J.Fluid Mech.(2010),vol.661,pp.482–510.c Cambridge University Press2010
doi:10.1017/S002211201000306X
Discrete particle simulation of particle–?uid ?ow:model formulations and their applicability Z.Y.Z H O U,S.B.K U A N G,K.W.C H U
A N D A.B.Y U?
Laboratory for Simulation and Modelling of Particulate Systems,School of Materials Science and Engineering,The University of New South Wales,Sydney NSW2052,Australia
(Received3September2009;revised28May2010;accepted28May2010;
?rst published online25August2010)
The approach of combining computational?uid dynamics(CFD)for continuum?uid and the discrete element method(DEM)for discrete particles has been increasingly used to study the fundamentals of coupled particle–?uid?ows.Di?erent CFD–DEM models have been used.However,the origin and the applicability of these models are not clearly understood.In this paper,the origin of di?erent model formulations is discussed?rst.It shows that,in connection with the continuum approach,three sets of formulations exist in the CFD–DEM approach:an original format set I, and subsequent derivations of set II and set III,respectively,corresponding to the so-called model A and model B in the literature.A comparison and the applicability of the three models are assessed theoretically and then veri?ed from the study of three representative particle–?uid?ow systems:?uidization,pneumatic conveying and hydrocyclones.It is demonstrated that sets I and II are essentially the same,with small di?erences resulting from di?erent mathematical or numerical treatments of a few terms in the original equation.Set III is however a simpli?ed version of set I. The testing cases show that all the three models are applicable to gas?uidization and,to a large extent,pneumatic conveying.However,the application of set III is conditional,as demonstrated in the case of hydrocyclones.Strictly speaking,set III is only valid when?uid?ow is steady and uniform.Set II and,in particular,set I,which is somehow forgotten in the literature,are recommended for the future CFD–DEM modelling of complex particle–?uid?ow.
Key words:?uidized beds,granular media,particle–?uid?ows
1.Introduction
Coupled particle–?uid?ow can be observed in almost all types of particulate processes which are widely used in industry.Understanding the fundamentals governing the?ow and formulating suitable governing equations and constitutive relationships are of paramount importance to the formulation of strategies for process development and control.This necessitates a multi-scale approach to understanding the phenomena at di?erent time and length scales(see e.g.Villermaux1996;Xu& Yu1997;Li2000;Tsuji2007;Zhu et al.2007).The existing approaches to modelling particle?ow can generally be classi?ed into two categories:the continuum approach at a macroscopic level and the discrete approach at a microscopic level.In the ?Email address for correspondence:a.yu@https://www.doczj.com/doc/612504007.html,.au
Discrete particle simulation of particle–?uid?ow483 continuum approach,the macroscopic behaviour is described by balance equations, e.g.mass and momentum,closed with constitutive relations together with initial and boundary conditions(see e.g.Anderson&Jackson1967;Ishii1975;Gidaspow 1994;Enwald,Peirano&Almstedt1996).The discrete approach is based on the analysis of the motion of individual particles,i.e.typically by means of the discrete element method(DEM)(Cundall&Strack1979).The method considers a?nite number of discrete particles interacting by means of contact and non-contact forces, and every particle in a considered system is described by Newton’s equations of motion.On the other hand,?uid?ow can be modelled at di?erent time and length scales from discrete(e.g.molecular dynamic simulation,lattice Boltzman,pseudo-particle method)to continuum(direct numerical simulation,large-eddy simulation and other conventional computational?uid dynamics(CFD)techniques).Di?erent combinations of models for the particle phase and?uid phase can be made,and their relative merits in describing particle–?uid?ow have been discussed(see e.g.Yu2005; Zhu et al.2007).
Two popular combinations are widely used to describe particle–?uid?ow:the two-?uid model(TFM)and CFD–DEM.In TFM,both?uid and solid phases are treated as interpenetrating continuum media in a computational cell which is much larger than individual particles but still small compared with the size of process equipment(Anderson&Jackson1967).However,its e?ective use heavily depends on the constitutive or closure relations for the solid phase and the momentum exchange between phases,which are often di?cult to obtain within its framework; this is particularly true when dealing with di?erent types of particles that should be treated as di?erent phases.In CFD–DEM,the motion of discrete particles is obtained by solving Newton’s second law of motion as used in DEM,and the?ow of continuum?uid by solving the Navier–Stokes equations based on the concept of local average as used in CFD,with the coupling of CFD and DEM through particle–?uid interaction forces(Xu&Yu1997).The main advantage of CFD–DEM is that it can generate detailed particle-scale information,such as the trajectories of and forces acting on individual particles,which is key to elucidating the mechanisms governing the complicated?ow behaviour.With the rapid development of computer technology, the CFD–DEM approach has been increasingly used by various investigators to study various particle–?uid?ow systems as,for example,reviewed by Zhu et al.(2007,2008). The implementation of a CFD–DEM model,as pointed out by Feng&Yu(2004a), lies in three aspects:the formulation of governing equations,the coupling scheme for numerical computation and the calculation of particle–?uid interaction forces.The latter two have been well discussed,particularly for monosized particles(Feng&Yu 2004a;Zhu et al.2007).However,the?rst aspect is not well established.In fact, two models,called model A and model B,have been used by di?erent investigators, and there are con?icting views regarding their applications(Hoomans et al.1998; Xu&Yu1998;Kafui,Thornton&Adams2002,2004;Feng&Yu2004a,b;Di Renzo&Di Maio2007).Xu&Yu(1998)pointed out that the interpretation of the ?uid–particle interaction force is di?erent for both models,but both the methods can meet the requirement that the bed pressure drop balances the bed weight at minimum ?uidization and hence are valid for?uidization.Kafui et al.(2002)discussed model A and model B,and summarized the models used by di?erent research groups. Nevertheless,their claim that model A best captures the essential features of a ?xed/?uidized bed was questionable,as noted by Feng&Yu(2004b)and Kafui et al.(2004).It is now clear that the two models have little signi?cant di?erence when applied to gas?uidization of monosized particles.It is not clear which is
484Z.Y.Zhou,S.B.Kuang,K.W.Chu and A.B.Yu
better when applied to the modelling of?uidization of particle mixtures,but this
problem is related to the calculation of particle–?uid interaction forces.In fact,how
to calculate the?uid drag force acting on a particle in a mixture is still an open
problem(Feng&Yu2004a;Beetstra,van der Hoef&Kuipers2007).More recently,
the two models were further discussed by Di Renzo&Di Maio(2007).These authors
claimed that model B is only valid at the minimum?uidization condition,contrary
to those by other investigators(Kafui et al.2004;Feng&Yu2004b).Therefore,
although the CFD–DEM approach is now widely used,its theoretical background
is not fully established.In fact,to date,there are still some basic questions which
need to be answered.For example,what are the origins of di?erent models such as
model A and model B?What are the exact di?erences between those models?What
is the applicability or limitation of a particular model,and which model is the most
appropriate for modelling di?erent particle–?uid?ow systems?
This paper provides our answers to those questions.Firstly,the origins of di?erent
formulations in the continuum approach are explored.It is argued that three models,
rather than two,exist in the continuum approach.Then,it is demonstrated that
corresponding to the continuum approach,there are three models in the CFD–
DEM approach.The relationships between the three models are discussed,and
their applicability is analysed theoretically and veri?ed in a comparative study of
three representative particle–?uid?ow systems:?uidization,pneumatic conveying
and hydrocyclones.
2.Theoretical treatments
2.1.Origin of di?erent model formulations in the continuum approach
The model formulation in the continuum approach to describing particle–?uid?ow,
focused on gas–solid?ow in?uidization,has been proposed since the1960s,including
those,for example,by Anderson&Jackson(1967),Ishii(1975),Gidaspow(1994),
Enwald et al.(1996)and Jackson(1997).In practice,di?erent sets of governing
equations from di?erent resources have been used(e.g.Arastoopour&Gidaspow
1979;Lee&Lyczkowski2000;van Wachem et al.2001).However,the area has
been well established,as recently summarized by Prosperetti&Tryggvason(2007).
Unfortunately,this is not the case in the CFD–DEM approach,as described in §1.On the other hand,the derivation of CFD–DEM models is closely related to the continuum approach due to the fact that?uid?ow is still modelled at the
macroscopic local average level.Thus,it is helpful to start our discussion with the
TFM approach.
In the continuum approach,both?uid and solid phases are treated as continuous
media.Anderson&Jackson(1967)used the local average method to directly derive
the?uid governing equation on the basis of the point equation of motion of the?uid,
and the solid phase governing equation on the basis of the equation of motion for the
centre of mass of a single particle.They obtained the?rst set of governing equations
(set I):
ρfεf[?(u)/?t+?·(uu)]=?·ξ?n f i+ρfεf g(?uid phase),(2.1)
ρsεs[?(v)/?t+?·(vv)]=nΦ??·S+n f i+ρsεs g(solid phase),(2.2) whereεf andεs(=1?εf)are,respectively,volume fractions of?uid and particles.ξis?uid stress tensor,Φis the local mean value of particle–particle interaction force,S is the tensor representing‘Reynolds stresses’for the particle phase,f i is
Discrete particle simulation of particle–?uid?ow485 the local mean value of the force on particle i by its surrounding?uid and n is the number of particles per unit volume.This cannot be used unless the undetermined terms or dependency ofξ,Φ,S and f i on the voidage,the local mean velocities and the pressure are known.In order to solve the problem,Anderson&Jackson(1967) derived some constitutive equations,including:(i)combination of nΦand??·S into ??·ξs which represents the solid stress tensor;(ii)ξandξs are analogous to that
for the stress tensor in a Newtonian?uid,and written intoξ=?pδk+f(λ,μ,u), where p is the local mean?uid pressure andλ,μare,respectively,the e?ective bulk and shear viscosities;and(iii)decomposition of n f i into two components,namely,a component due to‘macroscopic’variations in the?uid stress tensor on a large scale compared with the particle spacing,together with the other component representing the e?ect of detailed variations of the point stress tensor as the?uid?ows around a particle.That is,
n f i=n(V p?·ξ)/ V+n f i=εs?·ξ+n f i,(2.3) where V p is the volume of the particle and n f i represents the part of the total?uid–particle interaction force per unit bed volume arising from the detailed variations in the stress tensor induced by?uctuations in velocity as the?uid passes around individual particles and through the interstices between particles.It mainly includes the drag force in the direction of the relative velocity(u i?v i),and virtual mass force proportional to the mass of?uid displaced by a particle.Other forces such as the lift force can also be included.Thus,the interaction force n f i in(2.1)and(2.2)is replaced by(2.3)together with the consideration of nΦ??·S=??·ξs,giving the second set of equations(set II):
ρfεf[?(u)/?t+?·(uu)]=εf?·ξ?n f i+ρfεf g(?uid phase),(2.4)
ρsεs[?(v)/?t+?·(vv)]=εs?·ξ+n f i+ρsεs g+?·ξs(solid phase).(2.5) On comparing the governing equations in sets I and II,it can be seen that the di?erence is caused by the introduction of those constitutive equations.Anderson& Jackson(1967)commented that set I is derived directly from the basic equations of ?uid mechanics for the system,the subsequent set II re?ects their own opinion of the most appropriate form for the undermined terms in set I.
