Influence of surface tension implementation

Influence of surface tension implementation
Influence of surface tension implementation

In?uence of surface tension implementation in Volume of Fluid and coupled Volume of Fluid with Level Set methods for bubble growth and detachment

A.Albadawi a ,?,D.

B.Donoghue b ,A.J.Robinson b ,D.B.Murray b ,Y.M.

C.Delauréa ,?

a School of Mechanical and Manufacturing Engineering,Dublin City University,Glasnevin,Dublin,Ireland b

Department of Mechanical and Manufacturing Engineering,Trinity College Dublin,Ireland

a r t i c l e i n f o Article history:

Received 31July 2012

Received in revised form 10January 2013Accepted 11January 2013

Available online 1February 2013Keywords:

Gas–liquid ?ow Bubble growth

Bubble detachment Volume-of-Fluid Level Set

Coupled VOF with LS Static contact angle

a b s t r a c t

A simple coupled Volume of Fluid (VOF)with Level Set (LS)method (S-CLSVOF)for improved surface ten-sion implementation is proposed and tested by comparison against a standard VOF solver and experi-mental observations.A CFD Open source solver library (OpenFOAM ò)is used for the VOF method,where the volume fraction is advected algebraically using a compressive scheme.This method has been found not to be suitable for problems with high surface tension effects and it is extended by coupling it with a LS method which is used to calculate the surface tension and the interface curvature.Two test cases;a circular bubble at equilibrium and a free bubble rise,are studied ?rst to examine the accuracy of the S-CLSVOF method.The problem of 3D axi-symmetrical air bubble injection into quiescent water using different volumetric ?ow rates is then considered to assess the method under challenging capillary dominant conditions.An experimental study has been performed to validate the numerical methods with reference to the geometrical characteristics of the bubble during the full history of formation.The expo-nential power law controlling the detachment process is investigated.In addition,the in?uence of the static contact angle imposed at the rigid wall is considered.The results have shown that the coupling code (S-CLSVOF)improves the accuracy of the original VOF method when the surface tension in?uence is predominant.The two methods provide similar results during the detachment stage of the process due to the large increase of the gas inertia effect.Finally,the static contact angle boundary condition was shown to allow accurate modeling provided that the imposed static contact angle is less than the minimum instantaneous values observed experimentally.

ó2013Elsevier Ltd.All rights reserved.

1.Introduction

The study of bubble growth and detachment has attracted extensive attention over the last decades due to its occurrence in a wide range of applications such as heat exchangers,stirring ves-sels,and ?otation processes.It is considered also to be a fundamen-tal process for understanding more complicated phenomena such as boiling.Earlier theoretical studies of bubble growth focused on the development of analytical models of the gas/liquid interface assuming that the bubble retained a spherical shape (Davidson and Schuler,1960;Gaddis and Vogelpohl,1986;Oguz and Prosper-etti,1993).The main drawbacks of these early theoretical models include their inability to study viscous liquids,to model complex interface deformations or to account for solid boundaries.To over-come these issues,moving and ?xed grid methods,have been developed.In the moving grid method (Dandy and Leal,1989),the ?uid domain is divided into two ?uid sub-domains,while the ?xed grid methods,including the front tracking method (Unverdi and Tryggvason,1992)and the interface capturing method,assume that both ?uids acts as one mixture whose properties are deter-mined from the interface position.

Two main interface capturing approaches have been developed:the Volume of Fluid (VOF)and the Level Set (LS)methods.Recently,coupling between VOF and LS (CLSVOF)has also received signi?-cant attention in order to combine the advantages of both meth-ods.The LS Method was ?rst developed by Osher and Sethian (1988)and it has been implemented for multiphase ?ows by Suss-man et al.(1994).It relies on a signed distance function /to distin-guish between the two ?uids in the mixture.It has a positive value in one ?uid and a negative value in the other,and it provides a smooth variation of the physical properties across the interface de-?ned as the iso-contour /=0.The interface is advected by solving a transport equation.The LS function,however,ceases to act as a distance function after the ?rst time step advection and a re-ini-tialization process is required to recover the distancing property.Sussman et al.(1994)showed that the LS method does not pre-serve mass conservation due to the re-distancing process.More re-cently however a conservative Level Set method (Olsson and Kreiss,2005;Olsson et al.,2007)has been proposed.Tests in

0301-9322/$-see front matter ó2013Elsevier Ltd.All rights reserved.https://www.360docs.net/doc/275996177.html,/10.1016/j.ijmultiphase?ow.2013.01.005

Corresponding authors.Tel.:+353(0)17008886(Y.M.C.Delauré).

E-mail address:yan.delaure@dcu.ie (A.Albadawi).

two-and three-dimensions with structured and unstructured grids have con?rmed that signi?cant improvement in the mass conser-vation could be achieved including in cases of large density ratios. The reader is referred to the review by Losasso et al.(2006)for other improvements to the LS methods.

In the VOF method(Hirt and Nichols,1981),a color function, de?ned as a volume fraction a,is used to differentiate both?uids in the domain where a represents the amount of?uid in each cell. The interface is de?ned in the cells where a2]0,1[.In incompress-ible?ow,the mass conservation is achieved by using either a geo-metrical reconstruction coupled with a geometrical approximation of the Volume of Fluid advection or a compressive scheme.In the geometrical case,the position of the interface is determined by cal-culating the interface normal and the intersection points of the interface with the cell faces[SLIC‘‘Simple Line Interface Calcula-tion’’algorithm(Noh and Woodward,1976),PLIC‘‘Piecewise Lin-ear Interface Calculation’’(Rider and Kothe,1998;Youngs, 1982)].Early linear interface reconstruction and advection schemes relied on direction splitting techniques to account for multi-dimensionality and were typically?rst order accurate(e.g. Rudman,1997).Second order reconstruction and advection were achieved using more advanced reconstruction and un-split multi-dimensional advection schemes(Rider and Kothe,1998;López et al.,2004;Cervone et al.,2009)as well as split advection schemes (Aulisa et al.,2007).Pilliod and Puckett(2004)have shown that it is necessary and suf?cient for the reconstruction algorithm to be able to reconstruct a linear or planar interface exactly for it to be second order accurate on smooth interfaces.This is the case for several existing interface reconstruction schemes including the Least Square Volume-of-Fluid Interface Reconstruction Algorithm (LVIRA)(Puckett,1991),the Ef?cient Least Square Volume-of-Fluid Interface Reconstruction Algorithm(ELVIRA)(Pilliod,1992),the Least Square Fit(LSF)(Aulisa et al.,2007),and the3D Hybrid Lagrangian Eulerian method for multiphase?ows(HyLEM)(Le Chenadec and Pitsch,2013).The main drawback of the geometrical methods is their complexity for3D applications,in particular when coupled with an unstructured mesh.

With the compressive algorithms,the convective term of the VOF advection equation can be discretized using a compressive dif-ferencing scheme designed to preserve the interface sharpness [CICSAM(Ubbink,1997),HRIC(Muzaferija and Peric,1999),com-pressive model in OpenFOAMò(Weller,2008)].In these methods, the interface typically spreads over a few cells and low but un-bounded diffusion of the interface can occur under certain condi-tions(Ubbink,1997).With the algebraic VOF method used in the present work,the interface smearing is minimized by adding a compressive or Counter gradient term to the VOF advection equa-tion(Weller,2008)which guarantees the boundedness of the vol-ume fraction.Algebraic methods do not require any interface geometrical reconstruction and extension to three dimensions and unstructured mesh is straightforward.

In addition to capturing the interface,a surface tension model must be implemented at the gas/liquid interface.In the VOF meth-ods,it is represented as a source term in the momentum equation and generally calculated using the Continuous Surface Force model (CSF)(Brackbill et al.,1992).This relies on an approximation of the interface curvature from the gradient of the VOF function.The gra-dient cannot be calculated accurately since the VOF function is a discontinuous step function,and its discrete approximations are known to generate unphysical spurious currents at the interface (Lafaurie et al.,1994;Renardy and Renardy,2002).Renardy and Renardy(2002)developed the PROST algorithm(parabolic recon-struction of surface tension)which was shown to achieve a signif-icant reduction in the magnitude of the velocity induced by the spurious currents.In contrast to VOF,the LS method provides a sharp interface and a smooth transition in the physical properties across the interface.The LS method also con?nes the effect of the volumetric surface force to a narrow region around the interface by using the Dirac function.

