CFD model of a Hydrocyclone

PLEASE SCROLL DOWN FOR ARTICLEThis article was downloaded by: [Shanghai Jiaotong University]On: 15 September 2009Access details: Access Details: [subscription number 912295284]Publisher Taylor & FrancisInforma Ltd Registered in England and Wales Registered Number: 1072954 Registered office: Mortimer House,37-41 Mortimer Street, London W1T 3JH, UKInternational Journal of Computational Fluid DynamicsPublication details, including instructions for authors and subscription information:/smpp/title~content=t713455064Hydrodynamic modelling and CFD simulation of ferrofluids flow in magnetic targeting drug deliveryShigang Wang a ; Handan Liu a ; Wei Xu a aSchool of Mechanical Engineering, Shanghai Jiaotong University, Shanghai, China Online Publication Date: 01 December 2008To cite this Article Wang, Shigang, Liu, Handan and Xu, Wei(2008)'Hydrodynamic modelling and CFD simulation of ferrofluids flow inmagnetic targeting drug delivery',International Journal of Computational Fluid Dynamics,22:10,659 — 667To link to this Article: DOI: 10.1080/10618560802452009URL: /10.1080/10618560802452009Full terms and conditions of use: /terms-and-conditions-of-access.pdf This article may be used for research, teaching and private study purposes. Any substantial or systematic reproduction, re-distribution, re-selling, loan or sub-licensing, systematic supply or distribution in any form to anyone is expressly forbidden.The publisher does not give any warranty express or implied or make any representation that the contents will be complete or accurate or up to date. The accuracy of any instructions, formulae and drug doses should be independently verified with primary sources. The publisher shall not be liable for any loss,actions, claims, proceedings, demand or costs or damages whatsoever or howsoever caused arising directly or indirectly in connection with or arising out of the use of this material.Hydrodynamic modelling and CFD simulation of ferrofluids flow in magnetic targeting drugdeliveryShigang Wang,Handan Liu*and Wei XuSchool of Mechanical Engineering,Shanghai Jiaotong University,Shanghai 200240,China(Received 25January 2008;final version received 4October 2008)Magnetic targeting drug delivery is a method of carrying drug-loaded magnetic nanoparticles to a tissue target in the human body under the applied magnetic field.This method increases the drug concentration in the target and reduces the adverse side-effects.In this article,a mathematical model is presented to describe the hydrodynamics of ferrofluids as drug carriers flowing in a blood vessel under the applied magnetic field.Numerical simulations are performed to obtain better insight into the theoretical analysis with computational fluid dynamics.A 3D flow field of magnetic particles in an idealised blood vessel model containing an aneurysm is analysed to further understand clinical application of magnetic targeting drug delivery.Simulation samples demonstrate the important parameters leading to adequate drug delivery to the target site depending on the applied magnetic field in coincidence with reported results from animal experiments.Results of the analysis provide the important information and can suggest strategies for improving delivery in favour of the clinical application.Keywords:magnetic targeting drug delivery;ferrofluids;magnetic nanoparticles;hydrodynamic modelling;CFD simulation1.IntroductionIn conventional drug delivery the drug is administered by intravenous injection;it then travels to the heart from where it is pumped to all regions of the body.For the small target region that the drug is aimed at,this method is extremely inefficient and leads to much larger doses (often of toxic drugs)than necessary.To overcome this problem,a number of targeted drug delivery methods have been developed (Torchilin 2000,Lu bbe et al.2001,Vasir and Labhasetwar 2005).Among them,the mag-netic targeted drug delivery system is one of the most attractive strategies because of its non-invasiveness,high targeting efficiency and its ability to minimise the toxic side effects on healthy cells and tissues (Alexiou et al.2000,2005).Magnetic drug targeting therapy is a promising technique for the treatment of various diseases,especially cancer,arteriosclerosis,like stenosis,thrombosis and aneurysm,what is important is to keep the therapeutic drug in the targeting site,which is located along the inner wall of the blood vessel (Alksne et al.1967,Alexiou et al.2000,2005,Chen et al.2005,Udrea et al.2006).Some in vitro (Chen et al.2005,Udrea et al.2006)and in vivo (Alksne et al.1967,Goodwin et al.1999,Alexiou et al.2002,Jurgons et al.2006)experi-ments have been performed in this direction.Typically,this compound in which drugs are bound with nanoparticles is injected through a blood vesselsupplying the targeting tissue in the presence of an external magnetic field with sufficient field strength and gradient to retain the carrier at the target site.Recent development on carriers has largely focused on new polymeric or inorganic coatings on magnetite/maghemite nanoparticles (Ruuge and Rusetski 1993),such as ferrofluids.Ferrofluids are colloidal solutions of ferro or ferromagnetic nanoparticles in a carrier fluid,which are widely used in technical applications.Because of a high magnetic moment of nanoparticles in ferrofluids,ferrofluids are gaining increasing interest to be utilised as drug carriers in magnetic targeting for biological and medical applications (Riviere et al.2006).When they are used in medicine,ferrofluids must be bio-compatible and bio-degradable (Jurgons et al.2006).Recently,some theoretical studies of magnetically targeted drug delivery considered tracking individual particles under the influence of Stokes drag and a magnetic force alone (Grief and Richardson 2005),and formulated a two-dimensional (2D)model,suitable for studying the deposition of magnetic particles within a network of blood vessels (Richardson et al.2000).Other theoretical studies investigated the basic inter-action between magnetic and fluid shear forces in a blood vessel (Voltairas et al.2002)or utilised high gradient magnetic separation principles to study a*Corresponding author.Email:helenlew818@International Journal of Computational Fluid Dynamics Vol.22,No.10,December 2008,659–667ISSN 1061-8562print/ISSN 1029-0257online Ó2008Taylor &FrancisDOI:10.1080/10618560802452009D o w n l o a d e d B y : [S h a n g h a i J i a o t o n g U n i v e r s i t y ] A t : 16:26 15 S e p t e m b e r 2009magnetic drug targeting system(Ritter et al.2004). Although there have been a number of theoretical studies for magnetic drug targeting,very few research-ers have addressed the hydrodynamic models of magneticfluids in magnetic drug targeting delivery. Thus,the transport issues related to magnetic drug targeting delivery are yet poorly understood and it retards the extensive application of the magnetic drug targeting delivery.Therefore,it is very necessary to study theflow of the ferrofluids in the blood vessel under the action of the external magneticfield.In this article,we focused on investigating theflow rules of ferrofluids as drug carriers under the applied magneticfield.A mathematical model presented in this article describes the hydrodynamics of ferrofluids in a blood vessel under the action of the magneticfield. Numerical simulations are performed to obtain better insight into the theoretical analysis.Furthermore,the ferrofluidsflow is analysed numerically with com-putationalfluid dynamics(CFD)in a model of an idealised3D blood vessel containing an aneurysm to understand the clinical application of ferrofluids. Magneticfluids have been used in medicine since1960 for,e.g.the magnetically controlled metallic thrombosis of intracranial aneurysms(Alksne et al.1967).The biokinetic behaviour of ferrofluids in vivo was investi-gated and showed that the retention of ferrofluids in target region is dependent on the magneticfield strength(Goodwin et al.1999,Alexiou et al.2002, Jurgons et al.2006).Results of the analysis provided important information leading to adequate drug deliv-ery to the target site and can suggest strategies for improving delivery in favour of the clinical application. The simulation results coincide with these animal experiments.2.Mathematical modelFerrofluids is a nano-scale colloid mixture.Because of the magnitude of nanometre scale of the magnetic particle,the hysteresis of itsflow velocity and tempera-ture can be neglected.The body forces are the gravity as well as the magnetic force.In the absence of a magnetic field the stress is symmetric,whereas the momentum equation is the Navier-Stokes equation.In the