Based on set II,particle–?uid interaction force can be further written in another format(Jackson1963;Anderson&Jackson1967).In particular,to eliminate the?uid stress tensor term,an equation is obtained by multiplying(2.5)by(1?εf)/εf and subtracting from(2.4),giving
ρsεs[?(v)/?t+?·(vv)]=n f i/εf?ρfεs g+ρfεs[?(u)/?t+?·(uu)]+ρsεs g+?·ξs.
(2.6) This is an equation of motion for particles which does not contain the?uid stress tensorξ.When compared with(2.5),it can be seen that the elimination of?uid stress tensorξhas introduced a buoyancy term(?ρfεs g)and a termρfεs[?(u)/?t+?·(uu)] which represents the?uid acceleration into the particle equation of motion.The magnitude of the?uid acceleration term depends on?ow conditions.If this term approaches zero or much smaller than(n f i/εf?ρfεs g),according to(2.6),the total particle–?uid interaction force acting on particles can be written as
n f i=n f i/εf?ρfεs g.(2.7)
486Z.Y.Zhou,S.B.Kuang,K.W.Chu and A.B.Yu
Incorporating(2.7)into(2.1)and(2.2)and considering nΦ??·S=??·ξs give the third set of governing equations(set III):
ρfεf[?(u)/?t+?·(uu)]=?·ξ?[n f i/εf?ρfεs g]+ρfεf g(?uid phase),(2.8)ρsεs[?(v)/?t+?·(vv)]=?·ξs+[n f i/εf?ρfεs g]+ρsεs g(solid phase).(2.9) However,it should be pointed out that the derivation of this set of equations is conditional.Strictly speaking,the following conditions for the?uid phase should be satis?ed:
ρfεs[?(u)/?t+?·(uu)]=0.(2.10) This indicates that the?uid?ow through the particle phase should be steady and uniform(Anderson&Jackson1967;Gidaspow1994).
On the other hand,hydrodynamics models with concepts of the so-called models A and B have been widely used for the particle–?uid?ow,as discussed by Bouillard, Lyczkowski&Gidaspow(1989),and later by Gidaspow(1994)and Enwald et al. (1996).The di?erence between models A and B depends on the treatment of the pressure source term in the governing equations.Generally speaking,if the pressure is attributed to the?uid phase alone,it is referred to as model B.If the pressure is shared by both the?uid and solid phases,it is referred to as model A.Bouillard et al.(1989)attributed the origin of model A to Nakamura&Capes(1973)and Lee&Lyczkowski(1981),and that of model B to Rudinger&Chang(1964)and Lyczkowski(1978).The drag coe?cientsβA andβB are,respectively,de?ned in models A and B to calculate the particle–?uid interaction force.The applications of those two sets of governing equations and their comparison have been assessed for pneumatic conveying(Arastoopour&Gidaspow1979)and?uidization process(Bouillard et al. 1989),showing insigni?cant di?erence between the two models.Bouillard et al.(1989) commented that the main problem with model A is its stability,and being conditional on the absence of all viscous stresses and without the solid elastic modulus g(εf), while model B,which possesses all real characteristics,makes the set of equations well-posed.But Enwald et al.(1996)later clari?ed that nobody has yet proved well-posedness for a multi-dimensional initial-boundary value problem.To date,most researchers prefer model A,as re?ected by the fact that commercial software packages FLUENT and CFX both use model A.
On comparing the three formulations(sets I,II and III)with those hydrodynamics models A and B,it can be seen that in principle,model A is consistent with set II, and model B with set III.However,sets II and III are more general than models A and B but less detailed,which is another reason why the concepts of models A and B are more popular in TFM modelling.Mathematically,sets I and II(model A)are identical,as seen from the derivation of set II.Set III(or model B)is a simpli?ed form of set I with the assumption of(2.10).It should be noted that,according to the de?nition of model B,set I is also in a form of model B.Thus,model B has two types: an original model B(set I)and a simpli?ed model B.The de?ciency of simpli?ed model B has been realized by some investigators(e.g.Anderson&Jackson1967; Gidaspow1994).However,the di?erence between original model B and simpli?ed model B has not been fully recognized,and the original model B(set I)is somehow forgotten.The two models are mixed up,and only simpli?ed model B is commonly used.This has created some conceptual problems.For example,although model B or its treatment is argued to be well-posed,model A,which may be ill-posed,is more widely used due to its convenience in numerical implementation.When applied to CFD–DEM modelling,some investigators feel that the model B treatment is
Discrete particle simulation of particle–?uid?ow487 better than model A.However,because a simpli?ed model B was used,the treatment experiences problems,as discussed in§2.3.
Nevertheless,the governing equations in the continuum approach have been well established,particularly if the expressions for di?erent source terms are ignored.The challenge remaining is to develop closure laws to determine solid?ow parameters including dynamic/bulk viscosities and particle pressure,and interfacial momentum transfer in multi-sized system(Bouillard et al.1989;Enwald et al.1996;Arastoopour 2001;van Wachem et al.2001).Two approaches are commonly used to achieve this goal.One is to formulate empirical models mainly based on particle properties and(local)voidage.However,those models vary signi?cantly,depending on the conditions,as reviewed by Enwald et al.(1996).The other way is to use the so-called kinetic theory(e.g.Gidaspow1994;Iddir,Arastoopour&Hrenya2005).However, its general application is still questioned(see e.g.Campbell2006;Goldhirsch2008). Particles exhibit three?ow regimes:quasi-static,fast and in-between;to date,the success of TFM is largely limited to the fast?ow regime.This di?culty does not exist in the CFD–DEM approach,as discussed below.
2.2.Model formulations in the computational?uid dynamics–discrete element
method approach
Corresponding to the three set models in the continuum approach,CFD–DEM also has three models.However,the CFD–DEM approach is quite di?erent from the traditional TFM.In CFD–DEM,one has to consider the coupling between DEM at the particle scale and CFD at the computational cell scale.The main di?erence between the CFD–DEM and TFM approaches lies in the treatment of the particle phase.In CFD–DEM,for the particle phase,based on the soft sphere model originally proposed by Cundall&Strack(1979),a particle in a particle–?uid?ow system can have two types of motion:translational and rotational.The governing equations for the translational and rotational motion of particle i with radius R i,mass m i and moment of inertia I i can be written as
m i d v i
d t
=f pf,i+
k c
j=1
(f c,ij+f d,ij)+m i g,(2.11)
I i dωi
d t
=
k c
j=1
(M t,ij+M r,ij),(2.12)
where v i andωi are,respectively,the translational and angular velocities of the particle,and k c is the number of particles in interaction with the particle.The forces involved are:the particle–?uid interaction force f pf,i,the gravitational force m i g, and inter-particle forces between particles which include the elastic force f c,ij and viscous damping force f d,ij.The torque acting on particle i by particle j includes two components:M t,ij,generated by the tangential force,and M r,ij,commonly known as the rolling friction torque.The equations used to calculate the particle–particle interaction forces and torques have been well established in the literature(Zhu et al. 2007).Many of these have been used in our previous studies of particle–?uid?ow (Xu&Yu1997;Zhou et al.1999;Xu et al.2000;Feng&Yu2004a;Feng et al. 2004;Feng&Yu2007;Chu&Yu2008;Kuang et al.2008;Zhou,Yu&Zulli2009). The particle–?uid interaction force f pf,similar to f i in the continuum approach,is the sum of all types of particle–?uid interaction forces acting on individual particles
488Z.Y.Zhou,S.B.Kuang,K.W.Chu and A.B.Yu
by?uid,including the so-called drag force f d,pressure gradient force f?p,viscous force f?·τdue to the?uid shear stress or deviatoric stress tensor,virtual mass force f vm,Basset force f B and lift forces such as the Sa?man force f Sa?and Magnus force f Mag(Crowe,Sommerfeld&Tsuji1998).Unless otherwise speci?ed in later discussion, the buoyancy force is included in the pressure gradient force f?p.Therefore,the total particle–?uid interaction force on an individual particle i can be written as
f pf,i=f d,i+f?p,i+f?·τ,i+f vm,i+f B,i+f Sa?,i+f Mag,i.(2.13) Many correlations have been proposed to calculate the particle–?uid interaction forces,particularly the dra
g force whic
h can be based on the equation of Ergun (1952)and Wen&Yu(1966)equations,and correlation of D
i Felice(1994)or others. Details of those correlations can be found elsewhere(e.g.Crowe et al.1998;Zhu et al.2007).
For the?uid phase,its?ow is essentially governed by the Navier–Stokes equation to be satis?ed at every point of the?uid.As discussed earlier,the present interest is more focused on the particle behaviour,not?uid phase.The?ow of?uid can thus be determined at a large scale,such as a CFD cell,which may contain many particles. Consequently,the governing equations for?uid phase are obtained based on the local averaged method as used in TFM.The?uid governing equations corresponding to sets I,II and III are summarized in table1.Note that the equations to calculate the volumetric particle–?uid interaction force F pf di?er for di?erent sets,although they are all related to the particle–?uid interaction force f pf.
It should be noted thatτ=μ[?u+(?u)?1]?(2/3)μ(?·u)δk for Newtonian?uids. Corresponding to the volumetric particle–?uid interaction force terms in sets I,II and III,those force terms in(2.15)–(2.17)are respectively written by F set I
pf
(=n f i),
F set II
pf (=n f i)and F set III
pf
(=n f i/εf?ρfεs g).The de?nitions of n f i and n f i can be
found in§2.1,and their determination in CFD–DEM is described below.
The coupling of CFD and DEM is achieved mainly through the particle–?uid interaction force,which is at the computational cell level for the?uid phase(F pf in (2.15)–(2.17))and at the individual particle level for the solid phase(f pf in(2.13)). Three coupling schemes have been identi?ed(Feng&Yu2004a).In scheme1,the force on the?uid phase from particles is calculated by a local-average method as used in the TFM,whereas the force on a particle from the?uid phase is calculated separately according to individual particle velocity.In scheme2,the force on the?uid phase from particles is?rst calculated at a local-average scale as used in scheme1, then this force is distributed among individual particles according to a certain average rule.In scheme3,at each time step,the particle–?uid interaction forces on individual particles in a computational cell are calculated?rst,and the values are then summed to produce the particle–?uid interaction force at the cell scale.Theoretically,scheme 1is problematic because Newton’s third law of motion may not hold in describing the particle–?uid interaction.This problem is not there for schemes2and3,but the implementation of scheme2needs to introduce an extra assumption or numerical treatment at a CFD cell level to distribute the particle–?uid forces among the particles in the cell.Because scheme3represents the basic features of CFD–DEM modelling from particle scale to computational cell scale,it is more reasonable and logical.In fact,it has been widely used since its introduction by Xu&Yu(1997).Thus,the total volumetric particle–?uid interaction force n f i in a computational cell of volume V
Discrete particle simulation of particle–?uid?ow489
Mass conservation:?(εf)/?t+?·(εf u)=0.(2.14) Momentum conservation(and corresponding particle–?uid interaction force).
Set I:
?(ρfεf u)/?t+?·(ρfεf uu)=??p?F set I
pf
+?·τ+ρfεf g,(2.15a)
where F set I
pf =
1
V
n
i=1
f d,i+f?p,i+f?·τ,i+f i
,
and f pf,i=f d,i+f?p,i+f?·τ,i+f .(2.15b) Set II:
?(ρfεf u)/?t+?·(ρfεf uu)=?εf?p?F set II
pf
+εf?·τ+ρfεf g,(2.16a)
where F set II
pf =
1
V
n
i=1
f d,i+f i
,and f pf,i=f d,i+f?p,i+f?·τ,i+f .(2.16b)
Set III:
?(ρfεf u)/?t+?·(ρfεf uu)=??p?F set III
pf
+?·τ+ρfεf g,(2.17a)
where F set III
pf =
1
εf V
n
i=1
f d,i+f i
?1
V
n
i=1
ρf V p,i g
,
and f pf,i=(f d,i+f i)/εf?ρf V p,i g.(2.17b) Notes.(1)The governing equations for particle phase are given by(2.11)and(2.12).