Sussman and Puckett(2000)proposed a new method(CLSVOF) combining the advantages of both VOF(mass conservation)and LS (interface sharpness).The coupling is achieved by advecting the interface using the conservative VOF function,calculating the interface normal using the smoothed LS function,and updating the physical properties from a smoothed Heaviside function. Different strategies can be adopted for the coupling regarding the advection equations and the re-initialization procedure.Re-distancing the LS function was performed by using either a geo-metrical reconstruction(Sussman et al.,1994;Son and Hur, 2002)or an analytical solution(Ménard et al.,2007).Although most coupling models solve both the LS and the VOF advection equations(Sussman and Puckett,2000;Son and Hur,2002),Sun and Tao(2010)have proposed a coupled method which relies on the solution of the VOF advection equation with geometrical reconstruction of the LS function from the VOF function.Kunkel-mann and Stephan(2010)used the VOF equation implemented in OpenFOAM to advect the interface,while initializing the LS func-tion using the VOF function.This coupling method was used for studying the bubble growth due to evaporation relying on the interface reconstruction at the triple contact point in order to accu-rately calculate the mass transfer.

The process of bubble growth using interface capturing meth-ods has previously been studied using both LS and VOF methods. Valencia et al.(2002)used the geometrical VOF scheme imple-mented in the Fluent5.5.Chen and Fan(2004)and Chen et al. (2009)used the LS method to study bubble growth by injection. Son et al.(1999)and Mukherjee and Kandlikar(2007)used LS method for the evaporation processes.Gerlach et al.(2007),Buwa et al.(2007),Chakraborty et al.(2009),Chakraborty et al.(2011), and Ohta et al.(2011)used CLSVOF to track the interface for bubble growth and detachment at ori?ces.In spite of this extensive work, the complete history of the formation including detachment has not been quantitatively examined against experimental data and few comparative studies have veri?ed the in?uence of the surface tension implementation on detachment parameters.Gerlach et al. (2006)studied three different models(Kernel,PROST,and CLSVOF) using several test cases(equilibrium rod,capillary wave,and Ray-leigh–Taylor instability).The least spurious currents were obtained with the PROST method.However,the CLSVOF method was shown to be less computationally expensive.Although Gerlach et al. (2005,2006,2007)studied the bubble detachment parameters with respect to different geometrical and physical aspects,a com-parison of CLSVOF with other interface capturing method has not yet been done.Most studies of bubble growth with CLSVOF have focused on bubble perioding and growth frequency(Buwa et al., 2007;Chakraborty et al.,2011)using relatively large?ow rates (>100cm3/min).In contrast,the present study focuses on small ?ow rates so that part of the bubble formation is more dominated by the capillary forces so that any errors in the surface tension implementation can be expected to lead to unphysical bubble behavior.The effect of the imposed static contact angle on the bub-ble detachment volume has been studied using the CLSVOF meth-od(Buwa et al.,2007;Gerlach et al.,2007).The present study extend this to the study of the relationship between the imposed static contact angle,the experimentally observed angle,and the ori?ce radius is studied here along with the in?uence of the static contact angle on the bubble detachment time and volume.

In the present work,the VOF-Compressive scheme imple-mented in OpenFOAM is coupled to the LS method to improve sur-face tension models.An initial guess of the Level Set function is de?ned using the VOF function,and then,a re-initialization is per-formed to obtain the signed distance function.The volumetric

12 A.Albadawi et al./International Journal of Multiphase Flow53(2013)11–28

surface tension force is calculated similarly to LS method where a Dirac function is considered.The extended simple coupling code (S-CLSVOF)is validated?rst by studying a circular bubble at equi-librium in order to examine the spurious currents at the bubble interface,and then both VOF and S-CLSVOF are used for the study of free bubble rise that is without any interaction between the bub-ble free surface and the wall boundary conditions.The study of the adiabatic axi-symmetrical bubble growth until detachment is then considered.The growth process is characterized by complicated topological changes during the formation and the existence of a di-rect contact with the boundary condition where special care should be taken in this context.Experimental work is performed and used as a benchmark for the numerical methods.Finally,the effect of the imposed quasi-static contact angle on the instanta-neous contact angle during the growth is investigated using S-CLSVOF.The process of bubble formation from a wall ori?ce is per-formed using small volumetric?ow rate,so that the bubble grows in the static regime(McCann and Prince,1971)where isolated bubbles with the same detachment frequency are detached from the ori?ce.Under these conditions,the bubble grows quasi-stati-cally(Oguz and Prosperetti,1993),where the buoyancy and the surface tension are the dominant forces.

2.Numerical formulation

https://www.360docs.net/doc/275996177.html,erning equations

The governing equations for two isothermal,incompressible, immiscible?uids include the continuity,momentum,and interface capturing advection equations:

ráV?0e1T@eq VT

@t

tráeq VVT?àr Ptrástq gtF re2T

@a

tráea VTàaeráVT?0e3Twhere q is the?uid density,V the?uid velocity vector,s the viscous stress tensor de?ned as s=2l S=2l(0.5[(r V)+(r V)T]),P the scalar pressure,F r the volumetric surface tension force,g the gravitational acceleration and a the interface capturing function.The?uid do-main is de?ned for a single mixture where the function a is used to distinguish between the two?uids.The calculation of the volu-metric surface tension force and the?uid physical properties,the density q and viscosity l,vary according to the scalar?eld a.

2.2.Numerical formulation of coupling S-CLSVOF

The interface position is represented using two different inter-face capturing methods,based on an algebraic Volume of Fluid, and a Coupled Volume of Fluid with Level Set(S-CLSVOF)method. While the aim of this work is to extend the VOF compressive scheme implemented in OpenFOAM-1.7into a simple coupled scheme between VOF and LS for the study of bubble growth and rise,the principal governing equations of the VOF method will be explained?rst,and then the coupling technique will be introduced based on the principal equations of the VOF and LS methods.

2.2.1.Volume of Fluid

In the VOF method,the volume fraction function is de?ned as a step function which lies in the range[0,1].The continuous?uid(li-quid)is in the cells where a=1,while the dispersed?uid(gas)cor-responds to a=0.The interface is smeared over the cells where a2]0,1[.The interface capturing advection equation is simpli?ed using the continuity equation:@a

@t

tráea VT?0e4TFor large density ratios,the main challenge for advecting the a function is to preserve the mass conservativeness while guarantee-ing boundedness.OpenFOAM uses an algebraic approach based on the counter-gradient transport to advect the volume fraction a (Weller,1993).This scheme adds a compressive term to the a advection equation in order to retain the conservativeness,conver-gence,and boundedness(Weller,2008).The advection equation is re-formulated as:

@a

t$áeV aTt$áeV c a bT?0e5Twhere b=1àa,and V c=V làV g is the compressive velocity(Berbe-rovic′et al.,2009).The subscripts l and g stand for the liquid and the gas,respectively.

The compressive velocity is taken into consideration only in the region of the gas/liquid free surface and it is calculated in the nor-mal direction to the interface to avoid any dispersion.More over,a compressive factor c a is used to increase compression as:

V c?minec a j V j;maxej V jTT

r a

j r a j

e6T

All computational results presented here were obtained with a compression factor c a=2.The volume fraction advection equation is solved using the MULES method which is based on the method of ?ux corrected transport where an additional limiter is used to cut-off the face-?uxes at the critical values(Zalesak,1979).The phys-ical properties of the two immiscible?uids are calculated using a weighted average,so that the volume?uid fraction a has a signif-icant effect on determining these properties in each cell.

q?q

l

atq

g

e1àaTe7Tl?q

l

atl

g

e1àaTe8TIn the VOF method,the volumetric surface tension force is cal-culated using the Continuum Surface Force model(CSF)without the density averaging proposed by Brackbill et al.(1992):

F r?r jeaT$ae9Twhere j(a)is the interface curvature calculated based on the up-dated value of a after advection.The curvature represents the mag-nitude of the interface normal?ux at a speci?c face of the cell,and it indicates the direction of this?ux

j?à$áe^n cáS

f

Te10T

where S f is the surface vector of the cell face,f stands for the cell face,and^n c is the unit interface normal which is calculated using the phase fraction?eld and it refers to the direction of the phase ?eld changes in the numerical domain:

^n

c

?

er aTf

jer aTf j

e11T

At wall boundary conditions,the phase fraction is determined so that a static contact angle h0should be achieved at each time step,where this angle is de?ned as the angle between the interface normal and the face unit normal^n f at the wall:

^n

c

á^n f?cos he12TThe interface normal at the wall boundary condition is cor-rected to satisfy the static contact angle before calculating the cur-vature in Eq.(10).

