gathers at the mid-span and the efficiency declines to 76.6%. The performance of the volute whose structure angle of the trapezoid section is equal to 70 degree is better. Unlike uniform inlet condition in single passage, more appropriate inlet flow for the impeller is provided by the rectification effect of the volute in full passage calculation. Flow parameters are distributed more evenly along the blade span and are generally consistent between each passage at the outlet of the turbine.

Heat Transfer and Fluid Flow of Nanofluids in Laminar Radial Flow Cooling Systems

Nanofluids 被认为选择同样有趣到常规冷却剂。传统的液体限制了热转移能力，是众所周知的什么时候与普通金属相比。在传统的液体在暂停放的极其好的金属性的粒子的小数量将更加增加他们的热转移表演，因此是相当想得到的。数字调查进有在内的推迟的金属性的 nanoparticles 的冷却剂的热转移改进能力一光线， laminar 流动冷却配置被介绍。温度依赖 nanofluid 性质从在最近的文学可得到的试验性的数据被评估。结果显示可观的热转移增加与 nanoparticles 的相对小的体积部分的使用是可能的。然而，通常，这些被墙砍压力的可观的增加伴随。结果也证明与温度变量 nanofluid 性质获得的预言产出更大的热转移能力和更低的墙砍当时，强调与用经常的性质的预言相比。关键词 nanofluids - nanoparticles - 热转移 - laminar 流动 - 限制光线的流动 CLC 数字 TK

LOCAL DISCONTINUOUS GALERKIN METHOD FOR RADIAL POROUS FLOW WITH DISPERSION AND ADSORPTION

Based on the local discontinuous Galerkin methods for time-dependent convection-diffusion systems newly developed by Corkburn and Shu,according to the form of the generalized convection-diffusion equations which model the radial porous flow with dispersion and adsorption,a local discontinuous Galerkin method for radial porous flow with dispersion and adsorption was developed,a high order accurary new scheme for radial porous flow is obtained.The presented method was applied to the numerical tests of two cases of radial porous,i.e., the convection-dispersion flow and the convection-dispersion-adsorption flow,the corresponding parts of the numerical results are in good agreement with the published solutions,so the presented method is reliable.Reckoning of the computational cost also shows that the method is practicable.

Slip flow in an annular sector duct using radial eigenfunctions

The fully developed slip flow in an annular sector duct is solved by expansions of eigenfunctions in the radial direction and boundary collocation on the straight sides. The method is efficient and accurate. The flow field for slip flow differs much from that of no-slip flow. The Poiseuille number increases with increased inner radius, opening angle, and decreases with slip.