(2)f i=f vm,i+f B,i+f Sa?,i+f Mag,i is the sum of particle–?uid interaction forces on particle i, other than the drag,pressure gradient and viscous forces which are often regarded as the dominant forces in particle–?uid?ow.
Table1.Formulations of di?erent models in the CFD–DEM approach.
can be determined by
n f i=
1
V
n
i=1
(f pf,i)=
1
V
n
i=1
(f?p,i+f?·τ,i+f d,i+f vm,i+f B,i+f Sa?,i+f Mag,i).
(2.18)
Equation(2.18)represents the total particle–?uid interaction force in a cell determined at a particle scale.According to(2.3),the total force in a cell in the continuum approach can be further rewritten as
n f i=?εs?p+εs?·τ+n f i.(2.19) Equations(2.18)and(2.19)should be consistent.Then
n f
i =n f i?(?εs?p+εs?·τ)=
1
V
n
i=1
(f d,i+f vm,i+f B,i+f Sa?,i+f Mag,i).
(2.20)
Thus,the volumetric particle–?uid interaction force in each model can be written as
F set I
pf =n f i=
1
V
n
i=1
(f?p,i+f?·τ,i+f d,i+f vm,i+f B,i+f Sa?,i+f Mag,i),
(2.21)
490Z.Y.Zhou,S.B.Kuang,K.W.Chu and A.B.Yu
F set II
pf =n f i=
1
V
n
i=1
(f d,i+f vm,i+f B,i+f Sa?,i+f Mag,i),(2.22)
F set III
pf =n f i/εf?ρfεs g=
1
εf V
n
i=1
(f d,i+f vm,i+f B,i+f Sa?,i+f Mag,i)
?1
V
n
i=1
(ρf V p,i g).(2.23)
When coupling CFD with DEM,or vice versa,the governing equations should be consistent,as noted by Xu&Yu(1998).Generally speaking,for all the three models, the governing equations for particles can be the same,shown in(2.11)–(2.13).However, in order to satisfy the Newton’s third law of motion,for set III,the particle–?uid interaction force acting on particles,instead of(2.13),can be obtained from(2.23), and written as
f pf,i=1
εf
f d,i+f vm,i+f B,i+f Sa?,i+f Mag,i
?ρf V p,i g.(2.24)
https://www.doczj.com/doc/612504007.html,ments on di?erent computational?uid dynamics–discrete element method
models
Clearly,from the above discussion,there are three sets of governing equations in the CFD–DEM modelling of particle–?uid?ow.They correspond to those in TFM. By reference to the discussion presented in§2.1,the relationship and applicability of these models in the CFD–DEM approach can be obtained as discussed below. Firstly,set II is derived from set I mainly with the decomposition of particle–?uid interaction force n f i as shown in(2.3).Physically speaking,in set II,the pressure gradient force and viscous force on particles are separated from the volumetric particle–?uid interaction force F pf,while set I does not.However,such a treatment will not cause any signi?cant di?erence in the simulated results because they are mathematically the same,which will be veri?ed in§3.
Secondly,set III is a simpli?ed form of set I under the assumption of(2.10).In the
?uid governing equations,F set I
pf and F set III
pf
represent the total volumetric particle–?uid
interaction force.The di?erence between them is that F set I
pf is explicit while F set III
pf
is
implicit and lumps the drag force and pressure gradient force(excluding those caused
by buoyancy)together,as seen in table1.Both models are identical only when(2.10)
is satis?ed.
Thirdly,when comparing set III with model B in the literature,a slight di?erence
related to the viscous part exists(Xu et al.2000;Kafui et al.2002;Feng&Yu2004a).
In the literature,the particle–?uid interaction force F pf and f pf in model B includes
a component of the viscous forceεs?·τ,but it has been excluded in the present set III.From its derivation as shown in(2.6)–(2.9),it can be seen that the viscous part
together with the pressure has been hidden in the expression of(n f /ε-ρεs g)in(2.8)
and(2.9).
Most importantly,it should be noted that set III is not a general model,and
its application is conditional.Strictly speaking,it can be used only when(2.10)is
satis?ed.Alternatively,from the viewpoint of forces,the following condition obtained
from(2.4)and(2.10)should be satis?ed in a CFD cell:
F resid=εs?·ξ?n f εs/εf+ρfεs g=0.(2.25a)
Discrete particle simulation of particle–?uid?ow491 Note that
εs=
1
V
n
i=1
(V p,i),?·ξ=
1
V
n
i=1
(?V p,i?p+V p,i?·τ),
n f i=
1
V
n
i=1
(f d,i+f vm,i+f B,i+f Sa?,i+f Mag,i),
?
???
?
???
?
(2.25b)
then(2.25a)can be further written as
F resid=
1
V
n
i=1
(f resid)=
1
V
n
i=1
[?V p,i?p?(f d,i+f vm,i+f B,i+f Sa?,i
+f Mag,i)εs/εf+V p,i?·τ+ρf V p,i g]=0.(2.25c)
According to(2.7),the total particle–?uid interaction force in a cell should be
F total=
1
V
n
i=1
f total,i
=
1
V
n
i=1
f e?ective,i+f resid,i
,(2.26)
where f e?ective,i=(f d,i+f vm,i+f B,i+f Sa?,i+f Mag,i)/εf?ρf V p,i g according to (2.24).
Strictly speaking,the?uid?ow in a real particle–?uid system is non-uniform and unsteady.That is,F resid calculated according to(2.25c)is not equal to zero.Thus,the applicability of set III can be assessed by the value of F resid relative to F total in(2.26). That is,a parameterηto assess the applicability of set III can be de?ned as
η=|f resid|/|f total|×100%,(2.27) where f resid and f total are,respectively,the forces acting on individual particles determined by(2.25c)and(2.26).ηfor each particle in a considered system can be traced in a CFD–DEM simulation.
3.Applicability of di?erent CFD–DEM model formulations
Three typical particle–?uid?ow systems are used to test the applicability of the three models in the present simulation:?uidization,pneumatic conveying and hydrocyc-lones.Fluidization and pneumatic conveying have been extensively studied,therefore our focus here is to examine the reliability of the published results based on the di?er-ent CFD–DEM models.A hydrocyclone gives a more complicated?ow,o?ering a very representative example to examine the applicability of di?erent model formulations. To eliminate the e?ects of CFD–DEM algorithms and other unexpected factors on numerical results,the simulations for each particle–?uid system are carried out based on the following conditions:(i)the same CFD–DEM code except for the necessary minor changes for the implementation of di?erent models;(ii)the same equations to calculate the particle–particle and particle–?uid interaction forces as listed in table2, where the drag force is based on the correlation formulated by Di Felice(1994);(iii)the same initial and boundary conditions.Ideally,all simulations should be performed with one computational code.However,this is di?cult to achieve at the moment. On the other hand,our aim is to examine the di?erence of the three models for a given system.This aim can be achieved by ensuring that the same code is used for all the models for each of the?ow systems considered.This treatment can better correspond to the real application because di?erent investigators often use di?erent codes,although they are developed based on the same principle.The results analysis is
492Z.Y .Zhou,S.B.Kuang,K.W .Chu and A.B.Yu
Forces and torques
Equations ?Normal elastic force (f cn,ij )
?43E ?√R ?δ3/2n n Normal damping force (f dn,ij )
?c n 8m ij E ?√R ?δn 1/2v n,ij Tangential elastic force (f ct,ij )
?μs f cn,ij (1?(1?δt /δt ,max )3/2)?δt (δt <δt ,max )Tangential damping force (f dt,ij )
?c t 6μs m ij |f cn,ij | 1?|δt |/δt ,max /δt ,max 1/2×v t,ij (δt <δt ,max )Coulumb friction force (f t,ij )
?μs f cn,ij ?δt (δt >δt ,max )Torque by tangential forces (M t,ij )
R ij × f ct,ij +f dt,ij Rolling friction torque (M r,ij )
μr,ij f n,ij ωn ij Drag force (f d,i )
0.125C d 0,i ρf πd 2i ε2i |u i ?v i |(u i ?v i )ε?χi Pressure gradient force (f ?p,i )
??p ·V p,i
Viscous force (f ?·τ,i )?(?·τ)V p,i
where 1/m ij =1/m i +1/m j ,1/R ?=1/|R i |+1/|R j |,E ?=E/2(1?ν2), ωn ij =
ωn ij |ωn ij |,
?δ
t =δt /|δt |,δt ,max =μs ((2?ν)/2(1?ν))δn ,v ij =v j ?v i +ωj ×R j ?ωi ×R i ,v n,ij =(v ij ·n )·n ,v t,ij =(v ij ×n )×n ,χ=3.7?0.65exp[?(1.5?log 10Re i )2/2],C d 0,i =(0.63+4.8/Re 0.5i )2,Re i =ρf d pi εi |u i ?v i |/μf ,τ=μf [(?u )+(?u )?1],εi =1? n i =1V p,i / V.Note that tangential forces (f ct,ij +f dt,ij )should be replaced by
f t,ij when δt >δt ,max .
?Parameters in these equations are explained in tables 3–5.
Table https://www.doczj.com/doc/612504007.html,ponents of forces and torques acting on particle i .
mainly carried out in terms of ?ow patterns,forces,and parameter ηde?ned by (2.27).For convenience,the simulation conditions for each case are described,respectively.The methods for the numerical solution of CFD and DEM have been well established in the literature (e.g.Xu &Yu 1997).For convenience,it is brie?y described here.An explicit time integration method is used for DEM to solve the translational and rotational motions of discrete particles (Cundall &Strack 1979).The conventional semi-implicit method for pressure-linked equations (SIMPLE)method is used for CFD to solve the ?uid governing equations (Patankar 1980).The governing equations are discretized in ?nite volume form on a uniform staggered grid.The second-order central di?erence scheme is used for the pressure gradient and divergence terms,the ?rst-order up-wind scheme for the convection term,and a second-order Crank–Nicolson scheme for the time derivative.The CFD–DEM coupling scheme 3as discussed earlier,is used in all the simulation cases.At each time step,DEM will give information,such as the positions and velocities of individual particles,for the evaluation of porosity and volumetric ?uid drag force in a computational cell.CFD will then use these data to determine the gas ?ow ?eld which then yields the ?uid drag forces acting on individual particles.Incorporation of the resulting forces into DEM will produce information about the motion of individual particles for the next
time step.All the simulations are carried out on the Intel R ?
Xeon R ?CPU51302.0GHz,and the simulation time varies from hours for a case of gas ?uidization or pneumatic conveying to days for a case of hydrocyclones.