presence of a magneticfield,the magneticfield brings an asymmetric stress and produces a magnetic force. Hereby,except for the conventional Navier-Stokes equation,the magnetic force and the asymmetric stress are included in the momentum equation.Thefluidflows from macroscopically to microscopically through the artery to arterioles and to capillary vessels.If still considered the microfluidflow with continuum theory, the viscous force is more dominant than the gravity force,in addition to magnetic force as a new body force.So,the equations of motion for incompressible ferro-fluids dynamics are(Liu Han-dan et al.2008)as follows: Continuity equationrÁu¼0ð1ÞMomentum equationrD uD t¼Àr pþZ r2uþm0MÁrðÞHð2ÞWhen the magnetisation M is aligned with the applied magneticfield H or H is large enough,the magnetisation equation isM¼w Hð3ÞMaxwell equationrÂH¼0ð4ÞThis set of equations represents10equations for10 variables(p(1),u(3),M(3)and H(3)).The viscosity Z, density r,and magnetic susceptibility w are considered as known and constants.m0is the magnetic perme-ability in free space and is equal to4p61077H/m. The numerical solution for these equations is obtained from the CFD.The Gauss law gives the magnetic induction B asrÁB¼0ð5ÞB¼m0HþMðÞ¼m01þwðÞH¼m Hð6Þputational modelling and numerical simulation In this research,thefinite volume method is used to obtain the numerical simulations of ferrofluidsflowing in a blood vessel.In thefinite volume method the general formation of the governing equations is (Versteeg and Malalasekera1995):@rfðÞ@t¼divÀgrad fðÞþSwhere f is the general variable,Àis the generalised diffusive coefficient and S is the generalised source term.Its physical meaning is the conservation princi-ples of dependent variable f in thefinite control volume.In Equation(2)f is the velocity and S indicates the pressure gradient and the magnetic force.When studying theflow in a blood vessel,Netti et al.(1996)presented the ratio of resistance toflow660S.Wang et al.DownloadedBy:[ShanghaiJiaotongUniversity]At:16:2615September20 9along the vessels to that through the vessel walls to denote the relative size of extravasations from a blood vessel.b¼128Z0L p l2=d3where Z0is the blood viscosity,L p is the vascular permeability and the vessel is of length l and diameter d.The value of the parameter b for a single vessel is within the order of magnitude of1073,and hence the amount offluidfiltration across the vascular wall of a blood vessel will always be negligible compared to the amount of perfusionflow(the range of b is from10to100).So theflow in a blood vessel is primarily an axialflow(Netti et al.1996).As arepresentative application the laminar,incompressible, three-dimensional,fully developed viscousflow of a Newtonianfluid in a straight cylindrical duct for simplified aneurysm geometry is numerically studied (Castro et al.2006).The ferrofluids as drug carriers flowing in the blood vessel is studied under the action of the applied magneticfield,and the change of the pressure and velocity at the target site is analysed as the change of the magnetic intensity.3.1.Simulation modelTo further understand the clinical application of ferrofluids,the ferrofluidsflow is analysed in an idealised3D model of a blood vessel containing an aneurysm.Aneurysms are common vascular abnor-malities that represent a disruption in arterial wall continuity.Except for the traditional surgical option, the drug injection option is used for therapy,such as thrombin(Gorge et al.2003).Under the action of the applied magneticfield,ferrofluids are concentrated on the aneurysm wall and then release therapeutic agents. An aneurysm is a bulge that is formed in a blood vessel.A schematic drawing of an aneurysm is shown in Figure1.Simplifying the computational domain of the aneurysm,we chose the diameter of the blood vessel of the aneurysm d¼0.8mm,and the length L¼10mm. In the Cartesian coordinates,the axial direction is in the X direction with X¼0set at the inlet and the origin is set at the centre of the circle at the cross-section of the inlet.There is a bulge at X¼5mm from the origin of the X direction and down from Y¼70.4mm,which is the spherical centre of the aneurysm blood vessel. The aneurysm is modelled as a sphere whose diameter is1mm.The applied magneticfield acts on the whole segment of the aneurysm blood vessel.The grid distribution in the above computational domain is generated by GAMBIT.Illustrations of the computational mesh are given in Figure2.3.2.Boundary conditionsFor3D computation,the computational domain is the whole segment,as shown in Figure 2.The applied magneticfield acts on the whole segment of the aneurysm blood vessel.(1)Boundary of the inlet.A parabolic inlet velocityprofile is applied at the inlet,where the axialvelocity u is given by White(1974)asu y;zðÞ¼16d2ZpÀd^pdxX1i¼1;3;5;...ÂÀ1ðÞiÀ1ðÞ21Àcosh i p z2dcosh i p2"#Âcos i p y2dwhere d is the diameter of the blood vessel,Zis the viscosity and^p¼pþr gz.The othercomponents of the velocity v and w are0.(2)Boundary of the outlet.A fully developedassumption is applied at the outlet.The normalderivatives of the physical variables along theoutlet section are0.(3)Boundary of the blood vessel wall.It is definedas solid,no slip conditions.And the wallboundary is assumed as an insulating stateunder the applied magneticfield.(4)Initial pressure.As the blood pressure of anadult arteriole is about30mm Hg,i.e.4kPa,the initial pressure value is set to4,000Pascals.The below-mentioned pressure drop values inFigures7and8are based on this initialpressure value tofluctuate.3.3.ParametersWhen the water is the carrierfluid at a temperature of298K,the related physical properties of Fe3O4 Figure1.Schematic drawing of an aneurysm.International Journal of Computational Fluid Dynamics661DownloadedBy:[ShanghaiJiaotongUniversity]At:16:2615September20 9Figure2.(a)The grid distribution of Computational domain.(b)The various directions of views after being meshed.Available in colour online.ferrofluids(Rosensweig1997)are the density r¼1460 kg/m3,the viscosity Z¼0.035N s/m2(measured in the absence of a magneticfield),the magnetic satura-tion M s¼15.9kA/m.In addition,the diameter of magnetic particles is20nm and the volume fraction is 0.046.After confirming the governing equations and the boundary conditions of the model,the CFD software FLUENT is used to perform steady state numerical simulation by means of thefinite volume method. User-defined functions are written in the C program-ming language to describe the applied magneticfield and the velocity.The pressure term of the momentum equation is dealt with by SIMPLEC algorithm.The solution was obtained under four different magnetic fields,namely B¼0,0.1,0.5,1.0T.When the residuals of the source term of mass in the continuity equation and each component of the velocity are less than 1.061073,the iteration is considered as the putation results and discussion4.1.Distribution of induced current density and electromagnetic forceThe vector diagrams of induced current density and electromagnetic force are given in Figure3.Ferrofluids move through the static magneticfield and the induced current is formed in the blood vessel as shown in Figure3(a).An electromagnetic force is formed by the interaction between the current and magneticfield, whose direction is opposite to theflow direction of ferrofluids as shown in Figure3(b).This force reduces theflow of ferrofluids.4.2.The effect of magnetic induction intensity on velocityfieldAt different magnetic induction intensity B¼0,0.1,0.5, 1.0T,the velocity contours near the bulge in x–y plane (z¼0)are as shown in Figure4(a–d),respectively.662S.Wang et al.DownloadedBy:[ShanghaiJiaotongUniversity]At:16:2615September29Figure 3.(a)The vector diagram of induced current density in the blood vessel.(b)The vector diagram of electromagnetic force in the bloodvessel.Figure 4.Velocity contours in x-y plane at different magnetic fields.(a)B ¼0T,(b)B ¼0.1T,(c)B ¼0.5T,(d)B ¼1.0T.Available in colour online.International Journal of Computational Fluid Dynamics 663D o w n l o a d e d B y : [S h a n g h a i J i a o t o n g U n i v e r s i t y ] A t : 16:26 15 S e p t e m b e r 2009Figure 5gives the velocity field of the cross-section of the bulge of the aneurysm when x ¼5mm,i.e.the most outstanding part in the bulge of the aneurysm,at different magnetic fields B ¼0,0.1,0.5,1.0T.As Figures 4and 5shows,without magnetic field the ferrofluids flow slowly and flux is low,nothing is changed after the ferrofluids flow near the bulge region of the aneurysm.At a weaker magnetic field of B ¼0.1T there is no obvious change near the bulge region,as shown in Figure 5(b).With anincrease of the magnetic field,the flux into the bulge increases.Figure 6shows the distribution curves of velocity along y ¼0in x –y plane (z ¼0)at different magnetic fields B ¼0,0.1,0.5,1.0T.As Figure 6shows,the ferrofluids velocity decreases when flowing through the bulge region.When under no magnetic field (B ¼0T)or a weaker magnetic field (B ¼0.1T),the velocity is slow or has no obvious change.As the magneticinductionFigure 5.Velocity Fields in the cross-section of the aneurysm when x ¼5mm at different magnetic fields.