2.2.2.Coupling VOF with LS(S-CLSVOF)

The extension of VOF-Compressive implemented in OpenFOAM into a new coupling method(S-CLSVOF)is explained here.The

A.Albadawi et al./International Journal of Multiphase Flow53(2013)11–2813

coupling takes advantage of the mass conservativeness of the VOF method and the interface smoothness of the LS method.In the S-CLSVOF solver,a new Level Set?eld/is introduced where the interface position is de?ned by the iso-line/=0.Although two separate?elds,namely VOF and LS,are de?ned to represent the ?uid domain,only the VOF advection equation(Eq.(5))is solved instead of the two Level Set and Volume fraction equations as re-quired in the standard CLSVOF methods(Sussman and Puckett, 2000).The?rst step of the coupling is to assign an initial value to the Level Set function using the advected VOF fraction function and assuming that the interface position is de?ned at the iso-line contour a=0.5:

/

?e2aà1TáCe13Twhere C is a small non-dimensional number whose value depends on the mesh step size D x where C=0.75D x.The main criterion in choosing this value is to satisfy an initial value of/which is close to the mesh step size.This initial function/0is a signed function since it has a positive value in the liquid and a negative value in the gas.This value/0is then re-distanced by solving the re-initial-ization equation:

@/

s

?Se/0Te1àj$/jT

/ex;0T?/

0exT

(

e14Twhere s is the arti?cial time step,x is the position vector,and S(/0) is a sign function.The solution converges to a signed distance func-tion achieving j r/j=1.Its function is therefore to re-distance the level set function starting from the initial interface and moving to-wards both?uids.The arti?cial time step is chosen as D s=0.1D x,so that there are no sharp changes in the LS function during the reini-tialization.Since the re-initialization equation gives a distance func-tion around the interface before spreading towards each?uid,only a few iterations(/corr)are required.For the chosen values of C and D s,the number of iterations(/corr)is found to meet the condition:

/corr?

se15T

where e is the interface thickness which de?nes the number of cells used for the transition between both?uids,and is chosen as 2e=3D x where D x is the mesh step size.

Since the Level Set function is a continuous function,it helps in determining accurately the interface normal as^n?$/=j$/j. Hence,it provides a more precise and smoother interface curvature j?$á^n.It is important to mention here that special care should be taken when considering a contact angle boundary condition since the interface normal should be corrected to satisfy the im-posed static contact angle similarly to the VOF method.The volu-metric surface tension force can then be calculated as:

F r?r je/Tde/T$/e16Twhere r is the surface tension coef?cient,and d is the Dirac function used to limit the in?uence of the surface tension to a narrow region around the interface.This function is centered at the interface and takes a zero value in both?uids,and is de?ned as:

de/T?

0if j/j>

1

2

1tcos p/

àá

àá

if j/j6

(

e17T

The physical properties and the?uxes across the cell faces(2nd term on the left hand side(l.h.s)of Eq.(2))can be de?ned either as in the VOF method(Eqs.(7)and(8))or calculated using a Heavi-side function(Eqs.(19)and(20)).

He/T?

0if/<à

1

2

1t/ t1p sin p/

àá

??

if j/j6

1if/>

8

><

>:e18T

qe/T?q

g

teq làq gTHe19T

le/T?l

g

tel làl gTHe20T

Although the latter method(Eqs.(19)and(20))gives smoother

transition of the properties across the interface than using(Eqs.(7)

and(8)),both methods have been found to give similar results for

bubble growth problems.Eqs.(7)and(8)are used in this study.Eq.

(16)means that the in?uence of surface tension is spread over a?-

nite interface thickness.The extent of the interface smearing,

which is determined in terms of the e parameter,is shown in Sec-

tion4.1to have a signi?cant in?uence on the solution.Results

however indicate that accurate models can be achieved by limiting

the interface spread.Alternative sharp interface methods have

been developed based on the Level Set method(Raessi and Pitsch,

2012)using the Ghost Fluid approach(Fedkiw et al.,1999;Kang

et al.,2000),or based on coupled Level Set and Volume of Fluid

methods(Sussman et al.,2007;Ohta et al.,2011).These have been

shown to achieve stable solutions even with a large density ratio

and in the case of the coupled Level Set and Volume of Fluid

method of Sussman et al.(2007),second order accuracy in the li-

quid solution could be achieved with a second order curvature esti-

mation under high Reynolds number.Sharp interface methods

remove the dependence on the parameter e but crucially,the

extension to unstructured mesh is far from straightforward.A

sharp interface model based on a Finite Element formulation has

also been developed by Gross and Reusken(2007a)by combining

the extended?nite element space(XFEM)of Moes et al.(1999)

to a new accurate surface tension model introduced in Gross and

Reusken(2007b).Numerical results from two2D static test cases

show substantial reductions in spurious currents but the authors

have also highlighted the need for further research notably to ad-

dress stability issues arising with non-stationary Navier–Stokes

two-phase?ow problems.

The S-CLSVOF solver can be described in eight main steps:

1.De?ne vector and scalar?elds for the multiphase?ow problem

including V,P,q,l,H,d,a,and/.Note that the pressure used in

the OpenFOAM VOF solver is the dynamic pressure P rgh where

P rgh=Pàq gh,where h is the liquid height.P rgh is used to avoid

any sudden changes in the pressure at the boundaries for

hydrostatic problems(Rusche,2002).

2.Initialize the numerical?elds,reinitialize the Level Set function

and calculate the initial values of the Heaviside and Dirac

functions.

3.Start the time loop by correcting the interface and the volume

fraction at the boundaries(if necessary).

4.Solve the volume fraction advection equation(Eq.(5)),and cor-

rect the new values of a at the boundaries.The correction takes

place only at the boundaries where a static contact angle is

imposed so that the interface normal calculated from the gradi-

ent of the volume fraction and used by Eq.(16)is corrected to

satisfy the imposed static angle(Eq.(12)).Then,calculate the

new LS function(Eq.(13))using the results of the advection

equation.

5.Re-initialize the LS function using Eq.(14)in order to obtain the

signed distance function and correct the interface at the bound-

aries.Then,calculate the new values of the Heaviside function,

the Dirac functions,and the interface curvature.

6.Update the?uid physical properties and the?uxes using the

volume fraction function a(Eqs.(7)and(8)).

7.Solve the Navier Stokes system of equations for velocity and

pressure using the Pressure Implicit with Splitting of Operators

(PISO)(Issa,1986).Details of its implementation in OpenFOAM

are provided in the Appendix.In the present study three pres-

sure correction steps were used and ensured that the continuity

residual remained always below10à6.

14 A.Albadawi et al./International Journal of Multiphase Flow53(2013)11–28

8.Move to the next time step (starting from 3).

The pressure correction equation (Eq.(37))is solved in this study using a Conjugate Gradient iterative solver preconditioned with a Diagonal incomplete-Cholesky (DIC)method.The pressure solution is converged to a normalized absolute residual of 10à7,leading to continuity residual,de?ned as the cell volume weighted average of the rate of volume creation over the whole domain,which is always lower than 10à6.

2.3.Discretization schemes and solution solvers

The governing equations are discretized based on a Finite Vol-ume formulation.The discretization is performed in this study on a ?xed uniform structured grid.All the variables are stored at the cell centers,where a non-staggered grid arrangement is used.In order to avoid a checkerboarding effect in the momentum equa-tion,the Rhie-Chow momentum interpolation (Rhie and Chow,1983)is applied.The equations are integrated in time using the Eu-ler implicit scheme,while the spatial derivatives are discretized using second order schemes.

Gradients and divergence terms are discretised using the Gauss Theorem.The volume integral of the convective term in the momentum equation,which is expressed in conservative form r á(q VV )is written as a discrete summation over the cell faces:

Z

v

$áeq VV Td v ?

X

f

V f F f

e21T

where f is the cell face iteration index,F f =(q V )f áS f is the mass ?ux through the cell face f and S f is the face area vector de?ned to point in the outward direction from the cell.See Fig.1for a description of the mesh structure and associated terminology as de?ned in the OpenFOAM programmers guide (OpenFOAM,2009).The mass ?ux is calculated as part of the PISO algorithm separately from the cell center velocity as part of the Rhie and Chow algorithm (Rhie and Chow,1983).In cells containing the interface,F f is calculated based on its position that is on the volume fraction ?eld from:

F f ?X f

S f áea V Tf tX f

S f áeàa e1àa TV c Tf "#eq l àq g T

t?X

f S f áV f q g

e22T

where the volume fraction convective term S f á(a V )f is calculated using the Van Leer second order Total Variation diminishing scheme (TVD)(Van Leer,1979),while the compressive term is discretized using the interface compression scheme described by Weller (2008).

The interpolated cell face value of velocity V f is obtained in this study using the second order TVD scheme named LinearLimitedV

developed by OpenFOAM following the unstructured mesh method proposed by Darwish and Moukalled (2003).The method de?nes V f according to:

V f ?k eV p àV N TtV N e23T

where k is the interpolation factor de?ned in terms of the TVD lim-iter w (r )and the linear interpolation weight f d ?eT=ePN T(for uni-form grid f d =1/2):

k ?w er Tf d te1àw er TTv eV f áS f T

e24T

v accounts for the ?ow direction and is de?nd by:

v eV f áS f T?