3.1.Fluidization
Fluidization is one of the most popular particle–?uid ?ow systems in the CFD–DEM modelling.The con?icting views,if any,about the applicability of di?erence model
Discrete particle simulation of particle–?uid?ow493
Variables Values
Bed geometry:
Bed width150mm
Bed thickness24mm
Initial bed height240mm
Total CFD cells15×120
Cell size( x× z)10mm×10mm
Particle properties:
Number of particles(N)15000
Particle diameter(d p)4mm
Particle density(ρp)2500kg m?3
Particle–particle/wall sliding friction(μs)0.4
Particle–particle/wall rolling friction(μr)1%d p mm
Particle–particle/wall damping(c n=c t)0.3
Particle Young’s modulus(E)1.0×107Pa
Particle Poisson ratio(ν)0.3
Time step( t)1.75×10?7s
Fluid properties:
Gas density1.2kg m?3
Gas viscosity1.8×10?5Pa s
Table3.Parameters used in the present gas?uidization.
formulations mainly stem from the study of this?ow system(Hoomans et al.1998; Xu&Yu1998;Kafui et al.2002,2004;Feng&Yu2004a,b;Di Renzo&Di Maio 2007).However,previous studies did not examine this issue theoretically but focused on the result comparison.The outcomes are not as general and convincing.This de?ciency can be overcome with the support of the theoretical arguments presented in§2.Therefore,as the?rst step to examine the applicability of di?erent models listed in table1,?uidization is taken as our?rst case study.The simulation condition is similar to that of Feng&Yu(2004b),but the structure used in this work has a thickness of six-particle diameter with front and rear wall boundary conditions.It should be noted that CFD for the?uid?ow is assumed to be two-dimensional due to the thin bed thickness.However,DEM for the particle?ow is three-dimensional. Such a technique of coupling two-dimensional CFD with three-dimensional DEM has been successfully used in the literature(e.g.Xu&Yu1998;Kafui et al.2002, 2004;Feng&Yu2004a,b).It is adopted in the present study of?uidization.Table 3lists the parameters used.It should be noted that the initial bed conditions for all the simulation cases of?uidization are identical.The bed is produced by randomly dropping particles into the rectangular box as done elsewhere(Zhou et al.2009),and its porosity is0.418.
Figure1shows the initial response of particles to the introduction of gas using the three models when the gas super?cial velocity is3.0m s?1.It can be observed that the ?ow patterns obtained are quite comparable,although the bed height generated by set III is slightly higher than those generated by sets I and II.This is consistent with the previous?ndings(Kafui et al.2004;Feng&Yu2004b).The relationship between the pressure drop and gas super?cial velocity is an important feature in gas?uidization. Figure2shows such a relationship generated by the three models,indicating again that di?erent model formulations do not yield any signi?cant di?erences.
The examination of di?erent particle–?uid interaction forces is useful in identifying any di?erence between the three models at a more fundamental level.It should be noted that the virtual mass,Basset and lift forces are not considered in all?uidization
494Z.Y.Zhou,S.B.Kuang,K.W.Chu and A.B.Yu
0.252 s
(a)
(b)
(c)0.707 s0.959 s 1.111 s 1.464 s 1.767 s 2.374 s
0.252 s0.707 s0.959 s 1.111 s 1.464 s 1.767 s 2.374 s
0.252 s0.707 s0.959 s 1.111 s 1.464 s 1.767 s 2.374 s
Figure 1.Snapshots showing the?ow patterns of particles at the early stage for di?erent CFD–DEM models when gas super?cial velocity is3.0m s?1:(a)set I,(b)set II and(c)set III.
Discrete particle simulation of particle–?uid ?ow 4954000
3500
3000
25002000
1500
1000
500
01234
Set I
Set II
Set III Bed weight 3424 Pa Gas superficial velocity (m s –1)
P r e s s u r e d r o p (P a )Figure 2.The relationship between bed pressure drop and gas super?cial velocity for the
three models in gas ?uidization.
10
(a )
(b )9
8
7
6
5
4
3
2
1
02018161412108642
024Time (s)Time (s)
T o t a l p a r t i c l e –f l u i d i n t e r a c t i o n f o r c e (N ) P r e s s u r e g r a d i e n t f o r c e (N )Set I Set I U = 0.8 m s –1U = 0.8 m s –1U = 1.6 m s –1U = 1.6 m s –1U = 2.8 m s –1U = 2.8 m s –1Set II Set III Set II 6810246810
Figure 3.Variation of (a )the pressure gradient force with time for sets I and II;and (b )the total particle–?uid interaction force (= N i =1(f d,i +f ?p,i +f ?·τ,i )for sets I &II;and N
i =1(f d,i /εf ?ρf V p,i g )for set III)for the three models.
cases in this work,because they are insigni?cant compared with the pressure gradient force and drag force,particularly in gas ?uidization (Crowe et al.1998;Zhu et al.2007).The pressure gradient force and drag force are two dominant particle–?uid interaction forces,and their variations with time are given in ?gure 3.As shown in
496Z.Y.Zhou,S.B.Kuang,K.W.Chu and A.B.Yu
?gure3(a),the di?erence in the pressure gradient force between sets I and II exists, even in the?xed bed.However,such a di?erence is still small,which cannot be re?ected by?ow patterns(?gures1a and1b).The di?erence is mainly caused by the di?erent treatments of the pressure gradient force in the model formulation and hence the numerical scheme.In set II,the pressure gradient force is incorporated into the?uid governing equations,based on the cell properties such as porosity and pressure drop. However,in set I,the pressure gradient force acting on the individual particles in a cell are summed together with the drag force.It is treated as a property on the particle scale.In theory,as discussed by Feng&Yu(2004a),information transfer from particle scale to cell scale is more reasonable as it can avoid the unnecessary assumption of distributing a cell property among particles.Therefore,set I should be more reliable. Figure3(b)shows the total particle–?uid interaction forces(including the drag force, pressure gradient force and viscous force)for the three models in the vertical direction, thus showing some slight di?erences.It can be seen that the particle–?uid interaction force generated by set III is larger than the other two,explaining why the bed height from set III is slightly higher as shown in?gure1.It indicates that,in set III,the total particle–?uid interaction force represented by(2.23)is slightly overestimated. This must be caused by the assumption made in(2.10)or(2.25).
The assumption as given by(2.25)can be examined by parameterη.For each particle in the bed,the total particle–?uid interaction force f total can be determined by(2.26)while the ignored force f resid in set III is calculated by(2.25c).Thus, according to(2.27),each particle has a value ofη.Figure4(a)shows the variations of bed averagedηwith time when gas super?cial velocity is3.4m s?1.It can be seen thatηis small,?uctuating around9%.Figure4(b)further shows a snapshot of solid ?ow patterns with spatial distributions ofη,together with the solid and gas?ow?elds and porosity spatial distribution.It can be seen that largeηmainly locates in areas where voids or bubbles exist,indicating a larger variation in porosity,pressure and velocity.Such a spatial variation ofηcan explain the observed di?erences of set III with other two models such as higher bed height or particle–?uid interaction force. It indicates that(2.25)is not always satis?ed,particularly in those regions with gas voids and bubbles.Nevertheless,the overall di?erences between the three models in gas?uidization are not signi?cant.
It should be noted that the simulation cases above are all carried out in a narrow ?uidized bed.The solid?ow in such a narrow bed is more one-dimensional.However, in the real?uidization process,it is featured with the formation of gas bubbles,particle clusters and rigorous two-dimensional or three-dimensional motion of particles.It is necessary to examine the e?ect of bed geometry onη.Thus,a case is chosen with the bed width3times larger than the one in table3,and total60000particles involved. Figure5(a)shows the variations of bed averagedηat around7%,slightly smaller than that in the narrow bed(?gure4a).A snapshot of solid?ow patterns is also shown in?gure5(b)withηspatial distribution,together with the corresponding solid and gas?ow?elds and porosity distribution.It can be seen that the largeηstill mainly locates in the boundary region of gas bubbles and the interface between dense and dilute particle?ow regions,which is consistent with those in?gure4(b).
In gas?uidization,the drag force is almost equally as important as the pressure gradient force where the buoyancy force is negligible.However,in liquid?uidization, the buoyancy force becomes more important.The?ow features of liquid?uidization are also di?erent from those in gas?uidization.Thus,as part of the present study, liquid?uidization is also considered.The three models show results consistent with the gas?uidization.Thus,for brevity,they are not presented here.
Discrete particle simulation of particle–?uid?ow
497
14 (a)
(b)
13
12
11
10
9
8
7
6
5
4
024
Time (s)
P
a
r
a
m
e
t
e
r
η
6810 0204060
5 m s–1
20 m s–1
80100
0.65
0.400.560.730.89
2.61 4.57 6.53
Figure 4.(a)Variations of bed averagedηwhen gas super?cial velocity is3.4m s?1,and (b)a snapshot at t=6.341s showing the solid?ow patterns with spatial distribution ofη, and the corresponding particle velocity?eld,gas?ow?eld and porosity distribution(data are generated by set I).
Therefore,it can be concluded that the di?erences in the simulated results based on sets I,II and III are very small.All the three models can be applied to such a system,although theoretically set I is most acceptable.They also con?rm that the results reported in the literature,produced by either set II or set III(i.e.models A or B),are reasonable.
498
Z.Y .Zhou,S.B.Kuang,K.W .Chu and A.B.
Yu 024Time (s)
68
(a )(b )
12
11
10
9
8
7
6
5
4P a r a m e t e r η10 m s –1
20 m s –10200.8 3.4 5.90.440.660.898.511.0406080100Figure 5.(a )Variations of bed averaged ηwhen gas super?cial velocity is 3.4m s ?1in a wider bed,and (b )a snapshot at t =5.853s showing the solid ?ow patterns with spatial distribution of η,and the corresponding particle velocity ?eld,gas ?ow ?eld and porosity distribution (data are generated by set I).
3.2.Pneumatic conveying
Pneumatic conveying is one of the most commonly used methods of transporting granular materials from one place to another.Depending on solid loading and conveying speeds,one can distinguish between dilute phase,dispersed and dense
Discrete particle simulation of particle–?uid?ow499
Variables Values
Pipe geometry:
Diameter50mm
Length0.8m
Number of body-?tted cells7×7×100
Particle properties:
Number of particles(N)33000
Particle diameter(d p)3mm
Particle density(ρp)1000kg m?3
Particle–particle/wall sliding friction(μs)0.4
Particle–particle/wall rolling friction(μr)1%d p mm
Particle–particle/wall damping(c n=c t)0.1
Particle Young’s modulus(E)5.0×109Pa
Particle poisson ratio(ν)0.33
Time step( t)3.8×10?6s
Gas properties:
Density 1.2kg m?3
Viscosity1.8×10?5Pa s
Table4.Parameters used in the present simulation of pneumatic conveying.
phase slug?ow regimes where the latter is most commonly used.To understand the fundamentals of slug?ow,the CFD–DEM approach in a set II or set III format has been increasingly used in recent years(see e.g.the review of Zhu et al.2008and Kuang et al.2008).It is therefore important to know the applicability of di?erent model formulations to this system.Table4shows the parameters used in the present simulations of the horizontal pneumatic conveying.For computational e?ciency,a 0.8m horizontal pipe with internal diameter of0.04m is chosen as the computation domain,facilitated by periodic boundaries for gas and particles in the?ow direction as used by Kuang et al.(2008).In all the simulations,the same initial particle con?guration is used,which consists of a stationary slug and a stationary settled layer.The?ow of both gas and solid phases is three-dimensional.
Figure6shows the snapshots of particle?ow patterns in the slug?ow regime for the three models.It can be seen that throughout the entire physical time considered, there is no signi?cant di?erence in the shape of slugs,and the height of settled layers predicted by the three models.In each simulation,a slug locates at almost the same axial position in the pipe with the evolution of time.This shows that the three models predict the same slug velocity.Note that slug velocity as well as slug shape and settled layer height are the three key process parameters usually used to characterize slug ?ow.The variations of pressure drop with time for the three models are also traced, and shown in?gure7.It can be observed that the di?erences in the pressure drop generated by the three models are small.The variations of particle–?uid interaction forces in the horizontal direction are also examined and shown in?gure8.Again, it can be seen that the three models produce comparable results with negligible di?erences.