(a)B ¼0T,(b)B ¼0.1T,(c)B ¼0.5T,(d)B ¼1.0T.Available in colouronline.Figure 6.Velocity curves in x-y plane when y ¼0at different magnetic induction intensity.(a)B ¼0T,(b)B ¼0.1T,(c)B ¼0.5T,(d)B ¼1.0T.Available in colour online.664S.Wang et al.D o w n l o a d e d B y : [S h a n g h a i J i a o t o n g U n i v e r s i t y ] A t : 16:26 15 S e p t e m b e r 2009intensity increases,the velocity decreases,especially into the bulge zone.This will make more stagnancy of ferrofluids in the target site.The concentration of ferrofluids in the target increases and the carriers have more chance to relieve drugs.4.3.The effect of magnetic induction intensity on pressure fieldAt different magnetic induction intensities,Figure 7shows the distribution curves of pressure drop near the bulge region along y ¼70.4mm in x –yplane,i.e.along the line of the vessel wall growing the bulge.Figure 8shows the comparison of the above four curves in the same coordinate.The blood pressure of an adult arteriole is about 30mmHg,i.e.4kPa,as an initial pressure.As shown in Figures 7and 8,the pressure falls as the flow field from the inlet to the outlet in accordance with the specialty of human haemodynamics (Fung 1984).In simulation cases,if the length of a vessel is 20times more than its diameter,the effect of import and export can be neglected (Fung 1984).InthisFigure 7.Pressure drop near the bulge along y ¼70.4mm in x-y plane at the different magnetic fields.(a)B ¼0T,(b)B ¼0.1T,(c)B ¼0.5T,(d)B ¼1.0T.Available in colour online.International Journal of Computational Fluid Dynamics665D o w n l o a d e d B y : [S h a n g h a i J i a o t o n g U n i v e r s i t y ] A t : 16:26 15 S e p t e m b e r 2009case,as the length of the vessel is not enough long,the pressure drop at the inlet and outlet is affected more or less as shown in Figures 7and 8.So the pressure changes more near the inlet and outlet.In the presence of the magnetic field,the pressure drop increases.The reason is that the formation of magnetisation pressure of ferrofluids results in the increase of pressure drop with the increasing of magnetic field intensity (Rosensweig 1997).The pressure drop of the fluid increases to stagnate ferrofluids at the targeting region.5.ConclusionFor magnetic targeting drug delivery,we have formulated a dynamic model of ferrofluids as drug carriers flowing in a blood vessel,which introduce the magnetic force.This model allows better understand-ing the flow of ferrofluids under the applied magnetic field.All of the required physical parameters such as magnetic induced intensity,viscosity,velocity,etc.are incorporated in the model.A 3D numerical simulation and analysis of ferrofluids flow are carried out in a blood vessel to understand the clinical application for magnetic targeting drug delivery.From the simulation results and analysis,after imposing a magnetic field the velocity decreases and the pressure drop increases at the target position as the magnetic field intensity increases.It makes more stagnancy of ferrofluids to get the required concentration of drug delivery.Thus,this model better simulates the flow state in the blood vessel for magnetic targeting drug delivery.Simulation results are provided in accordance with those animalexperiments (Alksne et al.1967,Goodwin et al.1999,Alexiou et al.2002,Jurgons et al.2006).In summary,the numerical study of the mathema-tical model characterises the ferrofluid accumulation and dispersion in a simplified case for magnetic targeting drug delivery.The ferrofluid pressure profile,mass flux vectors and velocity nature provide important information about the specialty of the ferrofluid aggregate at the target region.This is vital for the biomedical transport that will allow a therapeutic agent to be used for various magnetic drug targeting applications.AcknowledgementsThis research work was supported by the National Basic Research Program of China (973Program,2007CB936004)and the National Nature Science Foundation of China (No.50875169)for fundamental research.The authors would like to express their gratitude to Prof.Zunji Ke (Shanghai Institutes for Biological Sciences,Chinese Academy of Sciences)for helpful discussions.ReferencesAlexiou,C.,et al .,2000.Locoregional cancer treatment withmagnetic drug targeting.Cancer Research ,60(23),6641–6648.Alexiou,C.,et al .,2002.Magnetic drug targeting:biodis-tribution and dependency on magnetic field strength.Journal of Magnetism and Magnetic Materials ,252,363.Alexiou,C.,et al .,2005.Magnetic drug targeting –a newapproach in locoregional tumortherapy with chemo-therapeutic agents.Experimental animal studies.HNO ,53(7),618–622.Alksne,J.F.,Fingerhut, A.G.,and Rand,RW.,1967.Magnetic probe for the stereotactic thrombosis of intracranial aneurysms.Journal of Neurology,Neuro-surgery and Psychiatry ,30(2),159–162.Castro,M.A.,Putman, C.M.,and Cebral,J.R.,2006.Computational fluid dynamics modeling of intracranial aneurysms:effects of parent artery segmentation on intraaneurysmal hemodynamics.American Journal of Neuroradiology ,27,1703–1709.Chen,H.,et al .,2005.Analysis of magnetic drug carrierparticle capture by a magnetisable intravascular stent-2:parametric study with multi-wire two-dimensional model.Journal of Magnetism and Magnetic Materials ,293(1),616–632.Fung,Y.C.,1984.Biodynamics:circulation .New York:Springer-Verlag.Goodwin,S.,et al .,1999.Targeting and retention ofmagnetic targeted carriers (MTCs)enhancing intra-arterial chemotherapy.Journal of Magnetism and Magnetic Materials ,194(1–3),132–139.Gorge,G.,Kunz,T.,and Kirstein,M.,2003.Non-surgicaltherany of iatrogenic false aneurysms.Deutsche Medizi-nische Wochenschrift ,128(1–2),36–40.Grief,A.and Richardson,G.,2005.Mathematical modellingof magnetically targeted drug delivery.Journal of Magnetism and Magnetic Materials ,293(1),455–463.Jurgons,R.,et al .,2006.Drug loaded magnetic nanoparticlesfor cancer therapy.Journal of Physics-Condensed Matter ,18(38),S2893–S2902.Figure 8.Pressure drop near the bulge along y ¼70.4mm in x-y plane at the different magnetic fields (in the same coordinate).Available in colour online.666S.Wang et al.D o w n l o a d e d B y : [S h a n g h a i J i a o t o n g U n i v e r s i t y ] A t : 16:26 15 S e p t e m b e r 2009Liu,Han-dan,Xu,Wei,and Wang,Shi-gang,2008.Mathe-matical modeling of the magnetic drug targeting delivery.Journal of Shanghai Jiaotong University,42(1),1–4.Lu bbe,A.S.,Alexiou,C.,and Bergemann,C.,2001.Clinical application of magnetic drug targeting.Journal of Surgical Research,95(2),200–206.Netti,P.A.,et al.,1996.Effect of transvascularfluid exchange on pressure-flow relationship in tumors:a proposed mechanism for tumor bloodflow heterogene-ity.Microvascular Research,52,27–46.Richardson,G.W.,et al.,2000.Drug delivery by magnetic microspheres.In:Proceedings of the1st mathematics in medicine study group,Nottingham.Ritter,J.,et al.,2004.Application of high gradient magnetic separation principles to magnetic drug targeting.Journal of Magnetism and Magnetic Materials,280(2,3),184–201. Riviere,C.,et al.,2006.Nanosystems for medical applica-tions:biological detection,drug delivery,diagnosis and therapy.Annales de Chimie-Science des Materiaux, 31(3),351–367.Rosensweig,R.E.,1997.Ferrohydrodynamics.New York: Dover Publications.Ruuge,E.and Rusetski,A.,1993.Magneticfluids as drug carriers–targeted transport of drugs by a magnetic-field.Biotechnology Progress,122(1–3),335–339. Torchilin,V.P.,2000.Drug targeting.European Journal of Pharmaceutical Science,11(Suppl)(2),S81–S91. Udrea,L.,et al.,2006.An in vitro study of magnetic particle targeting in small blood vessels.Physics in Medicine and Biology,51(19),4869–4881.Vasir,J.and Labhasetwar,V.,2005.Targeted drug delivery in cancer therapy.Technology in Cancer Research and Treatment,4(4),363–374.Versteeg,H.K.and Malalasekera,W.,1995.An introduction to computationalfluid dynamics:thefinite volume method.New York:Wiley.Voltairas,P.,et al.,2002.Hydrodynamics of magnetic drug targeting.Journal of Biomechanics,35(6),813–821. White,F.M.,1974.Viscousfluidflow.New York:McGraw-Hill Book Company.International Journal of Computational Fluid Dynamics667DownloadedBy:[ShanghaiJiaotongUniversity]At:16:2615September20 9。