0for V f áS f >0eoutflow T

1for V f áS f 60einflow T

&

e25T

r is the so-called r-factor used to de?ne the TVD limiter in terms of consecutive gradients of the ?uxed quantity,i.e.in the case of the convection term,the velocity vector V .In the so-called exact r-fac-tor formulation proposed by Darwish and Moukalled (2003),r is de-?ned by:

r ?

2d pN áer j V jT

p

N

p

à1for V f áS f >0

2d pN áer j V jTN N

p

à1for V f áS f 60

8<:e26T

where d pN is the distance vector between the cell center p and the center N of the neighboring cell which shares the face f .The gradi-ent at the numerator is evaluated from the interpolated face values and the Gauss Theorem.The limiter in this LimitedLinearV scheme used in this study is de?ned by:

w er T?max emin e2r ;1T;0T

e27T

which satis?es the second order TVD condition.3.Numerical validation 3.1.Circular bubble at equilibrium

The implementation of the CSF model in the momentum equa-tion for interface tracking methods generates spurious currents in the vicinity of the interface (Renardy and Renardy,2002).These currents are considered as numerical errors and evidenced as vor-tices in the interface region.A circular bubble at equilibrium in a zero gravity ?eld is used to assess the strength of the currents and to characterize the ?uid ?ow in the absence of any external forces.The physical properties of the gas phase are q g =1kg/m 3,l g =10à5kg/m s,and the liquid phase are q l =1000kg/m 3,l l =0.001kg/m s.The surface tension is r =0.01kg/s 2.The mesh domain is 0.05?0.05m 2.The initial bubble of radius R ini =0.005m is positioned at the center (0.025,0.025).The exact pressure differ-ence between inside and outside the bubble is r /R ini while the ex-act curvature is 1/R ini .Two different mesh resolutions are used:Coarse (?ne)mesh with 10(20)cells per bubble diameter.The time step size is 10à5s for the coarse mesh and 5?10à6s for the ?ne mesh,and the results are considered at the physical time 0.1s.The error in the interface curvature is displayed in Table 1and is calculated based on the calculated curvature j in the VOF method and on both j and d in the S-CLSVOF method.

l VOF ?

??????????????????????????????????????????P M i ?1ej R àj exact R T2

M

s e28Tl S àCVOFLS ?

??????????????????????????????????????????P N i ?1ej R àj exact R T2

N

s e29T

where M is the number of cells in the numerical domain and N is the number of cells where the surface tension is calculated with the S-CLSVOF method (d –0).The error in the magnitude of the spurious

Schematic shape of the discretized domain (the owner and A.Albadawi et al./International Journal of Multiphase Flow 53(2013)11–2815

currents is calculated using the averaged velocity norm error l1and the maximum velocity norm error l1(Renardy and Renardy,2002) l1?max

i;j

ek V i;j kTe30T

l1?

1

N x N y

X

i;j

k V i;j ke31T

Three different pressure de?nitions are considered in this anal-ysis(Francois et al.,2006):

D P0?P in

0àP out

1

where P in

and P out

1

are the value of the pressure

at the bubble center and at the wall boundary,respectively.

D P total?P in

total àP out

total

where P in

total

and P out

total

are the averaged value

of the pressure inside(0.5P a P0)and outside(1P a P0.5) the bubble,respectively.

D P partial?P in

partial àP out

partial

where P in

partial

and P out

partial

are the averaged

value of the pressure inside(0.05P a P0)and outside (1P a P0.95)the bubble,respectively.This value ignores the pressure in?uence inside the diffusive interface region.

The relative pressure error E0=j D P0àD P exact j/D P exact is used to calculate the error in D P0where D P exact is the exact pressure differ-ence.The norm errors obtained with the two mesh resolutions are given in Table1for both the VOF and S-COVFLS methods.These re-sults con?rm that the curvature error does not converge with grid re?nement with either method.However,the error from the S-CLSVOF curvature estimate is one order of magnitude smaller than the VOF estimate.A similar conclusion can be reached by consider-ing the errors for the pressure drop across the interface.A one or-der of magnitude reduction in E0,in particular,is achieved with the S-CLSVOF method.In this case,however,the error from the region around the interface(E int=E totalàE partial)of arbitrary thickness de-?ned by0.05

If the reduction in spurious currents under grid re?nement with S-CLSVOF is indeed due to a narrowing of the interface and focus-sing of surface tension force towards a region of higher density, grid convergence should fail in the case of uniform density across the interface and between the two phases.The two-dimensional stationary bubble test under zero gravity was repeated with den-sity and viscosity ratios q l/q g=1and l l/l g=1and a bubble diam-eter D=0.01m.This test was implemented by Popinet and Zaleski (1999)to con?rm the linear proportionality between spurious cur-rents and the surface tension to viscosity ratio r/l for a broad range of Ohnesorge numbers(Oh=l l/(rq l D)0.5).The result was achieved with a VOF method and surface tension model which was shown to converge to machine accuracy.The current test uses the same domain as considered above in this section with a mesh resolution ranging from50?50to500?500that is from10to 100cells per bubble diameter and with1/Oh2=1000.The time step in this case is de?ned by D t=0.1D x.Results from both VOF and S-CLSVOF are reported in Table2in terms of the curvature error and a capillary number Ca=U l/r where U is the l1norm of the spuri-ous current velocity measured at the physical time0.1s that is10 characteristic time scales(t=t phys r/(D l)).

The two methods are shown to give amplitudes of spurious cur-rents which are of similar orders of magnitude but approximately two times smaller with the S-CLSVOF,while the curvature norm error is as observed in Table2.Broadly similar results were ob-served when using adaptive time stepping with a Courant number Co=0.1.Although grid re?nement does induce some changes at the coarsest grid,the convergence of Ca SàCLSVOF tapers off quickly as the mesh is further re?ned and spurious currents are shown to increase again with the most re?ned mesh.This suggests that the bene?t of the S-CLSVOF method presented here are limited to the improved curvature estimate in the case of low density ratio but further improvement can be expected in terms of the damping of spurious current at larger density ratio.In particular when con-cerned with gas–liquid?ow,previous results indicate that a non-negligible reduction in spurious currents can be expected as the zone of in?uence of surface tension is reduced.

3.2.Free bubble rise

The experimental study of free bubble rise in viscous liquids due to buoyancy has received considerable attention in the litera-ture over the last decades(Grace,1973;Clift et al.,1978;Raymond and Rosant,2000).This work has aimed to study the bubble behav-ior and classify its geometrical characteristics under different physical properties in order to understand the in?uence of the bub-ble and the wake generated behind it on mass and heat transfer problems.It has been found that the bubble can deform to different shapes depending on three dimensionless numbers:the Morton number Mo?g l4l D q=q2l r3

àá

,the E?tv?s number g D q D2eq=r

, and the Reynolds number(q l V1D eq/l l)(Clift et al.,1978;Grace, 1973),where D eq is the bubble equivalent diameter.Numerically, the bubble motion due to gravity has been successfully simulated

Table1

Norms of velocity and curvature,and errors in the pressure jump at0.1s with time step D t=10à5s(Coarse mesh)and D t=5?10à6s(Fine mesh).

Method Mesh size(m)l VOF l SàCLSVOF l1(m/s)l1(m/s)E0(%)E total(%)E partial(%)E int(%)

S-CLSVOF0.001–0.24780.01710.000290.41613.302 2.52610.778 S-CLSVOF0.0005–0.15270.00680.000110.8757.866 2.198 5.668

VOF0.001 1.1752–0.01290.0001914.52324.96815.6729.296 VOF0.0005 1.3289–0.02610.0001711.72919.61114.144 5.467 16 A.Albadawi et al./International Journal of Multiphase Flow53(2013)11–28

using different methods.In the present work,the coupled code (S-CLSVOF)is validated by modeling a single air bubble rising in a viscous liquid.This problem has been considered as an appropri-ate test case for validating different numerical interface advection schemes (LS in Son (2001),3D-VOF in Van Sint Annaland et al.(2005),CLSVOF in Ohta et al.(2005),VOSET in Sun and Tao (2010))since the bubble does not interact with the boundary con-ditions and the accuracy of the numerical methods can be assessed by comparing against broadly available experimental data.