Figure9(a)shows the spatial distribution ofη.It can be seen thatηis close to zero within a slug,but may have a relatively large magnitude within settled layers. This result suggests that set III is not so suitable in the simulation of inhomogeneous pneumatic conveying,such as strati?ed?ow and dispersed?ow with clusters.This is because gas mainly?ows over settled layers,and its?ow is non-uniform,hence
500Z.Y.Zhou,S.B.Kuang,K.W.Chu and A.B.Yu t = 0.450 s
(a)
(b)
(c)t = 1.245 s
t = 2.550 s
t = 3.405 s
t = 0.450 s
t = 1.245 s
t = 2.550 s
t = 3.405 s
t = 0.450 s
t = 1.245 s
t = 2.550 s
t = 3.405 s
00.20.40.60.8 00.20.40.60.8 00.20.40.60.8
Figure 6.Side views of particle?ow patterns in slug-?ow pneumatic conveying when gas super?cial velocity is2.1m s?1,calculated by(a)set I,(b)set II and(c)set III..
Discrete particle simulation of particle–?uid ?ow 5010.41500
10002000
2500P r e s s u r e d r o p (P a )Time (s)
30003500
4000
1.4
2.4Set I Set II
Set III 3.4 4.4
Figure 7.Variation of the pressure drop with time for the three models under the conditions
corresponding to ?gure 6.
0.42.01.52.53.0P r e s s u r e g r a d i e n t f o r c e (N )Time (s)3.54.0(a )(b )1.4 2.4Set I Set II 3.4 4.40.44.03.05.06.0T o t a l p a r t i c l e –f l u i d i n t e r a c t i o n f o r c e (N )Time (s)
7.0 1.4 2.4Set I Set II Set III 3.4 4.4
Figure 8.Variation of:(a )the pressure gradient force with time for sets I and II;and (b ),the total particle–?uid interaction force (= N i =1(f d,i +f ?p,i +f ?·τ,i )for sets I and II;and N
i =1(f d,i /εf ?ρf V p,i g )for set III)for the three models.
the assumption induced by (2.10)or (2.25)is not satis?ed.However,it is relatively uniform within a slug,as shown in ?gure 9(b ).Hence,set III can be applied in this ?ow regime.It should be pointed out that in a slug ?ow,slug behaviour depends on particle motion and gas ?ow within a slug,e.g.the pressure drop in the whole conveying pipeline is the result of the pressure di?erence when gas ?ows across slugs,as demonstrated in ?gure 9(c ).As a result,although ηdeviates from zero within settled layers,set III still produces gas and solid ?ow patterns similar to those given by sets I and II.
快速入门 说明：本篇快速入门为一套完整的SimTrade实际业务操作，交易方式为L/C + CIF，由于不同交易方式下贸易流程不尽相同，本例中的数据资料(加横线部份)仅供参考，请依具体情况来完成实际操作。 (一) 交易准备阶段 1 学生以出口商角色登录，输入用户名(如xyz)，在"选择用户类型"下拉框中选择"出口商"，点"登录系统"，进入出口商业务主页面； 2 创建公司。点"资料"，可查看公司注册资金、帐号、单位代码、邮件地址等信息，还可以修改登陆密码，其它资料逐项填写如下： 公司全称(中文)：宏昌国际股份有限公司 公司全称(英文)：GRAND WESTERN FOODS CORP. 公司简称(中文)：宏昌
公司简称(英文)：GRAND 企业法人(中文)：刘铭华 企业法人(英文)：Minghua Liu 电话：86-25-23501213 传真：86-25-23500638 邮政编码：210005 网址：https://www.doczj.com/doc/612504007.html, 公司地址(中文)：南京市北京西路嘉发大厦2501室 公司地址(英文)：Room2501,Jiafa Mansion, Beijing West road, Nanjing 210005, P.R.China 公司介绍：我们是一家专营食品的公司，长期以来致力于提高产品质量，信誉卓著，欢迎来函与我公司洽谈业务！ 可自由添加图片 注意事项：最好使用GIF或JPG格式的图片，尺寸建议在120*120(像素)左右。 填写完毕后，点"确定"； 3 以同样方法登陆其他四个角色(进口商、工厂、出口地及进口地银行)，分别创建基本资料。 (1)进口商资料如： 公司全称：Carters Trading Company, LLC 公司简称：Carters 企业法人：Carter 电话：0016137893503 传真：0016137895107 网址：https://www.doczj.com/doc/612504007.html, 公司地址(注意应根据所属国家来填写)：P.O.Box8935,New Terminal, Lata. Vista, Ottawa, Canada 公司介绍：We are importers in all items enjoying good reputation！ (2)工厂资料如： 公司全称：冠驰股份有限公司 公司简称：冠驰 企业法人：张弛 电话：86-25-29072727 传真：86-25-29072626 邮政编码：210016 网址：https://www.doczj.com/doc/612504007.html, 公司地址：南京市中正路651号3楼 公司介绍：我公司为信誉卓著的厂商，产品深受客户喜爱，欢迎与我公司洽谈业务，我们
渗碳过程中表层碳含量的预测与验证 摘要 渗碳是机械制造业中应用最广泛的一种化学热处理工艺，采用渗碳的多为低碳钢或低合金钢，具体方法是将工件置入具有活性渗碳介质中，加热并保温使渗碳介质中分解出的活性碳原子渗入钢件表层，从而获得表层高碳，心部仍保持原有成分。它可以使渗过碳的工件表面获得很高的硬度，提高其耐磨程度。 为了了解工件渗碳后的碳浓度分布情况，本设计根据渗碳过程的基本理论和数学模型，通过MATLAB软件编写渗碳过程各种不同边界条件的解析解以及一维数值解的程序，并对不同渗碳时间，渗碳温度以及不同渗碳碳势下的渗碳过程进行模拟，得到渗碳后的碳浓度分布情况。通过计算模拟得到的结果，可以得到不同渗碳工艺条件对渗碳层的组织和性能的影响，进而优化工艺参数。通过合理的控制渗碳时间，渗碳温度和渗碳碳势，我们可以得到渗碳后工件预期的碳浓度分布。在本文中，渗碳时间的延长，渗碳温度的提高以及渗碳碳势的增加都可以增加渗碳层的深度和碳浓度。同时通过计算模拟的出的碳浓度分布与实测的碳浓度分布做比较之后，计算模拟得到的结果和实测值比较符合. 关键词：渗碳；模拟；MATLAB；解析解；数值解
Abstract Carburizing is one of the most widely used chemical heat treatment in mechanical industry, which is mostly applied to low-carbon steel and low alloy steel.In the specific method, the workpiece is placed in an active carburizing medium,heated and keeping one holding time, which could make the active carbon atoms decomposed from carburizing medium diffuse into the surface of the workpiece, and then the affected area can vary in carbon content.it can make the surface of the workpiece obtain a high hardness and improve its abrasion. In order to find out the carbon concentration distribution of the workpiece after carburizing ,this article is based on the basic theory and mathematical model of the carburizing, using MATLAB to write a program of analytical solution and numerical solution of one-dimensional for various boundary conditions during the carburizing process, as well as calculating and simulating the carburizing process at different carburizing time, carburizing temperature and carburizing carbon potential, finally we obtain the distribution of the carbon concentration after the carburizing. Through the final result, we can get the different affects to the structure property of the carburized layer, and then optimize the process parameters. By mean of controlling the carburizing time, carburizing temperature and carburizing carbon potential, the expected Carbon concentration distribution could be gotten. In this text,longer carburizing times, higher temperatures and higher carbon potential lead to greater carbon diffusion into the part as well as increased depth of carbon diffusion. In addition, the results of calculating and simulating are compared to the measured value, the carbon concentration distribution of the workpiece of the results agrees well with the measured value. Key words: Carburizing, Simulate, MATLAB, Analytical solution, Numerical solution