计算流体力学大模型英文回答：Computational Fluid Dynamics (CFD) in Large-Scale Models.Computational fluid dynamics (CFD) is a powerful tool that can be used to simulate the flow of fluids. This makes it a valuable tool for a wide range of applications, including the design of aircraft, cars, and other vehicles; the optimization of industrial processes; and the study of environmental flows.In recent years, there has been a growing interest in using CFD to simulate large-scale flows. This is due to the increasing availability of powerful computers and the development of new CFD algorithms. As a result, CFD is now being used to simulate flows in a wide range of applications, including:The design of wind turbines and other renewable energy devices.The study of weather and climate patterns.The simulation of blood flow in the human body.The design of nuclear reactors.CFD simulations of large-scale flows can be very complex and challenging. However, they can provide valuable insights into the flow physics and can help to improve the design and operation of fluid systems.中文回答：计算流体力学在大规模模型中的应用。

基于CFD-DEM耦合的水力旋流器水沙运动三维数值模拟喻黎明;邹小艳;谭弘;严为光;陈立志;熊子维【摘要】针对水力旋流器内流场运动复杂、沙粒运动规律难以掌握的问题,运用基于颗粒动力学理论的欧拉-拉格朗日液固多相湍流模型,对水力旋流器内的水沙两相三维流动进行了CFD-DEM耦合数值模拟研究,分析了水力旋流器内单个沙粒的轨迹线、速度和沙粒群的运动规律、分布特性等.模拟结果表明,沙粒粒径越小,沙粒向下运行的距离越短,越容易从下降流中进入到上升流中,越难以分离.粒径为40μm的沙粒,在圆柱体与圆锥体交界面处出现沙粒峰值,分离效果易受影响,而50μm和60μm沙粒在圆锥体部分出现峰值,具有较好的分离效果.通过跟踪单个沙粒和沙粒群的运动可知,沙粒在圆柱体内主要作圆周运动,进入到圆锥体部分,沙粒既有圆周运动,又有明显的进入沉沙口的直线运动.分析大量沙粒个体和群体运动以及群体分布情况能从微观角度了解水力旋流器的分离效率,是水力旋流器性能研究的有效手段.【期刊名称】《农业机械学报》【年(卷),期】2016(047)001【总页数】7页(P126-132)【关键词】水力旋流器;水沙运动;离散元法;计算流体力学;耦合;数值模拟【作者】喻黎明;邹小艳;谭弘;严为光;陈立志;熊子维【作者单位】长沙理工大学水利工程学院,长沙410004;长沙理工大学水沙科学与水灾害防治湖南省重点实验室,长沙410004;长沙理工大学水利工程学院,长沙410004;长沙理工大学水沙科学与水灾害防治湖南省重点实验室,长沙410004;长沙理工大学水利工程学院,长沙410004;长沙理工大学水沙科学与水灾害防治湖南省重点实验室,长沙410004;长沙理工大学水利工程学院,长沙410004;长沙理工大学水沙科学与水灾害防治湖南省重点实验室,长沙410004;中南大学机电工程学院,长沙410083;湖南农业大学工学院,长沙410128【正文语种】中文【中图分类】S275.6;TQ028.5+4水力旋流器是利用离心力分离固液两相流体的高效分离设备，其结构简单、操作方便、分离效率高、占地面积小，目前被广泛应用于农业灌溉、水利等领域的水沙分离处理。

第50卷第2期2021年2月应用化工Applied ehemicoi IndustyVo550No52Fed.9021超临界水氧化/气化反应器的CFD模拟研究进展唐旭20，陈海峰2,阳明君5,徐愿坚4,陈忠49(2.陕西科技大学机电工程学院，陕西西安716242;2.中国科学院重庆绿色智能技术研究院，重庆402714；3.四川轻化工大学过程装备与控制工程四川省高校重点实验室，四川自贡643602-摘要:基于前期研究和国内外相关文献，分别从数学模型、物性数据和模拟实例三个方面回溯了CFD的发展历程，综述了最新研究进展。

总结出RNG k-v.EDC分别是纯流态、湍流-化学反应两种体系普遍采用且模拟效果最好的模型，但在面对水热燃烧、水膜形成和非均相催化等典型水热过程时,仍不能有效兼顾流体力学问题与化学反应问题;其次，超临界水热环境下多相流体的基础物性数据匮乏是CFD模拟研究的另一瓶颈;最后，指出了开发新模型并结合原位探测实验新技术是未来的重点研究方向。

关键词:反应器结构;水热燃烧;模拟;超临界水氧化;超临界水气化中图分类号:TQ09；TQ0/文献标识码:A文章编号;1671-3702(2071)02-0504-02Current resenrch precesses in CFD simulation oOsopercritichi water oxioation/gasiocetion renctoc TANG Xu p,CHEN Hai-feng1,LANG Ming-jurg,XU Yuag-jiarg,CHEN Zhong-(1.Co/eye of Mechanical and ElectWcal EngineeOngphaani University of Science&Technology,Xi'an710021,China；6.Chongqing Ins/tute of Green and InOlligent Technology,ChOese Academy of Sciences,Chongqing400714,China；3.Sichuan Provincial Kep Lad of Process Equipment and Control,Sichuan University ofScience&EngineeOng,Zigong643000,China)Abstract:Based ox tho previous research basis,tho dubopmut his//of CFD is reviewed from threo as­pects:mathematical model,physical data and simulation u—lplaspnd tho latest research is revealed.It is founded thot RNG k-s and EDC models,which result in tho bettor simulation data,are commonly used in tho situation of pure flow reyimo and turUuPut-chemicat reaction.Whita tho fluid mechanics and chemical reaction canpot bo UUt/ely tabes into scconut,whu applied in typical theonal process,such as wator theonal comUus/ox,wator film foonatiox and hbooguuxs catalysis.Moreovar, tho lach of basic physical data of multiphase fluid in supvcO/cal hypytheonal euvioxmeut is auothor Uott/uech of CFD sioula-Pon.Therefore,tho upPi/t/p of mathematical modb,which upeOout/to comUiued with tho ix-s/u detection techuoPgo wilt bo tho key poidt in tho future research.Key wordt:reactor stmctura；hypytheonal flamy；simulation;supeoO/cat water oxidation;supe/OP-cat wator pasi/catiox超临界水氧化(SupeoOtO/wator oxiOafox,SC-WO)是以超临界水(P>27.2MPp,T>374°C)为反应介质，在富氧条件下，将有机废弃物彻底矿化为H0和co-等小分子物质的高级氧化技术。

科技资讯 SCIENCE & TECHNOLOGY INFORMATION 工 业 技 术旋风分离器广泛应用于石油化工、燃煤发电和环保等许多行业。

它作为一种重要的气固分离设备,与其他气固分离设备的技术相比具有机构简单、无运动部件、分离效率高和压降适中等特点,尤其适用于高温、高压和含尘浓度高的工况。

旋风分离器内的流体是一个复杂的三维旋转流动,流体的旋转运动简称涡流。

到现在为止还不能用理论分析的方法来阐明旋流器内部的流体力学规律。

近年来,随着计算机的飞速发展,应用计算机根据计算流体力学(CF D)的原理和方法,对旋流器内部流场进行数值模拟受到越来越多学者的重视。

1 旋风分离技术旋风分离器的实际工作原理涉及到不同的学科,尤其是与旋转流动有关的流体力学、流体中颗粒的流动、颗粒特性等知识。

旋风分离器的性能评价主要是总分离效率、分级效率和压降。

因此我们可以分析得出影响旋风分离器性能的主要因素为结构参数、粉尘的物理性质和分离器的运行参数。

为了可以实现对结构参数和运行参数的合理性和高度可控性,有必要研究旋风分离器的内部流场特性,在这过程中CFD技术是除了实验外的可准确分析内部流场特性的唯一手段。

2 CFD技术C F D软件将一些难懂的程序代码打包,因此该项技术更易于掌握和使用,它可以快速地、相对准确地计算并表示旋风分离器内部流场的流动情况,如速度、压力、浓度甚至湍流动能的分布,可以进一步对流场进行预测和分析,同时也可以通过分析提出问题和解决问题。