In this problem,the single bubble rise in a quiescent liquid is simulated using both the VOF and S-CLSVOF methods.The analysis is performed for a wide range of physical properties as shown in Table 3and for three different equivalent diameters (3,5and 7mm).The simulation parameters and the corresponding dimen-sional numbers are listed in Table 4.Both the bubble terminal velocity (V 1)and aspect ratio (AR )are analyzed in this study using 2-dimensional (2D)and 3-dimensional (3D)numerical simula-tions.The experimental observations by Raymond and Rosant (2000)are used to assess the bubble terminal velocity and aspect ratio in the 3D domain.The size of the numerical domain is (0.04m,0.075m,0.04m)which corresponds to (8D eq ,15D eq ,8D eq )for bubble diameter 5mm.For the same physical and geo-metrical properties,Hua and Lou (2007)have shown that this size ensures no liquid in?uence from the boundary walls on the bubble motion.A regular mesh is used to discretize the ?uid domain so

that 25cells are distributed along the bubble diameter.This mesh size has been shown to be suf?cient for guaranteeing the conver-gence of the numerical results [Kumar and Delauré(2012)and Hua and Lou (2007)used 25cells/diameter while 12cells/diameter were with Van Sint Annaland et al.(2005)].

The terminal bubble shape for the different bubble diameters with the S5?uid is displayed in Fig.3where the initial spherical bubble is shown to deform from spherical to ellipsoidal shape as the initial diameter increases.The bubble shape compares well with the bubble diagram of Grace (1973)and similar behavior was also noticed by Raymond and Rosant (2000)due to the in-crease in both Re and Eo numbers.

Fig.4presents a quantitative comparison between the numeri-cal simulations using the S-CLSVOF method and the experimental observations by Raymond and Rosant (2000).The numerical re-sults are displayed for both the 2D and 3D simulations.Fig.4a shows that the bubble terminal velocity increases as larger equiv-alent diameters are considered.An increase in bubble velocity can be obtained also by using ?uids with smaller Mo numbers.For small bubble diameters,the 2D simulation gives bubble terminal velocity which compare reasonably well with experimental data.However,it fails to predict the correct V 1at high equivalent diam-eters,contrary to the 3D simulations.The discrepancy between the

Table 3

Physical properties used for numerical bubble rise simulations.Series l l (Pa s)

q l (kg/m 3)

r (N/m)

Mo

S10.68712500.0637.5287S30.24212300.0630.1057

S5

0.0733

1205

0.064

7.4492?10à4

Table 4

Simulation parameters for the rising of different sized bubbles in the series ?uids.Diameter (m)

Bubble S1S3S5Mo

Eo Mo Eo Mo

Eo 0.0037.529 1.750.106 1.72217.4492?10à4 1.66070.0057.529 4.8620.106 4.78367.4492?10à4 4.61310.007

7.529

9.529

0.106

9.3759

7.4492?10à4

9.0416

plot at 10th time steps,D t =1?10à05s and D x =5?10à04m for (a)S-CLSVOF (max.velocity 0.0068m/s)and (b)VOF (max.dark blue (min velocity)to dark red (max velocity).(For interpretation of the references to colour in this ?gure legend,the reader Table 2

Convergence of non-dimensional maximum velocity with grid re?nement for both VOF and S-CLSVOF,q l /q g =1and l l /l g =1.Grid size Number of cells per diameter Ca VOF

L VOF Ca S àCLSVOF L S àCLSVOF 5010 1.64?10à3 1.184 1.38?10à30.26210020 2.33?10à3 1.284 1.34?10à30.14915030 2.49?10à3 1.379 1.29?10à30.15320040 2.41?10à3 1.455 1.23?10à30.20625050 2.01?10à3 1.550 1.01?10à30.23630060 2.01?10à3 1.630 1.00?10à30.266500

100

1.92?10à3

1.921

1.13?10à3

0.361

2D and 3D cases is more apparent when considering the bubble as-pect ratio (Fig.4b )which highlights the importance to model the free bubble rise with large radii using 3D simulations.This differ-ence is due to the nature of the wake behind the bubble which drives the bubble to follow a 3-directional trajectory during its rise when it has an oblate ellipsoidal shape (Clift et al.,1978

).

The bubble shape and the velocity vector plots for three diameters (a)D eq =0.003m,(b)D eq =0.005m,(c)D eq =0.007m predicted by S-CLSVOF at time 024********

50

100

150

200

250D eq [mm]

3D S13D S33D S5S1?Exp S3?Exp S5?Exp 2D S12D S32D S5

Comparison of bubble terminal velocity predicted by simulations (2D and S-CLSVOF)with experimental observations (Raymond and Rosant,2000).

024*******

0.2

0.4

0.6

0.8

1

1.2

D eq [mm]

A R [m m /m m ]

3D S13D S33D S5S1?Exp S3?Exp S5?Exp 2D S12D S32D S5

https://www.360docs.net/doc/275996177.html,parison of bubble aspect ratio predicted by simulations (2D CLSVOF)with experimental observations (Raymond and Rosant,2000

https://www.360docs.net/doc/275996177.html,putational setup

The bubble formation process is studied numerically using axi-symmetrical simulations since it grows vertically without any lat-eral oscillations due to the absence of any shear ?ow in the bulk ?uid (Duhar and Colin,2006).The schematic diagram of the numerical domain is shown in Fig.5.The air bubble is injected through an ori?ce of radius R c =0.5?10à3m or R c =0.8?10à3m submerged in initially quiescent water.The gravitational accelera-tion is imposed in the axi-symmetrical direction,while the surface tension coef?cient is assumed to be constant.The physical proper-ties of both air and water are also constant and taken at room tem-perature (Table 6).The gas injection is assumed to be under

constant ?ow rate (_Q

?2:778?10à8m 3/s)and lower than the critical value determined by Oguz and Prosperetti (1993)for qua-si-static ?ows _Q crit %p 163g 2

1=6r L R c q

L

5=6

?1:82?10à6m 3=s .The numerical domain has a width 2.5D eq and height 5D eq ,equivalent to 10?20mm 2,where D eq is the bubble equivalent diameter.The domain width is similar to that of Gerlach et al.(2007)and Chakraborty et al.(2009)who have reported that the bubble growth is not affected by any liquid circulations close to the wall.The bubble passes through two stages during its growth.They are de?ned as the expansion stage and the collapse (detachment)stage (Longuet-Higgins et al.,1991).The bubble detachment happens when the neck diameter is less than 10%of the ori?ce diameter (Oguz and Prosperetti,1993).In the present work,several mesh sizes were tested for convergence analysis as shown in Table 7.The time step size used for each simulation is D t =0.2D x .Results are reported in Table 7in terms of the bubble detachment volume and time.The error for each two successive mesh re?ne-ments is calculated with reference to the coarser mesh (100?(V ?ner àV coarser )/V ?ner ).The results show that the bubble

detachment characteristics increases with mesh re?nement as ob-served by Chakraborty et al.(2009)under similar mesh re?nement.When the number of cells per ori?ce diameter is increased from 32to 64cells,the bubble detachment volume has increased by approximately 1.68%which corresponds to an error in the bubble equivalent radius of about 1.19%.Fixing the time step as a function of the mesh size does not guarantee a bounded Courant Number Co =(V max D t )/D x which can be affected by spurious currents and,

Schematic diagram of the experimental rig and computational boundary conditions.

Table 6

Fluids’physical properties for bubble growth analysis.Parameters Symbol

Values Units Liquid density q l 998.2kg/m 3Liquid viscosity l l 0.001kg/m.s Gas density q g 1.225

kg/m 3Gas viscosity l g 1.79?10à5kg/m s Surface tension r

0.073N/m Gravity

g

9.81

m/s 2

Table 7

Convergence analysis of mesh discretization using S-CLSVOF with R c =0.8mm and _Q

?200mlph.Nb/

diameter D x D t V det

(mm 3)t det (s)E vol (%)E t (%)8 2.0?10à4 4.0?10à526.5950.455––16 1.0?10à4 2.0?10à528.0820.484 5.30 6.01208.0?10à5 1.6?10à530.2830.5257.277.7932 5.0?10à5 1.0?10à531.4480.547 3.70 4.0264

2.5?10à5

5.0?10à6

31.985

0.560

1.68

2.32

A.Albadawi et al./International Journal of Multiphase Flow 53(2013)11–28

19

to a larger extent,the ?ow acceleration which characteristics detachment.Further tests were conducted to assess the in?uence of the time step on the bubble detachment time and volume (see Table 8).The time step D t =5?10à6s gives similar results to D t =10à6s with a relative difference in the detachment volume of approximately 0.2%.Results obtained with D t =5?10à6s are also compared against adaptive time step computations controlled with Co =0.2.Other values of Co were considered and in all cases the relative error in the bubble detachment time and volume al-ways remain below 0.5%.To conclude,D x =5?10à5m and D t =5?10à6s (32cells per ori?ce diameter)were selected for all simulations in this study so that the detachment can be consid-ered to occur when the neck radius is less than 50l m.This resolu-tion is comparable to or smaller than that used in previous bubble growth studies [D x =0.2?10à3m in (Buwa et al.,2007)and D x =0.25?10à3m in (Gerlach et al.,2007;Chakraborty et al.,2009)].