单项选择题（5X2=10分） 1. 海运提单和航空提单（ C ） A.均为物权凭证 B.均为可转让的物权凭证 C.前者作物权凭证，后者不可转让，不作物权凭证 D.前者不作物权凭证，后者作物权凭证 2. CIF合同的货物在刚装船后因火灾被焚，应由（D） A. 卖方负担损失 B. 卖方请求保险公司赔偿 C. 买方委托卖方向保险公司索赔 D.买方负担损失并请求保险公司赔偿 3.关于接受的生效，英美法系实行的原则是（A） Ａ．投邮生效Ｂ．签署日生效 Ｃ．到达生效Ｄ．双方协商 4.海运提单之所以能够向银行办理抵押贷款，是因为（D ） A.海运提单是承运人签发的货物收据 B.海运提单可以转让 C.海运提单是运输契约的证明 D.海运提单具有物权凭证的性质 5.为防止运输途中货物被窃，应该投保（C ）。 A. 一切险、偷窃险 B. 水渍险 C. 平安险、偷窃险 D. 一切险、平安险、偷窃险 6.汇票根据（B ）不同，分为银行汇票和商业汇票。 A.出票人 B.付款人 C.受款人 D.承兑 7.银行审单议付的依据是（ C ）。 A. 合同和信用证 B. 合同和单据 C. 单据和信用证 D. 信用证和委托书 计算题(10分) 1.某商品出口我对外报FOB净价180美元，若国外客户要求改报含佣4%的价格时，我应对外报价多少？ 解：FOBC4%价=净价/（1-佣金率）=180/（1-4%）=187.5（美元）。 2.某批商品的卖方报价为每打60美元CIF香港，若该批商品的运费是CIF价的2％，保险费是CIF价的1％，现外商要求将价格改报为FOBC3%.问FOBC3%应报多少？ 解:FOB价=CIF价—运费—保险费=60—60×2%—60×1%=58.2美元 FOBc3%=FOB价/（1—佣金率）=58.2/（1-3%）=60美元 3.一批出口货物做CFR价为250000美元，现客户要求改报CIF价加20%投保海运一切险，我方同意照办，如保险费率为0.6%时，我方应向客户报价多少？ 解:CIF=CFR/(1-投保加成*保险费率)=CFR÷（1-120%×0.6%） =250000÷0.9928 =251813.05美元 案例分析（30分） 1.某口岸出口公司按CIF London向英商出售一批核桃仁，由于该商品季节性较强，双方在 合同中规定：买方须于9月底前将信用证开到，卖方保证运货船只不得迟于12月2日驶抵目的港。如货轮迟于12月2日抵达目的港，买方有权取消合同。如货款已收，卖方须将货款退还买方。问这一合同的性质是否属于CIF合同？ 按CIF条件签订的合同属于装运合同，其特点是“凭单据履行交货义务，并凭单据付款”。只要卖方按合同的规定将货物装船并提供齐全的、正确的单据，即使货物在运输途中已遭灭失，买方也不能拒收单据和拒付货款。所以，本案例的合同不属于CIF合同。
《国际贸易实务》实训大纲 适用对象：经济学专业 一、课程性质、目的与任务： 国际贸易实务实训是市场营销本科专业重要的综合性实践教学内容之一。主要是对国际贸易的整个流程进行模拟训练，包括、交易磋商、合同的签订、合同的履行等，涉及到银行、保险、海关、运输等各个部门，需要填制各种单据，包括信用证申请书、报验单、报关单、出口结汇单据等。 二、教学基本要求： 国际贸易实务实训覆盖了国际贸易市场营销、国际贸易商法、国际贸易实务、电子商务等课程教学的主要内容，其操作性很强。通过实验可以使学生全面掌握进出口业务的整个流程及具体内容，主要包括： 1．进出口贸易合同的磋商与签订。 2．进出口贸易合同履行的整个流程。 3．进出口业务中各种单据的制作。 实验方式：本课程实验内容进行上机操作。 基本要求： 1．认真阅读实验指导书，以便顺利完成实验要求。 2．每人至少完成一笔进口业务和一笔出口业务。进口业务与出口业务可以同时进行。 3．写出实验日记。 4．实验完毕后应编写实验报告，实验报告为按实验指导书要求编写的实验结果，包括进口业务和出口业务所涉及的各项内容，交打印版和电子版各一份。 三、课程内容与学时分配：
四、考核方法与规定 本课程实验教学的成绩评定采用考查方法进行，根据实验态度、出勤率、实验质量、实验日记、实验总结、实验报告等综合评定。成绩分为优、良、中、及格、不及格五等。 五、综合训练其它有关问题的说明与建议： 1．本课程与其相关课程的联系与分工： 本课程的先修课程是《国际贸易》、《国际贸易实务》等。 2．课外练习方面的要求： 要求学生课外多阅读贸易谈判方面的参考书籍；查找外贸业务的相关案例。 \大纲制定人：田小伟大纲审定人 制定时间：2014.08.27
浅析水文地质数值模拟的立足点 [摘要]对于当前水文地质数值的模拟以及研究，在实践应用过程中出现了新的问题，呈现出来的反差现象比较明显。文章通过数据收集，为研究水文地质数值奠定基础，从而获得数值模拟的立足点。然而该工作应该基于地质以及水文地质条件都符合需求的基础下开展，这样才能保障工作的可行性。在当前的社会发展中，模拟已经成为认识客观事物的重要方式，而其中最重要的就是获取客观科学理论的支撑。因此立足点对于开展水文地质数值模拟有着重要影响，当立足点确定了才能更好的开展工作。 [关键词]水文数值模拟立足点 [中图分类号] P641.73 [文献码] B [文章编号] 1000-405X（2014）-5-175-1 1解析数值模拟立足点 1.1数据收集 众所周知，水文地质学是一门应用性很强的学科，该学科的理论形成与地下水的工作开发紧密结合在一起。人类在使用地下水的过程中，对于地下水的运动规律、动态变化以及地下水贮存有着一些认识和了解，
并且随着学科知识不断发展，对这些认识也有了一些总结。水文地质学研究和解决的问题主要是对地质条件的认识和研究，从气象、水文还有一些人为因素进行深入分析，基于水文概念的基础上建立起一个完整的数学模型。每个区域的水文地质特征不尽相同，每个地区的水质情况也不尽相同，这些问题非常复杂。而且在研究过程中还发现，影响地下水的动态因素非常繁杂，这是一种多变的因素。因此在进行研究的时候，可以从水文地质测绘、物探以及钻探角度入手，这样开展工作取得的效果才更加明显和突出。一般在进行野外数据收集时，都希望能够获得立体、综合的效果，这样才可以在掌握了一定的数据资料后能够建立起一套数据库，数据库建立对于模型建立成功有着决定性作用。 1.2建立模型 水文地质数学模型它是一个复杂且庞大的关系体，是众多的数学关系表达出来的，这是一种极其客观但同时也很复杂的表达形式。寻找建立起一个水文地质数学模型，会涉及到诸多的参数问题。想要解决参数问题应该从函数关系入手解析，而且函数表示并不是一个简单的数学表现方式。它会受到各个因素的影响，它不是确定不变的，而是随机改变的个体。在
一单项选择题 1、我方出口大宗商品，按CIF Singapore 成交，运输方式为Voyage Charter,，我方不愿承担卸货费用，则我方应选择的贸易术语的变形是 （ C ）。 A、CIF Liner Terms Singapore B、CIF Landed Singapore C、CIF E x Ship’s Hold Singapore D、CIF Ex Tackle Singapore 2、按照《INCOTERMS2000》的解释，以FOBST成交，则买卖双方风险的划分界限是（B以船舷为界）。 4、在CIF条件下，Bill of Lading对运费的表示应为( A )。 A．Freight Prepaid B．Freight Collect C．Freight Pre-payable D．Freight Unpaid 5、在进出口业务中，能够作为物权凭证的运输单据有( B )。 A．Rail Waybill B．Bill of Lading C．Air Waybill D．Parcel Post Receipt 6、预约保险以（ B ）代替投保单，说明投保的一方已办理了投保手 续。 A、B/L B、Shipping advise from abroad C、Mate，s receipt D、Sales contract 7、我某公司与外商签订一份CIF出口合同，以L/C为支付方式。国外 银行开来的信用证中规定：“Latest shipment 31st, May, L/C validity till 10th, June.”我方加紧备货出运，于5月21日取得大副收据，并换回正本已装船清洁提单，我方应不迟于（ C ）向银行提交单据。 A．5月21日 B．5月31日 C．6月10日 D．6月11日 8、某批出口货物投保了CIC 的WPA，在运输过程中由于雨淋致使货物遭受部分损失，这样的损失保险公司将（ C ）。 A、负责赔偿整批货物 B、负责赔偿被雨淋湿的部分 C、不给于赔偿 D、在被保险人同意的情况下，保险公司负责赔偿被雨淋湿的部分 9．在短卸情况下，通常向( B )提出索赔。 A. the seller B. the carrier
湖南女子学院 外贸单证实训报告 （2014年下学期） 院系经济与管理系专业国际经济与贸易班级11级国贸一班姓名王珏 学号2011111129 指导教师袁学军 成绩 2014年12 月
一、引言 国际贸易是跨国的商品买卖，不能用简单的货物和货款交换来形容这种特殊性的跨国交易，跨国的商品买卖以单证作为交换的媒介手段，故外贸单证是国际贸易中最重要的环节，买卖双方处理的只是与货物相符的单据。单证工作是国际贸易业务中最重要的环节，贯穿于进出口合同履行的全过程。 二、实训目的 外贸单证制作实训是在《外贸单证实务》课程的基础上开设的，通过综合业务模拟制单，使学生能够将课程中比较零散的制单练习贯穿起来，从而系统地了解外贸企业单证工作流转程序和具体的制单要求，加强对所学专业知识的理解，明确掌握各种进出口单证的制单技巧，以培养学生的实际操作能力，提高自身的制单水平，同时也培养了学生耐心、细致的工作作风。 三、实训时间：2014年9月-12月 四、实训地点：实训楼504 五、实训内容 本实训要求学生根据信用证、合同、订单等各种材料及相关信息，进行综合制单训练。由于信用证项下制单对单证的要求最为严格，所以本实训内容也主要以信用证制单为主，结合托收和汇付方式的制单，材料涉及到信用证、合同、订单等各种外贸文件，实习素材也基本上来自于外贸公司的真实业务，模拟了不同的贸易术语、分批交货、选择港的确定等各种贸易情形，使学生能够熟练掌握各种外贸单证的制单技巧，逐步学会独立制作各种外贸单证，丰富制单经验。 具体包括： (一) 审核信用证 1、目的与要求 信用证的开立是以合同为基础的，而其下的制单要求是:单证一致，单单一致。信用证受益人只有提交的单据合格，才能获得银行的付款保证。因而认真审核国外开来的信用证，关系到受益人能否收到货款。通过实训操作，使学生进一步掌握审证的基本规律和方法，了解“UCP600”和国际标准银行实务的规定的有关规定，同时会及时联系进口商通过开证行对信用证进行修改。 2、实训内容 (1)审核信用证主要是信用证内容的审核，是否与合同一致，以及一些特别条款的审核。 (2)修改信用证撰写一封完整的改证函 (二) 出口托运 1、目的与要求 出口方在合同的履行过程中，如需要订舱，则出口方必须负责与承运人订立运输合同、预订船只或舱位。通过实训操作，要求了解出口货物托运的程序，会托运单、订舱委托书的填写。 2、实训内容 (1)出口订舱流程会查阅各班轮公司的船舶、船期、挂靠港及船舱箱位数等具体情况，然后选择合适的船只订舱。(2)会缮制有关单据，如订舱委托书、托运单 (三) 出口货物报检 1、目的与要求 商品检验检疫是商品出口过程中的一个重要环节。通过实训操作，使学生掌握报验流程，