常用的CFD商用软件有P HOENICS、CFX、STAR－CD、FIDIP、FLUENT等多个商用CFD软件,这些软件的功能比较全面、适用性强;具有比较易用的前后处理系统和与其他CAD及CFD软件的接口能力;具有比较完备的容错机制和操作界面,稳定性高;可在多种计算机、多种操作系统,包括并行环境下运行。

本文中主要应用了ANSYS ICEM CFD和FLUENT CFD应用软件进行模拟和分析。

CFD SIMULATIONS OF HYDROCYCLONES WITHAN AIR COREComparison Between Large Eddy Simulations and a SecondMoment ClosureM.BRENNANÃThe Julius Kruttschnitt Mineral Research Centre,The University of Queensland,Queensland,AustraliaC FD simulations of the75mm hydrocyclone of Hsieh(1988)have been conductedusing Fluent TM.The simulations used3-dimensional bodyfitted grids.The simu-lations were two phase simulations where the air core was resolved using the mixture (Manninen et al.,1996)and VOF(Hirt and Nichols,1981)models.Velocity predictionsfrom large eddy simulations(LES),using the Smagorinsky–Lilly sub grid scale model(Smagorinsky,1963;Lilly,1966)and RANS simulations using the differential Reynoldsstress turbulence model(Launder et al.,1975)were compared with Hsieh’s experimental vel-ocity data.The LES simulations gave very good agreement with Hsieh’s data but requiredveryfine grids to predict the velocities correctly in the bottom of the apex.The DRSM/RANS simulations under predicted tangential velocities,and there was little differencebetween the velocity predictions using the linear(Launder,1989)and quadratic(Spezialeet al.,1991)pressure strain models.Velocity predictions using the DRSM turbulencemodel and the linear pressure strain model could be improved by adjusting the pressurestrain model constants.Keywords:computationalfluid mechanics;hydrocyclone;turbulence;second-momentclosure;large eddy simulation.INTRODUCTIONCyclone separators are used extensively in the chemical and mineral processing industries to remove or classify par-ticles in particle ladenfluidflows.Cyclones rely on the cen-trifugal forces that develop under the swirlingflow inside the cyclone body to effect the separation and can classify on density or particle size.Cyclone separators are essen-tially passive devices,with a short residence time,which makes them easy to run.However,the fact that cyclones treat particle-ladenflows means that wear and its minimiz-ation is a major operational problem.Further the classifi-cation behaviour is influenced by the cyclone shape,the flowfield and theflow turbulence.Modelling the hydrodynamics of hydrocyclones by com-putationalfluid dynamics(CFD)is a key to understanding how they behave,however,the CFD is a non-trivial computational challenge for several reasons.Theflow is turbulent.Hydro-cyclones operate with a strong swirl together with aflow reversal,and aflow separation,near the underflow.This makes theflow strained and introduces anisotropy into the turbulence.Further the short residence time implies that the turbulence is not at equilibrium. Hydro-cyclones are often operated with the outlets open to the atmosphere and thus develop an air core along the axis because the swirlingflow generates an axial region of negative gauge pressure which draws air in.The free sur-face between the air and the water phase introduces further turbulence anisotropy because the turbulent stresses normal to the free surface drop to zero as the free surface is approached.Finally hydrocyclones treat particle laden flows,which influences the turbulence because particles, which are smaller than the length scale of the turbulence, are known to damp the turbulence,whilst the turbulence also influences the mixing of the particles and thus affects the partition behaviour.In this paper the results of two phase water/air CFD studies of the75mm cyclone of Hsieh(1988)are reported. In particular velocity predictions from large eddyÃCorrespondence to:Dr M.Brennan,The Julius Kruttschnitt Mineral Research Centre,The University of Queensland,Isles Rd,Indooroopilly, Queensland,4068,Australia.E-mail:m.brennan@.au4950263–8762/06/$30.00+0.00 #2006Institution of Chemical Engineers/cherd Trans IChemE,Part A,June2006 doi:10.1205/cherd.05111Chemical Engineering Research and Design,84(A6):495–505simulations(LES)and the differential Reynolds stress turbulence model(DRSM)are compared Hsieh’s(1988) LDA data.PREVIOUS CFD WORKBoysan et al.(1982)solved the Reynolds averged Navier–Stokes equations for a single phase gas cyclone using an algebraic turbulence model.Subsequently,Hsieh (1988)investigated hydrocyclones,with further publi-cations by co-workers from the University of Utah. (Hsieh and Rajamani,1991;Monredon et al.,1992; Devulapalli and Rajamani,1994,1996).Hsieh(1988) measured the velocities and turbulence parameters in a 75mm glass cyclone with a water feed and operating with an air core using laser Doppler anemometry.This data was used to validate a two-dimensional axi-symmetric CFD simulation which used a mixing length eddy viscosity turbulence model where different mixing length constants were used for the two components of the momentum equation.Although Hsieh’s CFD model required calib-ration,it was able to simulate with reasonable accuracy the average velocity profiles inside the cyclone body and demonstrated the effect of swirl andflow reversal on turbulence behaviour.Subsequently the same approach was used by Devullapalli and Rajamani(1994,1996)who modelled and measured a250mm Krebs D10hydrocyclone design.CFD studies of cyclones have continued since Hsieh’s (1988)work where authors have used various forms of the k-1model to model the turbulence(Malhotra et al., 1994;Fraser et al.,1997;He et al.,1999)but recent studies (Slack and Wraith,1997;Slack et al.,2000;Suasnabar, 2000;Cullivan et al.,2003)have suggest that the turbu-lence in hydrocyclones is too anisotropic to simulate accu-rately with two equation turbulence models and that at least a second moment(or Reynolds stress)turbulence model is needed.Slack et al.(2000)also studied theflow inside single phase gas cyclones using LES on afiner grid,and LES seemed to give good predictions.Slack et al.(2000) in particular noted that the turbulence in gas cyclones was developing,i.e.,aflow where the production of turbu-lence exceeded the turbulent dissipation.These more recent studies(Slack et al.,2000;Suasnabar, 2000;Cullivan et al.,2003)have also indicated that CFD of hydrocyclones needs a three-dimensional grid to capture asymmetries in theflow.The JKMRC has completed initial CFD studies of dense medium and classifying cyclones using Fluent TM(Brennan et al.,2002;Brennan,2003)and is using gamma ray tomo-graphy to measure density profiles in dense medium cyclones(Subramanian,2002).The density profiles from this experimental work are being used to validate the CFD modelling.The initial CFD work was a3-D simu-lation of a350mm Dutch State Mines pattern body and was a two phase simulation(air/water)which predicted the position of the air core andflow splits with reasonable accuracy.The work used the volume offluid(VOF)model (Hirt and Nichols,1981)to predict the position of the air core and the Fluent TM implementation of the differential Reynolds stress turbulence(DRSM)model.Subsequently a DRSM based multiphase approach using the mixture model(Manninnen et al.,1996)was used to simulate medium segregation(Brennan,2003),but it was apparent that medium segregation was over predicted.CFD MODEL APPROACHAveraged and Filtered Equations of Motion CFD simulations of turbulentflows have traditionally used the Reynolds averaged Navier–Stokes equations (RANS),where the equations of motion are averaged over a time scale which is long relative to the time scale of the turbulentfluctuations and hence none of the turbulent fluctuations are resolved by the simulation.The averaging operation results in six additional unknowns in the Rey-nolds averaged form of the Navier–Stokes equations which account for the transfer of momentum by the unre-solved turbulence and these unknowns are commonly called the Reynolds stresses.Model equations,typically using either a2equation,or a second moment turbulence model,must be supplied to calculate the Reynolds stresses and obtain a numerical solution.RANS turbulence models are empirical and typically are calibrated forflows where the turbulence is fully developed (or at equilibrium with respect to turbulent production and dissipation).RANS models can be recalibrated for other flows but this immediately implies that RANS models lack universality.Various modifications to RANS models have been proposed to improve their universality and the literature in this area is immense.A good discussion of the issues associated with RANS turbulence modelling has been given by Wilcox(1998).Advances in computer hardware have meant that LES are becoming practical for engineering CFD problems.In LES the larger scales of the turbulence are resolved by inte-grating the equations of motion in time and only the turbu-lent scales which are smaller than the grid are modelled. The fact that an LES resolves much of the turbulence with-out modelling implies that LES should be more accurate than a RANS simulation.With LES,the equations of motion arefiltered and the filtering operation also results