Four boundary conditions are set to represent the borders of the numerical domain.The in?ow velocity is de?ned at the inlet where the gas is injected through the throat at a constant volumetric ?ow rate.Its velocity pro?le is parabolic and calculated as:

v ex T?v max

x R c

2"

#e32T

where x at set to zero at the axis of symmetry,and v max is the maximum in?ow velocity calculated as v max ?2v 0?2_Q =p R 20

?0:0276m/s.At the outlet,the out?ow pressure is set

to the atmospheric pressure (At y =Y max ?P =P 0and @V /@y =@a /@y =@//@y =0).Any reverse ?ow at the outlet is assumed to be li-quid.At the wall,a no slip boundary condition is imposed except for the lower wall where wall adhesion is considered.The wall sta-tic contact angle is h =20°so that the bubble interface does not spread along the wall.At the initial time,a semi-circular bubble is patched at the in?ow with a radius R i =R c =0.8?10à3m.The exis-tence of the initial bubble is essential to calculate the distance func-tion for the LS method,while it minimizes interface diffusion at the initial stages of bubble growth for the VOF method.

With the smeared interface approach used in the present study,the interface thickness e constitutes an additional numerical parameter which determines the band thickness around the inter-face where the surface tension source term is applied.Sussman et al.(1998)de?ned e as a function of the mesh size (D x ).The con-dition e P 1.5D x guarantees that surface tension is spread over at least one cell on either side of the interface while the larger the va-lue of e ,the more iterations are required for the solution of the re-distancing function as de?ned by Eq.(15).A value of 1.5D x has typ-ically been used for example by Sussman et al.(1994);Son and Hur (2002);Sun and Tao (2010)or in the case of bubble growth simu-lations using CLSVOF by Chakraborty et al.(2009).The sensitivity of the bubble growth simulations to this de?nition has been tested with (e =1.5D x ,3.0D x ,4.5D x )in terms of its effect on the bubble detachment time and volume for an injection ?ow rate _Q

?200mlph and an ori?ce diameter D =1.6mm.Results given in Table 9con?rm that as the interface thickness is increased bub-

ble detachment characteristics decrease to values which approach those modeled by the original VOF method (presented in Table 10).4.2.Experimental setup

The experimental apparatus consists of a lower adjustable bub-ble injection surface,with two swappable injection ori?ces.The side walls are constructed of 2mm glass bonded using water resis-tant silicone.The tank itself measures approximately 50?50?200mm 3.

Three ori?ce inserts were manufactured of Aluminum;1,and 1.6mm to control the size of bubbles generated.These inserts screw into the adjustable injection surface until level.From the base of the insert,a silicone tube with an internal diameter of 0.8mm,connects the ori?ce to a gas tight syringe.A Hamilton (GASTIGHT 1002series) 2.5ml syringe was utilized,allowing repeatable injection volumes.

The gas ?ow rate was controlled by a medical grade infusion pump manufactured by kdScienti?c (KDS 200cz),which is cali-brated for our speci?c syringe.The infusion pump is capable of supplying the correct gas ?ow rate up to a maximum of 300mlph.The total length of tubing used was 20mm.

The infusion pump was placed at the same vertical height as the injection ori?ce to mitigate the effect of a height differential.

A single NAC Hi-Dcam II high speed digital video camera,con-nected to a dedicated computer,has been utilized to capture high speed bubble growth.The camera was controlled by Lynk-sis cam-era software.For the present study,the camera was set to record at 500fps with an exposure time of 0.5ms.This set up ensures sharp images,along with good temporal detail.4.3.Experimental bubble formation

The numerical results obtained by both VOF and S-CLSVOF are ?rst assessed qualitatively by comparing the contour of the recon-structed interface against experimental observations.The snap-shots of the experimental bubble boundary are taken at six different frames (t /t det $0,0.2,0.4,0.6,0.8,1)as illustrated in Fig.6where t det is the corresponding detachment time for each method.The initial bubble shape at time t /t det =0is hemispherical.The bubble passes through several topological changes during its growth.At the early stages (t /t det $0.2),the bubble has a truncated spherical shape whose volume increases linearly due to the con-stant injected ?ow rate.With time,the bubble elongates in the ver-tical direction while it retains its spherical shape at the upper part.During the detachment stage (t /t det >0.8),three different regions can be distinguished;the bubble dome which forms the upper part,

Table 8

Convergence analysis of time step discretization using S-CLSVOF with R c =0.8mm and _Q ?200mlph.nb/diameter D x D t V det (mm 3)t det (s)E vol (%)E t (%)32

5.0?10à5 1.0?10à531.4480.547–

32 5.0?10à5 5.0?10à630.9190.537à1.71à1.8632 5.0?10à5 1.0?10à630.9810.5390.200.3732

5.0?10à5

Courant (0.2)

31.004

0.5395

0.27

0.46

Table 9

Bubble detachment characteristics at three different values of e obtained with _Q

?200mlph and D =1.6mm.D t =5?10à6s and D x =5?10à5m.Interface thickness

t det (s)V det (mm 3)e =4.5D x 0.446

25.87e =3.0D x 0.49228.4e =1.5D x

0.537

30.92

20 A.Albadawi et al./International Journal of Multiphase Flow 53(2013)11–28

the neck region which forms the lower part,and the transition re-gion where the bubble interface curvature converts from concave

to convex.

The analysis of the forces acting on the bubble and its evolution with time is presented in Fig.7giving information about the gov-erning forces that control the formation process.This analysis is performed on the experimental data primarily to highlight the

signi?cance of the capillary stress during the formation.Under quasi-static conditions,the forces acting on the bubble are divided into two main groups according to their in?uence on the formation (Duhar and Colin,2006;Di Bari and Robinson,2012).The ?rst group promotes the bubble detachment and includes the buoyancy force (F B =(q l àq g )V s )and the contact pressure force F CP ?p R 2c eP g àP T T ,where V s is the bubble volume in the regions radially outward the ori?ce rim,P g and P T are the gas pressure in-side the bubble and the liquid pressure at the bubble apex (Di Bari and Robinson,2012).The other group of forces resists bubble detachment and acts to keep the the bubble attached to the ori?ce.It is a combination of both the capillary force (F C =2p r R c sin h )and the dynamic force (F D =F C à(F CP +F B ))which represents both the liquid inertia close to the bubble interface and the viscous forces,where h is the instantaneous contact angle.Fig.7shows that the in?uence of the drag force is very small compared to the other forces.At the beginning of the growth,the bubble is controlled by a balance between the contact pressure force and the capillary force.During the growth,the in?uence of the buoyancy increases due to the increase in the bubble size while at the last stage of detachment,the in?uence of the capillary force decreases rapidly.Furthermore,the capillary force has a strong in?uence on the bub-ble during the whole process which highlights the importance of using an accurate surface tension model in the momentum equa-tion in order to avoid any numerical errors leading to unphysical bubble formation.

A comparison between the experimental bubble and the numerical interfaces predicted by both VOF and S-CLSVOF is pre-sented in Fig.8.The ori?ce diameter is 1.6mm and the volumetric

F

B

F

C

F

CP

F

D

bubble shape at six different frames t /t det $0,0.2,0.4,0.6,0.8,1ordered from top left to bottom right with R Table 10

Bubble detachment characteristics for four different volumetric ?ow rates _Q ?50;100;150;200mlph,R c =0.8mm.Flow rate (mlph)Method t (s)CGy (mm)V (mm 3)E t (%)E cg (%)E VOL (%)50mlph

Experiment

1.985 3.56828.3960

A.Albadawi et al./International Journal of Multiphase Flow 53(2013)11–28

21

?ow rate is200mlph.With the VOF method,the bubble boundary is assumed to be at the iso-line contour a=0.5,while the iso-line contour/=0is considered for reconstructing the interface in the S-CLSVOF method.It is evident that the different topological changes during the bubble growth are well predicted by both methods.With the VOF method,the bubble is shown to grow faster compared to experimental observations,and it detaches with smaller volumes and a maximum bubble height which is smaller than observed experimentally.In contrast,the bubble growth ob-tained with S-CLSVOF is in close agreement with experimental measurements.The early detachment modeled by the VOF method is most likely due to the implementation of surface tension(Eq.

(9)).With the VOF method,its in?uence is applied not only at the interface,but over the whole numerical domain.The analysis of the in?uence of the interface thickness parameter e in Section4.1 and the study of spurious currents in Section3.1,highlight the importance of restricting surface tension to a narrow region across the interface.In particular it was shown that increasing the inter-face smearing with S-CLSVOF tends to provide detachment param-eters which converge towards those predicted by the VOF method.