( 实习报告 ) 单位：_________________________姓名：_________________________日期：_________________________ 精品文档 / Word文档 / 文字可改 国际贸易实务实训总结Summary of international trade practice training
国际贸易实务实训总结 为期一周半的国际贸易与实务实训已经结束了，不能说完成得很圆满，但是有一点可以肯定的是，通过这次实训，我了解了国际贸易的基本流程，并且巩固了所学的理论知识，切身体会到了商品进出口贸易的全过程。 其实，说真的，还没实训之前心里总是有点忐忑不安，怕自己不能顺利完成这次实训任务。我们实训的第一步就是拟写建交函，由于我们之前并没有写过这种信函，对它的格式不是很清楚。所以，我就先在网上搜索了建交函的范文，知道了基本格式以后，然后就根据操作的要求写好建交函。这一步实际上并不难，所以所花的时间也不多，但这仅仅是第一步工作，接下来还有一连串的工作要做。 整个过程下来，对我来说最难也是我最欠缺的就是那一系列的核算。我们要做的有三个核算，出口报价核算、出口还盘核算和成
交核算。要进行核算首先要知道计算公式以及它们的转化公式。刚开始算的时候，可能是因为自己太过粗心，老是算错，算出来的结果总是对不上。后来还是在老师的帮助下，才找到了问题的症结所在，原来我小数点后面少加了一个零。这次教训让我知道了细心仔细的重要性。在进行核算的过程中，还应该引起注意的就是不同币制的转换，有的要的是美元，如进行对外报价时。而在计算利润率时则需要的是人民币。在做这一步时，最重要的就是要细心，还要有耐心，算错了不能心急，要耐心地找出错误的原因。 完成成交核算之后，接下来就是合同的签订。我们要根据合同基本条款的要求和双方在信函中确定的条件制作售货确认书，另外还要给对方寄出成交签约函。在这一过程中，合同的条款要全面、内容要完整；合同没有会签之前，买方是不可能签署的，这一点尤其值得注意。接下来就是审核信用证和写改证函，根据审核信用证的一般原则和方法对收到的信用证认真的审核，列明信用证存在的问题并陈述改证的理由。这个过程需要根据合同，把信用证和合同相比较，仔细认真地进行审核。收到对方的改证函后，接下来就要
双孔双渗，就是模型中有基质和裂缝两种孔隙体积，基质孔隙是主要的储油空间，裂缝是主要的流动通道，基质和裂缝都有孔隙体积和渗透率，所以叫双孔双渗。 什么是重启计算？ 历史拟合结束后需要进行产量预测，在进行产量预测计算时，不需要再从历史拟合开始时进行计算，可以直接从历史拟合结束的时间接着往下算。这种应用上一次计算的输出作为下一次计算的初始输入计算就叫重启计算。 要进行重启计算，首先要定义重启时间步的输出。可以用RPTRST来定义输出每时间步，每月，每年或每隔几月几年重启时间步文件。如果采用多文件格式输出，则文件后缀为：.X0000, .X0001等，如果是单文件输出，则输出文件为.UNRST. 重启文件记录了每时间步模型压力分布，饱和度分布，溶解油气比分布，同时也记录所有井的井位，射孔位置，产量控制。不过重启文件没有记录垂直管流表（VFP表），所以在应用垂直管流表时要记住重启时需加上垂直管流表。 ECLIPSE有两种重启计算方法，快速重启和完全重启。 快速重启不需要重新处理RUNSPEC,GRID,EDIT,PROPS和REGIONS部分，如果在历史拟合计算时设了SAVE关键字，这些部分将保存在输出的SAVE文件中，这样在重启计算时不用再计算传导率。 完全重启需要重新处理RUNSPEC,GRID,EDIT,PROPS和REGIONS部分，要重新计算传导率。 完全重启步骤： 在历史拟合部分用RPTRST要求输出重启文件。 在PRT文件中检查重启时间对应的重启文件步。 将历史拟合文件拷贝为重启文件。 删掉SOLUTION部分中的EQUIL和水体部分，用RESTART关键字设重启。 在SCHEDULE部分用SKIPREST或删掉所有历史拟合时间步。 如果有VFP表，要保留VFP表。 增加新时间步进行预测计算。 快速重启步骤： 在历史拟合部分用SAVE和RPTRST要求输出SAVE文件和重启文件。 将历史拟合文件拷贝为重启文件。 删掉所有SUMMARY以前部分。 用LOAD关键字装载SAVE文件。 用RESTART设重启时间。
《国际贸易实务》模拟题 一单选题 1.A公司5月18日向B公司发盘,限5月25日复到有效,A公司向B公司发盘的第二天,A公司收到B公司5月17日发出的,内容与A公司发盘内容完全相同的交叉发盘,此时(). A.合同即告成立 B.合同无效 C.A公司向B公司或B公司向A公司表示接受,当接受通知送达对方时,合同成立 D.必须是A公司向B公司表示接受,当接受通知送达对方时,合同成立 [答案]:C 2.CFR术语有多种变形,其目的是明确() A.装货费用由谁负担 B.卸货费用由谁负担 C.风险划分的界线 D.运费由谁负担 [答案]:B 3.CPT和CFR相同的是(). A.属装运合同 B.交货地点 C.费用划分界限 D.提交的单据 [答案]:A 4.CPT贸易术语条件下,卖方将合同中规定的货物(),完成交货. A.交到装运港船上 B.置于买方处置之下 C.交给买方自己指定的承运人 D.交给卖方自己指定的承运人或第一承运人 [答案]:D 5.FOB,CFR和CIF贸易术语,最宜采用()检验方法 A.出口国检验,进口国复验 B.在进口国检验 C.在出口国检验 D.装运港()检验重量,目的港()检验品质 [答案]:A 6.FOB条件下,风险划分的界线是() A.装运港船舷 B.装运港船舱 C.装运港船上 D.装运港码头
[答案]:C 7.SWIFT采用0-9的数字区别电文业务性质,7代表跟单信用证和保函.修改信用证的代码是(). A.MT700 B.MT707 C.MT720 D.MT705 [答案]:B 8.按CIF术语成交的贸易合同,货物在运输途中因火灾被焚,应由(). A.卖方承担货物损失 B.卖方负责向保险公司索赔 C.买方负责向保险公司索赔 D.买方负责向承运人索赔 [答案]:C 9.按照《2000通则》的解释,按DEQ成交,买卖双方的风险划分界限在(). A.装运港船上 B.目的地 C.目的港船上 D.目的地码头 [答案]:D 10.按照货物重量,体积或价值三者中较高的一种计收运费,运价表内以()表示. A.M/W B.W/MorAd.Val C.AdVal D.Open [答案]:B 11.包销业务中包销商与出口商之间是一种(). A.买卖关系 B.委托代理关系 C.互购关系 D.代销关系 [答案]:A 12.保险公司承担保险责任的期间通常是() A.钩至钩期间 B.舷至舷期间 C.仓至仓期间 D.水面责任期间 [答案]:C
国际贸易实务模拟实训报告 随着中国在国际贸易的地位的不断上升，我们学习国际贸易专业的学生们要掌握有关于国际贸易方面的知识也要不断增加，这次学校给了我们一个很好的实习锻炼机会，就是让我们模拟国际贸易实务操作，从而从中掌握国际贸易流程。 通过simtrade上机实习，可以使我们熟悉外贸实务的具体操作流程，增强感性认识，并可从中进一步了解、巩固与深化已经学过的理fg的运作方式；切身体会到国际贸易中不同当事人面临的具体工作与他们之间的互动关系；学会外贸公司利用各种方式控制成本以达到利润最大化的思路；认识供求平衡、竞争等宏观经济现象，并且能够合理地加以利用。老师通过在网站发布新闻、调整商品成本与价格、调整汇率及各项费率等方式对国际贸易环境实施宏观调控，使我们在实习中充分发挥主观能动性，真正理解并吸收课堂中所学到的知识，为将来走上工作岗位打下良好基础。 上机模拟操作 simtrade软件 **年5月16日——**年6月13日 经过一个多月的simtrade模拟训练，我们对国际贸易的业务流程及操作有了更进一步的了解和感触，现在我们对贸易的理解已经不在停留在单纯的理论层面。
在头一两个星期里，我们处理起业务是不知从何做起，填写单据那是相当的慢，算一笔进出口预算表都要算上一个多小时。经过两个星期的不间断联系，早后来的操作练习中我们处理的是得心应手，可谓从容自如。 在我国继续扩大开放、深化改革和加入世界贸易组织以来的新形势下，作为未来从事国际贸易方面业务的我们必须熟练掌握国际贸易的sdf这两年学习的一个大总结。从国际贸易理论，到国际贸易实务，再到上学期的外贸函电及本学期外贸合同的制定、国际货物运输风险和保险，在本次模拟训练中都一一体现，通过simtrade模拟训练我们对以前所学过的知识有了一次系统的回顾，又在训练中对国际贸易的流程及操作有了更加深刻的体会，这对我们未来的工作在思想上做了充分的准备。 通过本次的模拟实习，我们可以发现以前学习中薄弱环节，为今后的学习指明了方向，也会实际操作打下一个良好的基础。本次模拟训练给我最大的体会就是操作细节的细腻及流程的缜密，各个流程相互衔接，此流程的疏忽将会导致彼流程无法完成，某一细节的不慎错误或纰漏将会导致整个流程操作前功尽弃，这为未来的实际工作敲响了警钟：做贸易一定要仔细谨慎。 在本次实习中，我们充分利用了simtrade提供的各项资源。我们充分使用邮件系统进行业务磋商，这是我们未来
某路基工程施工过程数值模拟 摘要 本文首先对FLAC3D软件进行了介绍，简明阐述了其特点、应用范围及不足；然后结合具体路堤工程，采用FLAC3D软件对施工过程进行了模拟，生成了初始竖向和水平应力云图、第一次填筑及填筑结束时的沉降云图及水平位移云图；最后生成了路基中心点和坡脚节点的沉降曲线。 关键词：FLAC3D；数值模拟；应力云图；沉降云图；位移云图 1 FLAC3D的功能与特性 自R.W.Clough 1965年首次将有限元引入土石坝的稳定性分析以来，数值模拟技术在岩土工程领域获得了巨大的进步，并成功解决了许多重大工程问题。特别是个人电脑的出现及其计算性能的不断提高，使得分析人员在室内进行岩土工程数值模拟成为可能，也使得数值模拟技术逐渐成为岩土工程研究和设计的主流方法之一。数值模拟技术的优势在于有效延伸和扩展了分析人员的认知范围，为分析人员洞悉岩体、土体内部的破坏机理提供了强有力的可视化手段。FLAC系列软件的出现，为岩土工程研究工作者提供了一款功能强大的数值模拟工具。 1.1 FLAC3D主要特点 FLAC(Fast Lagrangian Analysis of Continua)是由Itasca公司研发推出的连续介质力学分析，是该公司旗下最知名的软件系统之一，FLAC目前已在全球七十多个国家得到广泛应用，在国际土木工程（尤其是岩土工程）学术界和工业界享有盛誉。 FLAC3D界面简洁明了，特点鲜明。其使用特征主要表现为：命令驱动模式、专一性、开放性。作为有限差分软件，相对于其他有限元软件，在算法上，FLAC3D 有以下几个优点：采用“混合离散法”来模拟材料的塑性破坏和塑性流动，比有限元中通常采用的“离散集成法”更准确、合理；即使模拟静态系统，也采用动态运动方程进行求解，这使得FLAC3D模拟物理上的不稳定过程不存在数值上的障碍；采用显示差分法求解微分方程。采用FLAC3D进行数值模拟时，必须指定有限差分网格、本构关系和材料特性、边界和初始条件，这是FLAC3D求解的一般流程。