in six additional unknowns which account for the transfer of momentum by turbulent eddies which are smaller than the grid.These unknowns are known as the sub grid scale(SGS)stresses and must be modelled if the equations of motion are to be solved. Whilst this re-introduces the same questions of accuracy and universality that apply to RANS models,in principle the grid can be made sufficiently small that the SGS stresses are isotropic and can be modelled simply.The disadvantages of LES are primarily computational; LES requires afiner mesh than a comparable RANS simu-lation and LES intrinsically produces an unsteady solution in time,whereas a time averaged steady state solution can usually be obtained for a RANS simulation.LES has pri-marily been used for the single phaseflows used in aerody-namic and meteorological applications and there are still unanswered questions about appropriate SGS models for the multiphaseflows encountered in mineral processing applications.The Reynolds averaged andfiltered equations of motion have a common form where t ij is a symmetric tensorTrans IChemE,Part A,Chemical Engineering Research and Design,2006,84(A6):495–505 496BRENNANcontaining the six unknown stresses which must be modelled:@r @t þ@r u i@x i¼0(1)@ @t (r u i)þ@@x j(r u i u j)¼À@@x ipþ@@x j(t m ijþt ij)þr g i(2)The Differential Reynolds Stress Turbulence Model(DRSM)The RANS simulations in this study have used the Fluent TM implementation of the DRSM which is based on the Launder et al.(1975)second moment closure and solves a transport equation for each of the six unique Reynolds stresses:t ij¼t ji¼Àr u0i u0j(3)The exact DRSM transport equations contain a number of unknown correlations which must be modelled.These unknowns are;the dissipation tensor1ij,the pressure strain correlation tensor P ij,and the turbulent diffusion of the Reynolds stresses expressed by the tensor C ijk.The Launder et al.(1975)model assumes that dissipation occurs only in the transport equations for the normal stresses and solves a transport equation for a scalar dissipation rate1(i.e.,isotropic dissipation).The Launder et al.(1975)model models C ijk using a generalized gradient diffusion hypothesis;however the Fluent TM implementation uses a simpler turbulent vis-cosity for stability reasons.The DRSM transport equations that are thus solved in Fluent TM areDDt(r u0i u0j)¼r P ijþr1ijÀr P ijþ@@x km@@x ku0iu0jþr C ijkP ij¼Àu0i u0k@u j@x kÀu0ju0k@u i@x kr C ijk¼m ts k@@x ku0iu0jr1ij¼À23d ij r1s k¼0:82(4)D Dt (r1)¼@@x jmþm te@@x j1þC1112P ii1kÀC21r12ks1¼1:09,C11¼1:44,C21¼1:92(5)The pressure strain correlation tensor P ij acts to redistribute the individual Reynolds stresses.In the case of the Launder et al.(1975)DRSM model,which assumes isotropic dissi-pation,P ij also provides the only sink in the transport equations for the shear components of the Reynolds stres-ses.Modelling P ij has been the subject of much research and most workers have taken the approach where P ij is the sum of slow and fast terms(Wilcox,1996):P ij¼A ijþM ijkl@u k@x l(6)Both the slow pressure strain term A ij and the fast pressure strain term M ijkl are assumed to be functions of the magni-tude of what is commonly called the Reynolds stress aniso-tropy tensor b ij:b ij¼u0iu0jÀð2=3Þk d ij2k(7)The slow pressure strain term A ij redistributes the Reynolds stresses based on their magnitude and is also called the return to isotropy term,whilst the fast pressure strain term M ijkl is multiplied by the velocity gradients and this sensitises the pressure strain model(and redistributes the Reynolds stresses according to)toflow strain,flow rotation, Reynolds stress production and convection of the Reynolds stresses.Most models for A ij and M ijkl are truncated taylor series expansions in b ij.However,the higher order expan-sions generate a large number of additional terms contain-ing adjustable constants and much of the research work seems to attend to reducing these terms to a manageable level.Fluent TM has a number of options for P ij and in this work the linear pressure strain(LPS)model of Launder et al.(1989)with the wall reflection term and the quadratic pressure strain(QPS)model of Speziale et al.(1991)were used.The LPS model is linear in b ij whilst the QPS is a quadratic expansion in b ij and the QPS allows for strained flows where Reynolds stress redistribution would be non-linear.In particular the QPS does not need the LPS wall reflection term,which introduces a non linear function into the LPS in the vicinity of a boundary,to model the cor-rectflow behaviour in wall bounded regions.Large Eddy Simulation(LES)In a LES,t ij in equation(2)contains the sub grid scale stresses,which in this work are modelled with the Smagorinsky–Lilly(Smagorinsky,1963;Lilly,1966)model:t ijÀ13t kk d ij¼À2m t,s S ij(8)The Smagorinsky–Lilly model calculates the SGS eddy vis-cosity algebraically from a length scale L s and the mean local strain ratem t,s¼r L s S j j(9)L s is normally equal to a third power of thefinite volume size at each grid point in regions of high turbulence but the Fluent TM implementation also makes L s a function of theTrans IChemE,Part A,Chemical Engineering Research and Design,2006,84(A6):495–505CFD SIMULATIONS OF HYDROCYCLONES WITH AN AIR CORE497distance from the wall in wall bounded regions:L s¼min(k d,C s V1=3g)(10) C s is the SGS calibration constant which in this work was0.1.Air Core ModellingMultiphaseflows can be simulated using a full Eulerian multiphase model,which is the most sophisticated approach but solves a full set of transport equations for each phase in the mixture.The mixture model(Manninnen et al.,1996)is a less numerically intensive approach to simulating multiphaseflows where one of the phases is dis-persed.The mixture model is derived from the full Eulerian multiphase transport equations by making two simplifying assumptions:(i)that the dispersed phases are moving at their terminal slip velocity relative to the continuousfluid phase and(ii)the interphase momentum transfer can be for-mulated by a simple drag calculation.Assumption(i)obvi-ates the need to solve separate momentum equations for each phase in the system and the mixture model only solves the equations of motion for thefluid mixture and transport equations for the volume fractions of any additional dispersed phases@@ta kþrÁ(a k u m)þrÁ(a k u km)¼0u km¼u kÀu m(11)The u km is the drift velocity of the phase k with respect to the mixture and is calculated from the slip velocities of the other dispersed phases:u km¼u kcÀX nl¼1a k r kr mu lcu kc¼u kÀu c(12)u kc is the slip velocity of the dispersed phase k relative to the continuousfluid phase c and is calculated from the equilibrium drag assumption.A further simplification of the mixture model is the VOF (Hirt and Nichols,1981).The VOF model is designed to model multiphaseflows where the phases segregate totally. It solves the equations of motion for the mixture and an additional transport equation for each additional phase which is essentially identical to equation(11)except that the drift velocity u km is not calculated.In this work the air core has been simulated with both the mixture and VOF models and the results are compared because both models have applications in solving CFD of the multi-phaseflows encountered in mineral processing.The VOF model is best suited to model CFD problems where there is a clear air/water free surface between a continuous air and a continuous water phase.By comparison the primary purpose of the mixture model is to model dispersed phases and should be suitable for modelling many mineral slurries because the slurry particles are often less than1mm in diam-eter,and accelerate to their terminal slip velocity quickly. However,the mixture model can be still be used to model a continuous air phase and in the context of hydro-cyclones can treat a case where air is present both as a dispersed phase in the feed,and as a continuous phase in the air core.Grid,Boundary Conditions and Problem Set Up The simulations used Fluent TM V6.Initial work was done using V6.1.22and more recent work used6.2.15. Three dimensional bodyfitted grids were used with an accurate geometric model of the Hsieh cyclone body con-sisting of the feed port,main body and vortexfinder.The grids were generated using Gambit TM using the Cooper meshing facility;however the grids have been set up so that in the main body they were essentially a cylindrical O grid.The feed port used a velocity inlet boundary con-dition,whilst the underflow and overflow were pressure Table1.Grids used in simulations showing number of grid points in each coordinate.Radial is the number of points between the vortexfinder and outer wall.Total is the total number of volume elementsPars1234Axial102112204224 Radial30406080 Tangential44448888 Total 2.31Â105 3.14Â10518.5Â10525.1Â105 Figure1.Image of grid used in hydrocyclone simulations showing feed port,and detail of underflow.Trans IChemE,Part A,Chemical Engineering Research and Design,2006,84(A6):495–505 498BRENNANoutlet