4.4.Quantitative comparison of bubble growth

The bubble detachment parameters,de?ned as the detachment time t det,the detachment volume V det,and the detachment center of gravity in the vertical direction CGy det,are used to validate the correctness of the numerical methods by comparison against experimental data.With the VOF method,the bubble volume is measured based on the volume fraction function a as V?

P

cells

e1àaTdV,while the bubble volume in the S-CLSVOF method is determined by the amount of air entrapped inside the iso-line contour/=0.The detachment time is assumed at the mo-ment before the bubble splits at the neck into two bubbles(see Fig.6).The detachment parameters for ori?ce radius0.8mm with four different?ow rates of50,100,150,200mlph are shown in Table10.The relative error of the bubble volume is calculated as E vol=100(V numàV exp)/V exp.The experimental results show that the bubble detachment time decreases exponentially with increas-ing?ow rate,following an exponential power lawet det?C_Q bTwhere b=0.96.Similar decay is observed with S-CLSVOF with b=0.95.However,the value b is very close to1indicating the lin-ear relationship between the detachment time and the?ow rate for quasi-static conditions.With the VOF method,the detachment time decreases exponentially with the increasing?ow rate,but the power exponent takes the value b=0.77.The small detachment time with the VOF method leads to small detachment volume compared to the experiments,while the detachment volume with S-CLSVOF is very close to the experimental results with maximum error of3%.Both numerical methods detach with smaller centers of gravity.However,the S-CLSVOF predicts well the detachment CGy with an error less than2%which corresponds to a difference smal-ler than70l m.

The larger detachment volumes predicted by S-CLSVOF suggest that the numerical bubble may have larger CGy det than observed experimentally,but this is not the case(see Table10).In order to investigate this discrepancy and to examine the suitability of the numerical models for predicting the bubble behavior during the growth,the physical parameters characterizing the bubble dynam-ics during the formation are studied.Fig.9shows the time evolu-tion of the bubble center of gravity for both the numerical methods and the experimental observations.The ori?ce diameter is1.6mm and the in?ow?ow rate is200mlph in this case.This?g-ure con?rms that using S-CLSVOF improves the prediction of the bubble center of gravity compared to the original VOF method. With VOF,the bubble is exposed to a series of contractions and expansions in the vertical direction which is interpreted as a small oscillation in the bubble center of gravity.With the S-CLSVOF method,the numerical predictions are similar to the observations from the experiments at the early stages of growth.At time t$0.35s,the neck starts to form when a sudden jump in the bubble center of gravity is observed.However,this motion is not

22 A.Albadawi et al./International Journal of Multiphase Flow53(2013)11–28

observed experimentally and it may be due to the static contact angle implementation at the ori?ce rim.

The bubble evolution in the radial direction is examined by measuring the bubble maximum width as shown in Fig.10.At the initial time,the bubble has a hemispherical shape with radius R=R c and its maximum width is1.6.It is clear that the maximum width is well predicted by both VOF and S-CLSVOF.However,the bubble detaches at an earlier time with the VOF method.During the detachment,the bubble width with S-CLSVOF is slightly larger than that with the experiments which explains the smaller CGy at detachment obtained with the S-CLSVOF method.

The bubble instantaneous contact angle during growth is de-?ned as the angle between the bubble interface and the wall and is measured in the liquid domain.Experimentally,this angle is re-lated to the ori?ce radius(as will be shown later),while it is controlled by the static contact angle in the numerical simulations (Eq.(12)).A comparison of its numerical predictions and experi-mental measurements is presented in Fig.11.During the early stages of growth,the angle decreases with time as the bubble de-forms from hemispherical to a truncated hemispherical shape, while the detachment stage is characterized by the increase in the contact angle due to the neck formation.Both numerical meth-ods predict similar behavior of the contact angle during the forma-tion.The bubble oscillations in the center of gravity CGy also affect the instantaneous contact angle with amplitudes of oscillations which grow gradually before the onset of detachment.The oscilla-tions appear when the bubble starts elongating in the vertical direction and when the capillary force F C reaches a maximum (see Fig.7).The imposed static angle which is a constant is gener-ally different from the instantaneous angle which is a?ow variable.

A large difference between the static and instantaneous angles en-sures that the bubble remains pinned to the injection ori?ce rim as discussed in Section4.6but also increases the magnitude of the numerically induced capillary force.The oscillation observed with the VOF method suggests that spurious currents induced by the surface tension model are thus intensi?ed by the static angle for-mulation.This is shown to have a severe effect on the accuracy of the VOF model.The improved surface tension modeling of the S-CLSVOF method,however,is also shown to remove the model sensitivity to the static contact angle.

For quasi-static bubble growth(Oguz and Prosperetti,1993), the bubble detachment volume and center of gravity remain con-stant regardless of the applied volumetric?ow rate.The in?uence of the?ow rate is limited only to the frequency of the bubble for-mation as increasing the in?ow rate leads to bubble detachment at

A.Albadawi et al./International Journal of Multiphase Flow53(2013)11–2823

earlier times.However,the ?ow rate should also affect the very last stages of bubble detachment when gas inertia is known to in?u-ence the neck pinching.Fig.12plots the bubble center of gravity for both VOF and S-CLSVOF methods using the non-dimensional time t n =t v 0/R c with the ori?ce radius of 0.8mm.It is clear that when using the S-CLSVOF method the bubble center of gravity fol-lows the same trend for all the ?ow rates contrary to the VOF method.This con?rms that the bubble dynamics are well predicted with S-CLSVOF since the bubble CGy history should follow the same trend,conforming to the conditions of quasi-static ?ow.With the VOF method,the bubble oscillates in the vertical direction be-fore detachment,and the amplitude of these oscillations decreases with increasing ?ow rate.With the S-CLSVOF method and during detachment,the bubble neck pinch off is shown to be prolonged as the ?ow rate increases.This behavior is also observed with the experimental https://www.360docs.net/doc/275996177.html,pared to the experiments (Fig.9),the S-CLSVOF method is clearly better for predicting the capillary dom-inant bubble growth than the VOF method at the low volumetric ?ow rates.

4.5.Bubble detachment process

The bubble detachment is characterized by very rapid changes in the bubble shape as the neck forms.The beginning of the neck formation is de?ned as the time when the bubble minimum radius (R 0),also known as the neck radius,falls below the ori?ce radius

(R c ).The local Weber number We local ?q l _R

20

R 0=r

at the neck is used to study the in?uence of the forces acting on the bubble dur-ing the detachment where e_R

0?dR 0=dt p Tis the neck radius veloc-ity.Fig.13shows the logarithmic plot of the bubble neck radius

versus the time to pinch-off (t p =t àt det )for the two numerical

methods with R c =0.8mm and _Q

?200mlph.The comparison does not include experimental data in this case as the image cap-ture used could not achieve a frame rate suitable for this analysis.

Numerical results however are assessed by reference to published power laws derived from previous experimental studies.It is shown that the time period for the detachment process is of the same order of magnitude for both methods.The two methods give similar trends during the collapse as the radius R 0decreases expo-nentially at the ?nal stages (t p <à10à2).The local Weber number during this process is of order 1indicating that this stage is con-trolled by a balance between the inertial forces and the surface tension forces.

The exponential decrease in the bubble neck radius during the detachment can be described using a power law (R 0/(àt p )c )where c $0.36for both VOF and S-CLSVOF methods.Thoroddsen et al.(2007)reported from experimental observations that this va-lue is close to 0.5for bubble growth from nozzle with water/air systems.On the other hand and based on a potential ?ow model,Gordillo et al.(2005)found that this power varies from 0.5to 1/3where the latter case occurs when the gas inertia effect in the neck region is very large.The latter power law is in good agreement with the present results.Fig.14shows the velocity vector plots at three different stages of the formation process where the norm errors l 1and l 2represent the maximum and the average velocity inside the bubble.The intensity of the velocity vector is depicted using a color map in this ?gure instead of a vector scaling.The exis-tence of large gas velocities inside the neck at detachment (t /t det -$1)compared to the other stages of bubble growth explains the large increase in the importance of the gas inertial effect during the detachment and,as a result,the value of c $0.36obtained.However,the power law may vary under the in?uence of other parameters such as using co?owing ?ow instead of injection from a wall ori?ce (Chakraborty et al.,2011).Furthermore,the onset of the detachment process varies based on the physical system such as injection through a needle or bubble in a straining ?ow (Gekle et al.,2009).To conclude,the analysis of the detachment process con?rms that both numerical methods give similar results as the surface tension in?uence on the bubble dynamics is less signi?cant than the case of the growth stage due to the large increase in the gas inertia effect inside the bubble.4.6.In?uence of contact angle model