一、把以下英文术语翻译成中文，是英文简称的需先写出其全称再翻译（本大题共5小题，每小题1分，共5分） 1、Neutral Packing 2、Insurance Policy 3、Order B/L 4、OCP 5、O/A 二、单项选择题（本大题共20小题，每小题1分，共20分） 1、我方出口大宗商品，按CIF Singapore 成交，运输方式为Voyage Charter,，我 方不愿承担卸货费用，则我方应选择的贸易术语的变形是（）。 A、CIF Liner Terms Singapore B、CIF Landed Singapore C、CIF E x Ship’s Hold Singapore D、CIF Ex Tackle Singapore 2、按照《INCOTERMS2000》的解释，以FOBST成交，则买卖双方风险的划分界限是（）。 A、货交承运人 B、货物越过装运港船舷 C、货物在目的港卸货后 D、装运港码头 3、山东渤海公司与日本东洋株式会社在万国博览会上签订了一份由日方向中方提供BX2-Q船用设备的买卖合同，采用的贸易术语是DES。运输途中由于不可抗力导致船舶起火，虽经及时抢救，仍有部分设备烧坏，则（）应来承担烧坏设备的损失。 A.东洋株式会社 B.山东渤海公司 C.船公司 D.保险公司 4、在CIF条件下，Bill of Lading对运费的表示应为( )。 A．Freight Prepaid B．Freight Collect C．Freight Pre-payable D．Freight Unpaid 5、在进出口业务中，能够作为物权凭证的运输单据有( )。 A．Rail Waybill B．Bill of Lading C．Air Waybill D．Parcel Post Receipt 6、预约保险以（）代替投保单，说明投保的一方已办理了投保手续。 A、B/L B、Shipping advise from abroad C、Mate，s receipt D、Sales contract 7、我某公司与外商签订一份CIF出口合同，以L/C为支付方式。国外银行开来的信
地下水数值模拟在我国——回顾与展望——为《水文地质工程地质》创刊40年而作 薛禹群 吴吉春(南京大学地球科学系,南京 210093) 今年《水文地质工程地质》将迎来它创刊40周年。40年来,它为发展我国的水文地质工程地质事业,提高我国水文地质学和工程地质学的整体水平作出了不可磨灭的贡献。回顾过去,成绩斐然;展望未来,前景灿烂。仅以此文纪念《水文地质工程地质》双月刊创刊40周年。 1 概貌 我国自1973年以来在地下水的数值模拟方面发展很快,它的应用已遍及与地下水有关的各个领域和各个产业部门。高校、科研院所与生产部门相结合,已运用数值模拟解决了很多国民经济建设中急需解决的各类问题,其中包括: 水资源评价问题(包括供水、排水、水利等各类问题中的地下水水位或压强预报和水量计算等);地下水污染问题,水2岩作用和生物降解作用的模拟;非饱和带水分和盐分运移问题;海水入侵、高浓度咸水 卤水入侵问题;热量运移和含水层贮能问题;地下水管理与合理开发、井渠合理布局和渠道渗漏问题;地下水2地面水联合评价调度问题;地面沉降问题;参数的确定问题。它所涉及的地质情况多种多样,有潜水,也有承压水;有单个含水层的情况,也有多个含水层存在越流的情况,以及种种复杂的地质构造和岩相变化情况。由此,探讨了相应的模型概化与边界条件的处理。模型有二维的(平面的、剖面的),也有三维的,但以二维为主。虽然国内一共建立了多少个模型无法精确统计,但从有限的资料可以看出,从模型类型上看,按国际地下水模拟中心(IG WM C)的分类,几种类型的模型我们都有了,即: (1)预报模型包括水流模型 物质运移模型(溶质运移模型);热量运移模型;形变模型;多目标模型。 (2)管理模型; (3)识别模型其中大部分(估计在90%左右,甚至有可能超过)是预报模型,用来预测水流、污染物、热量、地面变化的时空变化,包括水资源(水量)评价、矿山涌水量、渠系及水库渗漏量预测等。在这些模型中以水流模型为主(80年代早期以前基本上是清一色的水流模型),溶质运移模型次之,其它几类模型占的比例很少。水流模型有饱和的、非饱和的、饱和2非饱和的、地下水2地表水联合的几类,以饱和带模型为主。同时考虑地下水2地表水的模型只是个别的、探讨性的。水流模型一般只考虑均质流体,非均质流体的水流模型则是作为子模型和盐分运移子模型同时处理的。溶质运移模型在我国多数是处理低浓度的水质(地下水污染)问题。因此,由水流方程和对流2弥散方程分别组成的两个子模型可以独立求解,运动方程也以传统的达西定律为基础。只有少数研究海水入侵、卤水 咸水入侵和污水中高浓度污染物运移问题中,密度、粘度要由状态方程决定。此时,上述两个子模型要耦合起来求解。迭代法是解这类问题常用的解法。我国最早的三维可混溶海水入侵模型,是在80年代末期建立的。根据《W ater R esou rces R esearch》的评审意见,该模型发展了潜水含水层条件下的海水入侵模型。在此以前,国际上一直把潜水含水层简化作承压含水层处理,以回避处理降水入渗、潜水面波动对溶质运移的影响。在我国这些海水入侵、卤水 咸水入侵模型以及以后将要谈到的热量运移模型、运动方程中,除了根据传统的达西定律考虑以水头梯度为基础的强迫对流外,还考虑了自然对流。卤水 咸水入侵由于浓度高还考虑了由于粘滞性产生的切应力对水流运动的阻滞。溶质运移模型中,只考虑污染物运移的模型在我国粗略看来略多于同时考虑吸附、解吸等的模型。少数模型已深入探讨了海水入侵过程中,水2土间发生的N a+2Ca2+、M g2+2Ca2+阳离子交换。但,处理更为复杂的如氮素生物化学转换的模型尚未见报导。我国研究热量运移、形变的模型不多,且都和一些大城市的地面沉降及为控制地面沉降进行的回灌联系在一起。热量运移模型,已考虑了与热量运移有关的各种主要因素(对流、传导、热机械弥散、自然对流、水
篇一:《国际贸易实务模拟实验实训总结》 国际贸易实务模拟实验实训总结 经过两周的模拟实验实训，我们对国际贸易的业务流程及操作有了更进一步的了解和感触。现在我们对贸易的理解已经不再停留在单纯的理论层面，而是上升到了一定的高度。 在这次实训中，我们充分利用了世格外贸单证教学系统提供的各项资源进行练习。通过老师的悉心指导和查阅相关资料，我们对知识有了更深入的理解。 这次的模拟实验操作，大致上可以分为三个方面的内容，分别为出口磋商谈判、合同的签订、信用证的审核等。出口磋商谈判又包括建立业务关系、询盘、发盘、还盘、接受等内容。出口磋商谈判的各个环节是相互联系的，形成一个有机的整体。 实训第一天的时候，为了之后的练习能顺利进行，老师让我们在网上查找资料，在相关网站上了解一些与国际贸易相关的知识。开始做练习的时候，我们要建立业务关系、写贸易函电，由于这是在实践中第一次接触，所以就比较迷茫，不知从何做起，完全找不到头绪。后来在老师的指导下，结合上网查找相关资料，
我们慢慢找到了做题的方法。经过两个星期的不间断练习，在后来的操作练习中，我们处理起来就比较轻松，比较得心应手了。 实训过程中，信用证的审核相对来说比较难，但同时这部分也是重点，在进出口贸易中是比较重要的一部分。面对密密麻麻的文字，并且还是英文的，先不审核，自己就先晕了。所以，在做信用证审核的练习中，细心和耐心是必不可少的。刚开始时，面对陌生的合同和信用证，里边好多术语都不明白是什么意思。然后，老师就带着大家一起分析销售合同和信用证，逐句翻译。后来，题做得多了，慢慢就掌握了分析的方法。实训结束时，自己差不多可以独立阅读信用证了，上边的英文看着也不再那么陌生了。 这两周，我们一直坐在电脑前做各种国际贸易实务模拟操作的练习，每天盯着电脑很忙很累，但也收获了很多。在练习中，我了解和掌握了进出口贸易的基本操作程序和主要操作技能，使自己在模拟操作中进步了；同时也认识到了自己身上存在的很多不足点，发现对于国际贸易中的很多东西，我们都没有搞懂,尤其是里面的规则等等。 通过这次实训，我感觉在国际贸易中，出口商是最为重要的角色。在出口过 程中，出口商为了找到客户并顺利完成交易过程，需要经过准备、磋商、签约、履约、善后几个流程。在准备阶段，出口商需要及时了解市场行情，并同工厂和进口商建立广泛而牢固的业务关系，这是非常重要的。
材料加工数值模拟 论文 专业：材料加工 姓名：闫禹伯 学号：2013432109
目录
第一章．铸造过程的数值模拟分析 传统铸件的生产是根据经验确定铸造工艺，先试浇铸，检验试样是否存在浇铸缺陷，如有则修改工艺方案，然后重复上述过程，直至获得合格铸件。由于这种方法必须在浇铸后才能对铸件工艺是否合理进行评价，因而该方法存在设计周期长、生产成本高、效率低等缺点；而且得到的往往不是最终铸造工艺，对于大型或复杂形状铸件该缺点显得更加突出。铸造CAE模拟技术是利用计算机技术来改造和提升传统铸造术，对降低产品的成本、提高铸造企业的竞争力有着不可替代的作用。 一．铸造过程数值模拟的发展现状 计算机技术的飞速发展，已使其自电力发明以来最具生产潜力的工具之一，数字化时代正一步步向我们走来。计算机辅助设计（CAD）、计算机辅助工程分析（CAM）和计算机辅助制造（CAE）等技术在材料科学领域的应用正在不断扩大和深入，已经成为材料科学领域的技术前沿和十分活跃的研究领域。就铸造领域而言，铸造过程数值模拟已经成为计算机在铸造研究和生产应用中最为核心的内容之一，涉及铸造理论、凝固理论、传热学、工程力学、数值分析、计算机图形学等多个学科[1-5]，是公认的材料科学的前沿领域。 铸造过程数值模拟技术经过了四十年的发展历程，其间，从简单到复杂、从温度场发展到流动场、应力场，从宏观模拟深入到微观领域，从普通的重力铸造拓展到低压、压铸等特种铸造，从实验室研究进入到工业化实际应用。特别是近些年来，在包括计算机硬件、软件、信息处理技术以及相关学科的强有力的支持下，数值模拟技术在人类社会的各个领域得到了广泛的应用，取得了长足的进步。如果说10年前，大多数铸造技术人员对模拟仿真技术还抱有观望、怀疑的态度的话，那么10年后的今天，已有众多的企业纷纷采用数值模拟技术，应用于实际生产。目前欧美日等西方发达国家的铸造企业普遍应用了模拟技术，特别是汽车铸件生产商几乎全部装备了仿真系统，成为确定工艺的固定环节和必备工具。上世纪90年代中后期以来，国内铸造厂家逐渐认识到其重要性，纷纷引入该技术，目前已有超过200家铸造企业拥有模拟仿真手段，在实际生产中起到了较为
工程地质数值法 班级： 姓名： 学号： 指导老师：
某路基工程施工过程数值模拟 本文首先对FLAC3D软件进行了介绍，简明阐述了其特点、应用范围及不足，然后结合具体路堤工程，采用FLAC3D软件对施工过程进行了模拟，生成了初始竖向和水平应力云图、第一次填筑及填筑结束时的沉降云图及水平位移云图;最后生成了路基中心点和坡脚节点的沉降曲线。 关键词：FLAC3D:数值模拟；应力云图；沉降云图；位移云图 1、FLAC3D的功能与特性 自R.W.Clough 1965年首次将有限元引入土石坝的稳定性分析以来，数值模拟技术在岩土工程领域获得了巨大的进步，并成功解决了许多重大工程问题。特别是个人电脑的出现及其计算性能的不断提高，使得分析人员在室内进行岩土工程数值模拟成为可能，也使得数值模拟技术逐渐成为岩土工程研究和设计的主流方法之一。数值模拟技术的优势在于有效延伸和扩展了分析人员的认知范围，为分析人员洞悉岩体、土体内部的破坏机理提供了强有力的可视化手段。FLAC系列软件的出现，为岩土工程研究工作者提供了一款功能强大的数值模拟工具。 1.1 FLAC3D主要特点
FLAC(Fast Lagrangian Analysis of Continua)是由Itasca公司研发推出的连续介质力学分析，是该公司旗下最知名的软件系统之一，FLAC目前已在全球七十多个国家得到广泛应用，在国际土木工程（尤其是岩土工程）学术界和工业界享有盛誉。 FLAC3D界面简洁明了，特点鲜明。其使用特征主要表现为：命令驱动模式、专一性、开放性。作为有限差分软件，相对于其他有限元软件，在算法上，FLAC3D有以下几个优点：采用“混合离散法”来模拟材料的塑性破坏和塑性流动，比有限元中通常采用的“离散集成法”更准确、合理；即使模拟静态系统，也采用动态运动方程进行求解，这使得FLAC3D模拟物理上的不稳定过程不存在数值上的障碍；采用显示差分法求解微分方程。采用FLAC3D进行数值模拟时，必须指定有限差分网格、本构关系和材料特性、边界和初始条件，这是FLAC3D求解的一般流程。 1.2 FLAC3D的应用范围 FLAC3D的应用范围已拓展到土木建筑、交通、水利、地质、核废料处理、石油及环境工程等领域，成为这些专业领域进行分析和设计不可或缺的工具。其研究范围主要集中在以下几个方面： ●岩体、土体的渐进破坏和崩塌现象的研究； ●岩体中断层结构的影响和加固系统（如喷锚支护、喷射混凝土等）的模拟研究； ●岩体、土体材料固结过程的模拟研究； ●岩体、土体材料流变现象的研究； ●高放射性废料的地下存储效果的研究分析； ●岩体、土体材料的变形局部化剪切带的演化模拟研究； ●岩体、土体的动力稳定性分析、土与结构的相互作用分析以及液化现象的研究等。