boundary conditions.Figure1shows an outline of a typical grid and two features of the grid should be noted. Firstly a circular inlet port was used and this was meshed and merged with the main grid by projecting the face meshes from the port inlet and a surrounding section of the cyclone wall in to the outer wall face of the vortex finder.Secondly the grid was graded radially near the underflow so that a fairly coarse grid existed in the region expected to be occupied by the air-core.Four grids are reported here and the grid parameters are shown in Table1.The number of axial mesh points is the total number including the upper body and apex. The number of radial mesh points is the number between the wall and the vortexfinder,whilst10points were used radially inside the vortexfinder.Grids1and2,which are the coarser grids,were gener-ated directly using Gambit.However grid3and grid4 which are thefiner grids were generated using grid adap-tation where grid3was generated from grid1and grid4 was generated from grid2.The standard Fluent TM grid adaptation algorithm was used where the entire grid in a steady case study was adapted.The yþin wall bounded grid points was between50and 100for grid1and was between20and40for grid4,so standard wall functions were used for the DRSM simu-lations.In the cases of simulations using LES,these values of the wall bounded yþimply that the log layer was being resolved but the viscous sub layer and transition region were being modelled.Hsieh(1988)conducted measurements on a cyclone where the air core was fully developed and theflow and tur-bulence have reached a time averaged steady state.The simulations reported here are for similar steady operation. The following strategy was evolved because it could obtain,with reasonable reliability,a case study with steadyflow and a stable air core.Other approaches were tried but the cases invariably diverged:1.The case was initialised with a cyclone full of waterwith the backflow air volume fraction set to zero on overflow and underflow boundary conditions.2.The case was run using the steady solver and the stan-dard k-1model for approximately200iterations.3.The DRSM model with the LPS option was then enabledand the case ran for about25iterations using the steady solver and then the unsteady solver(fixed time step)was enabled and the simulation was ran as a time integration till a central axial core of negative pressure formed, which led to a reversedflow on the overflow and under-flow boundary conditions.4.The backflow air volume fraction on both the overflowand underflow boundary conditions was then set to1and the simulation was run using the unsteady solver until the air core was fully developed and overflow and underflow massflow rates matched the feedflow rate. The steady case study using DRSM/LPS/VOF was saved as a base case and was used as the starting case for other case studies using other model options.The methodology[steps(1)–(4)]does not realistically represent the actual dynamics of air core development, because in reality the backflow air volume fraction is1 from start up.However,perturbations of thefinal steady cases always saw the case stabilise back to the sameflow split and velocities and hence the predictions should be independent on how the case wasfirst evolved.The simulations were run on Silcon Graphics Altix ser-vers which are part of the Queensland Parallel Supercom-puting Foundation.PRESTO discretization was used for pressure.HRIC discretization was used for the air volume fraction with the VOF model and QUICK was used with the air volume fraction with the mixture model.All other equations used QUICK.HRIC and QUICK discretization have been compared using the VOF model and predict essentially the same velocities,but the HRIC option gave a sharper resolution of the air/water free surface.The simulations were time consuming.In the case of the DRSM simulations,a velocity data set could be generated after a week of simulations.The LES on thefiner grids took considerably longer even though parallel processing was used.ResultsHsieh(1988)reported time averaged velocities.LES is intrinsically a dynamic simulation and will resolve the large scale turbulentfluctuations plus any periodic effects, even when the simulation has reached a time-averaged steady state.To compare LES predictions with time averaged velocity data the LES instantaneous velocities must be aver-aged over a sufficiently long sample time.In this work each LES was run at time averaged steadyflow and a set of instan-taneous velocity predictions were generated from the LES at fixed1023s intervals.This set of instantaneous velocity pre-dictions was then averaged externally.Over200sets of instantaneous data from the LES were found to be sufficient to give good predictions of the mean velocities.The DRSM simulations reached a true steady state with no fluctuations in the computed velocities.Hence the predicted velocities for the DRSM simulations presented in this work are also an average of between four and10sets of instan-taneous velocities as calculated by the solver,generated at 0.1s intervals,after the simulation reached steadyflow.All simulations were conducted using a water feed rate of 1.1165kg s21which is equivalent to Hsieh’s(1988)series1 data.Hsieh(1988)measured axial velocities at four tangen-tial positions of08,908,1808and2708and measured tangen-tial velocities at0and1808where the0–1808plane was normal to the feed port.In this work,axial velocity predic-tions are reported in the90–2708plane and tangential vel-ocity predictions are reported in the0–1808plane at60, 120,180and240below the top of the cyclone.Figure2shows a comparison between the axial vel-ocities measured by Hsieh(1988)in the90–2708plane and those predicted by the CFD using the DRSM turbu-lence model with the linear pressure strain correlation and the VOF model whilst Figure3compares tangential velocities in the0–1808plane for the same simulations. The simulations are compared at60mm,120mm and 180mm,for grids1,2and3.The results for the axial velocities in Figure2show that the DRSM turbulence model predicts the axial velocities well at60mm,but under predicts the axial velocities at lower levels.Further the DRSM turbulence model does not predict correctly the asymmetry in the measured axial velo-cities.Figure3shows that the DRSM model consistently under predicts the tangential velocities at all levels andTrans IChemE,Part A,Chemical Engineering Research and Design,2006,84(A6):495–505CFD SIMULATIONS OF HYDROCYCLONES WITH AN AIR CORE499that this under prediction of the tangential velocities is actually worse with grids 2and 3,which are the finer grids.Figure 4shows a comparison between Hsieh’s (1988)measured velocities at 120mm and DRSM predictions using;the LPS option with the VOF model,the QPS option with the VOF model and the LPS option with the mixture model.The simulations with the mixture model treated the air as a dispersed phase with a notional particle size of 1.0Â1024m.The simulations with the Mixture model treated the air as a dispersed phase with a notional particle size of 1.0Â1024m.Figure 4shows that the VOF and mixture models predict essentially the same velocities.This is to be expected as the only difference between the two models is that the mixture model calculates a drift velocity in the air phase transport equation.This will only be non-zero in the region of the domain where the air /water free surface is located and this will have the effect of driving the air inwards under the centrifugal forces,resulting in a sharper numerical prediction of the phase boundary.This will feed back into the momentum equation through the density gradient across the free surface,but the density gradient is much the same with both models and is in the same location.Figure 4shows that the QPS model predicts marginally better axial velocities than the LPS model near the air /water phase boundary but in the main part of the flow the LPS and QPS axial velocity predictions are essentially the same.Figure 4also shows that tangential velocity predictions from the LPS and QPS are almost identical with both models under predicting the tangential velocities to the same extent.The fact that the DRSM turbulence model as used here under predicts the tangential velocities in Hsieh’s cyclone,irrespective of grid refinement,implies that there is a pro-blem with the DRSM turbulence model for thisflow.Figure parison between axial velocities measured by Hsieh (1988,Series 1)and axial velocities predicted by CFD using RSM with LPS and VOF for air core at 60mm,120mm and 180mm below the top of cyclone in the 90–2708plane.Shows effect of differentgrids.Figure parison between tangential velocities measured by Hsieh (1988,Series 1)and tangential velocities predicted by CFD using RSM with LPS and VOF for air core at 60mm,120mm and 180mm below the top of cyclone in the 0–1808plane.Shows effect of different grids.Trans IChemE,Part A,Chemical Engineering Research and Design ,2006,84(A6):495–505500BRENNAN。

CFD模拟注水涡轮叶片的清洗清洁涡轮叶片的水注入CFD模拟，已进行预测的水在一个固定刀片上进行覆盖，这将使的热气流和冷的水滴之间地相互作用变得更好理解。

一个通用配置中使用的一个之前已经验证的内部实验，为CFD验证提供试验数据。

两相流CFD 模型采用欧拉-拉格朗日方法，使空气流动被视为连续相，水液滴分散相。

CFD 预测与实验结果吻合较好的发现，特别是水覆盖对下游叶片排。

此外，CFD建模提供了进一步的细节，包括液滴的轨迹，这是很难获得的实验，但非常有用地了解了流动物理。

关键词：CFD数值模拟；注水；叶片清洗1.问题背景废气涡轮增压器是一个有效的增热装置，该提取物可回收能量，从发动机排气和用它最初的旋转涡轮压缩环境空气，因此，提高发动机输出功率[ 1-3 ]。

涡轮增压器的整体性能是直接与工作流体的温度、系统压力有关的，另外它还受到许多因素的影响。

一个典型的例子是燃料质量。

劣质柴油燃料的广泛应用降低运行成本，但它可以在一般的生产气体混合物包含有害污染物[ 4 ]。

这样做的后果是快速的喷嘴喉部被堵塞，叶片被腐蚀和损坏等等，导致发动机性能下降。

而由行业劣质柴油燃料的使用在可预见的未来似乎是不可避免的，一个工程问题的解决方案是将一个在线水冲洗系统的运作，每天取出一些存款累计。

该方法已在工业产品中的实现，提高了设备的使用寿命。

然而，在水洗机理的认识仍然有限，部分是由于环境的复杂性，即热气体的混合物与冷水流的相互作用，以及对实验数据的不足。

情况会变得更加复杂，在现场工况，情况会变得更加复杂，在现场的发动机运转条件下，其高度不稳定，由于脉冲的影响从柴油机活塞，通常是在室内试验的能力：很少有试验数据到目前为止指导产品设计。

随着数值方法的发展和改进的流等物理湍流的传热和传质的建模技术，进行了CFD研究预测广泛的流动行为，现在是可行的，在具体操作的免费环境。

鉴于此，结合实验和数值研究在热气流中水滴进行了了解，在一个固定的涡轮叶栅气水两相流动。

吸附储氢过程的CFD模拟彭荣1,2*，肖金生2,3,4，丹尼尔∙科瑟曼4,皮埃尔∙贝纳德4，理查德∙夏因4（1武汉理工大学材料科学与工程学院，湖北430070, E-mail：lingyunpeng85@）（2武汉理工大学材料复合新技术国家重点实验室，湖北430070）（3武汉理工大学汽车工程学院，湖北430070）（4加拿大三河城魁北克大学氢能研究所，魁北克G9A 5H70）摘要：高比表面积活性炭由于具有生产成本低、储氢量高等优点而成为近年的研究热点[1]，特别是吸附储氢的研究越来越受到重视[2]。

本文基于修正的D-A吸附等温线模型、线性驱动力（LDF）模型，运用计算流体动力学（CFD）软件Fluent模拟在冰水冷却情况下活性炭储氢的充气、休眠和放气过程，并利用氦气的充气、休眠和放气过程进行比较分析。

研究充气、休眠和放气过程中的压力变化、温度和吸附量的分布情况，并与实验结果进行比较验证，结果表明模拟值与实验值吻合较好。

在此基础上，分析有效热导率、活性炭热导率及等温吸附热对充、放气过程中储氢罐内压强、温度及吸附量的影响，确定线性驱动力方程中的k值、活性炭热导率及等温吸附热的合理取值。

部分结果如图1和图2所示。

关键词：活性炭;吸附; 储氢; Fluent；模拟[1]Bénard P, Chahine R. Comparison of hydrogen adsorption on nanoporous materials. Journal of Alloys andCompounds，2007, 446-447: 380-384[2]Ahluwalia R K, Peng J K. Automotive hydrogen storage system using cryo-adsorption on activated carbon.International Journal of Hydrogen Energy, 2009, 34: 5476-5487通讯作者介绍：彭荣，男，硕士研究生，研究方向新能源材料与技术CFD modeling process of adsorptive hydrogen storage on activated carbonRong Peng1, 2*, Jinsheng Xiao2, 3, 4, Daniel ∙ Ke Seman，Pierre Benard4, Richard Chahine4 (1School of Materials Science and Engineering, Wuhan University of Technology, Hubei 430070,China E-mail：lingyunpeng85@）(2State Key Laboratory of Advanced Technology for Materials Synthesis and Progressing,Wuhan University of Technology, Hubei 430070, China)(3School of Automotive Engineering, Wuhan University of Technology, Hubei 430070, China）(4Hydrogen Research Institute, University of Quebec at Trois-Rivieres, QC, G9A 5H7, Canada)Abstract: Due to the advantages of the low cost of production，high hydrogen storage capacity and so on, high surface area activated carbon have became a focus of research in recent years, especially the research of adsorptive hydrogen storage on activated carbon have been pay more and more attention to. This paper use computational fluid dynamics (CFD) Fluent software to simulates the hydrogen adsorption process of charging，dormancy and discharging in the case of i ce water cooling, and use the process of charging,dormancy and discharging of helium to study it, based on the revised D-A adsorption isotherm model and Linear Driving Force （LDF）model. We study the changes of temperature and pressure and the distribution of adsorption during the process of charging，dormancy and discharging, and the results are compared with experiment. The results show that the experimental value good agreement with the Simulation value .On this basis, we analysis the affect of effective thermal conductivity, thermal conductivity of activated carbon and isothermal heat of adsorption on the hydrogen storage tank pressure,temperature and adsorption capacity during the process of charging and discharging, and to determine the Rational k value in the linear driving force equation and the value of the isothermal heat of adsorption.Key words:activated carbon; adsorptive; hydrogen storage; Fluent；modelingRong Peng: Postgraduate;School of Materials Science and Engineering, Wuhan University ofTechnology, Hubei 430070, China。

现代制造工程2010年第4期试验研究CF D在计算船舶螺旋桨敞水性能中的应用研究3刘丹,陈凤馨(南京工业大学机械与动力工程学院,南京210009)摘要:对流场中螺旋桨的敞水性能进行研究。

利用Pr o/E软件对螺旋桨进行三维建模,通过剖面坐标转换绘出桨叶的剖面型线,利用创建实体功能得到螺旋桨实体模型。

用CF D软件对螺旋桨在不同进速系数下的推力系数、转矩系数以及推进效率进行模拟,并且对三种湍流模型的计算结果进行比较分析。

对采用Fluent软件计算螺旋桨敞水性能的过程进行详细介绍,并给出敞水性能曲线的计算结果。

与试验结果的比较分析表明,数值模拟的结果可以满足工程应用要求。

关键词:CF D软件;螺旋桨;敞水性能;三维建模中图分类号:TP391　文献标识码:A　文章编号:1671—3133(2010)04—0018—04Appli ca ti on research of CFD about ca lcul a ti on ofpropeller open wa ter performanceL IU Dan,CHE N Feng2xin(Nanjing University of Technol ogy,Nanjing210009,China)Abstract:Studied the open water perfor mance of p r opeller in the fl ow fields.Three2di m ensi onal model was built for p r opeller by the Pr o/E,the p r ofile line of blade is described based on coordinate transfor mati on,in additi on,by using the entity functi on,the s olid model of p r opeller was created.Under different advance coefficients,the thrust coefficient,t orque coefficient and p r opulsive efficiency of the p r opeller have been si m ulated by the CF D.The calculati on results of the three turbulent models were analyzed.The detail p r ocess of using Fluent t o calculate the open water perfor mance of p r opeller was intr oduced,thr ough which the open water perf or mance curve was p r ovided.A comparis on bet w een the analysis results and the experi m ental results showed that the nu merical si m ulati ons can be used for engineering app licati on.Key words:CF D;p r opeller;open water perf or mance;three2di m ensi onal model0　引言螺旋桨设计的主要问题是在满足螺旋桨吸收轴功率、拉力和转速的前提下,力求使螺旋桨的质量小,效率高,噪声小,并保证具有一定的结构安全余度。