When the surface around the ori?ce is made of hydrophilic materials,the bubble interface remains at the ori?ce rim during the formation.In contrast,the bubble spreads along the wall when using hydrophobic surfaces.The Young contact angle,h 0,is the material property which determines the wall wettability whereas the instantaneous contact angle during the growth from an ori?ce wall lies in the ranges (h 06h 6(180°àw )+h 0),where w is the rim angle (Chesters,1978;Gibbs,1906).The bubble spreads along the wall when the instantaneous contact angle falls below the Young angle (Gerlach et al.,2007).Numerically,different strategies have been followed for modeling and studying the contact angle.The Young Laplace equation was solved based on the pressure balance across the interface where two modes of formation were identi?ed (Gerlach et al.,2005).Chen et al.(2009)studied the bubble forma-tion process using the LS method with two models of contact angle based on the contact line velocity (model A)and a stick–slip model (model B).However,the results were dependent on the slip length chosen,and getting a correct numerical validation was found to be strongly in?uenced by the numerical parameters.Another simpler model based on a static contact angle formulation was also used for the study of bubble growth (Gerlach et al.,2007)where it has been found that the bubble detachment volume increases when the static contact angle increases above a certain value.In the pres-ent work,a static contact angle formulation is de?ned at the wall ori?ce and its in?uence on the bubble geometrical characteristics and detachment parameters is studied.The contact angle is calcu-lated directly after advecting the volume fraction equation and re-initializing the level set function.It is then corrected to satisfy the user de?ned static contact angle at the wall boundary.The relation between the experimentally observed contact angle with two dif-ferent ori?ce radii (0.5and 0.8mm)and the imposed static contact angle on the detachment parameters is considered.

Fig.15shows the bubble detachment volume and time for two ori?ce radii (0.5and 0.8mm)with the S-CLSVOF method where it is shown that increasing the imposed contact angle above a certain

24 A.Albadawi et al./International Journal of Multiphase Flow 53(2013)11–28

threshold gives larger detachment volumes and later detachment

time,con?rming observations that were made by Gerlach et al.(2007).The critical value of the static contact angle is shown,how-ever,to vary according to the ori?ce radius.For radius 0.8mm,the static contact angle is $60°,while it has the value $50°for the smaller ori?ce radius (0.5mm).

The dependence of this threshold value on the ori?ce is ex-plained by reference to the experimental observations of the bub-ble instantaneous contact angle during the growth (Fig.11for radius 0.8mm and Fig.16a for radius 0.5mm).It has been found that during the formation process,the experimental bubble takes a minimum instantaneous contact angle of 58.33°for the ori?ce ra-dius (0.8mm),while this angle decreases to 48.45°for the ori?ce radius (0.5mm).Fig.17combines the minimum contact angle ob-served experimentally [present work,(Di Bari and Robinson,2012;Vafaei et al.,2010)],estimated numerically (Di Bari,2011),and cal-culated by Capillary equation (Gerlach et al.,2005;Lesage,2012)along with the threshold contact angles estimated numerically.It is apparent that the numerical threshold corresponds to the mini-mum contact angle observed experimentally.This con?rms that the numerical predictions of the bubble detachment parameters can be within a 3%error (as shown in Table 10)as long as the static contact angle used as a boundary condition in the numerical for-mulation is less than that of the minimum instantaneous angle ob-served experimentally.Further increase in the static contact angle gives larger detachment characteristics.This increase is attributed to the changes in the bubble base radius during the growth.Fig.16b shows the time evolution of the bubble minimum radius for ori?ce radius 0.5mm and ?ow rate 200mlph.It is clear that the numerical bubble follows the same trend as the experimental measurements when using small static contact angles.For larger values of (h 0),the bubble spreads quickly on the wall leading to la-ter detachment with a relative difference of about 44%when using the static contact angle of 60°.The bubble interface spreading is due to the imposed static angle which encourages the bubble boundary to move away from the ori?ce rim.Fig.16a shows that the instantaneous contact angle decreases linearly during the growth when using static angles above the threshold 48.45°for the ori?ce radius (0.5mm).

The static contact angle corrects the gas/liquid interface in the cells adjacent to the wall.This leads to large velocities in the

local

S-CLSVOF at three different stages of bubble growth t /t det $0.4,0.8,1.The scale of the velocity vector is set red (maximum velocity).Norm errors are expressed in (m/s).R c =0.8mm,_Q

?200mlph.(For interpretation referred to the web version of this article.)

35

4045

50

5560

V

d e t

[m m 3

]

Detachment time Detachment volume

gas region as the corrected bubble interface normal at the ?rst cell is different than the calculated normal in the other neighbor-ing cells (see Fig.14).This large velocity is thought to be the rea-son for the jump in the bubble center of gravity at the beginning of the neck formation (Fig.9).To avoid this issue,different strat-egies may be followed such as imposing a liquid ?lm at the wall which prevents the bubble from spreading without any con-straints to the bubble contact angle,or using a dynamic contact angle model as in Chen et al.(2009)which may require mesh re?nement at the wall.In other studies,the bubble growth pro-cess with an interface pinned at the rim has been achieved by using a co-?owing principal with zero liquid velocity (Chakr-aborty et al.,2011)or by using a nozzle instead of a wall ori?ce (Quan and Hua,2008).To conclude,a strong in?uence of the con-tact angle on the bubble formation process is found when using static angles larger than the minimum instantaneous contact an-gle observed experimentally.The minimum value itself varies according to the ori?ce radius as it decreases with decreasing the ori?ce radius.5.Conclusion

This study focused on an extension of the original Volume of Fluid model implemented in the OpenFOAM òlibrary into a sim-ple coupled method (S-CLSVOF)which combines the advantages of both VOF and LS.The aim is to bene?t from the smoothed cur-vature and the Dirac function available in the surface tension model of LS.Both VOF and S-CLSVOF methods were used ?rst for the study of a circular bubbles in equilibrium and a freely ris-ing bubble for which exact analytical solutions and the experi-mental data are available.The two methods have then been used for the study of axi-symmetrical bubble growth and detach-ment using small volumetric ?ow rates selected to satisfy the quasi-static condition and to ensure that the capillary forces are predominant.The main points discussed in this paper can be summarized as:

For the circular bubble at equilibrium,the combination of the LS and Dirac functions improves the curvature estimate and reduces the magnitude of the spurious currents.Furthermore,the results’accuracy with S-CLSVOF can be improved by re?n-ing the mesh.

For the free rise bubble,both VOF and S-CLSVOF methods give similar bubble terminal velocities and aspect ratios with rela-tive differences less than 2.5%and 2%,respectively.For 3D bub-ble rise,the numerical results with S-CLSVOF were in good agreement with the experimental observations by Raymond and Rosant (2000).The two dimensional simulations with large bubble diameters fail to provide the correct bubble aspect ratio as expected due to the bubble motion in 3-directional direction. The analysis of the forces acting on the bubble during the growth showed the predominance of the capillary force during the bubble growth,which highlights the importance of using the accurate surface tension model.Both numerical methods are able to predict the complete process of bubble growth and detachment.However,the VOF method fails to provide the accurate bubble detachment time with a bubble growth rate substantially larger than the experimental observations.In con-trast,the S-CLSVOF method was found to accurately predict the bubble detachment volume and time with errors less than 3%.Furthermore,the geometrical characteristics,center of gravity,maximum width and contact angle,were also well predicted by the S-CLSVOF method.With the VOF method and using smal-ler ?ow rates,the bubble was exposed to small oscillations in the vertical direction.

26 A.Albadawi et al./International Journal of Multiphase Flow 53(2013)11–28

Both numerical methods predict similar behaviors during the detachment stage with an exponential power law$0.36consis-tent with a?ow where the in?uence of the surface tension and gas inertia inside the neck region are of similar magnitude.

The static contact angle has a strong in?uence on the formation process.Increasing this angle above a certain value can signi?-cantly increase the bubble detachment volume and time by allowing the interface to spread away from the ori?ce rim.This threshold angle was found to be equal to the minimum contact angle observed experimentally which itself decreases with the ori?ce radii.

Acknowledgement

The authors wish to acknowledge the support of Science Foun-dation Ireland under its Research Frontiers Programme(Grant No. 09/RFP/ENM2151).Recommendations from the reviewers are also gratefully acknowledged.

Appendix A

The OpenFOAM implementation of the PISO pressure–velocity coupling is summarized below but further details on the formula-tion may be found in Brennan(2001).The momentum equation (Eq.(2))implemented in the interFOAM VOF solver of OpenFOAM for incompressible?uids has the following form before discretisation

@eq VT

@t

t$áeq VVTà$áel$VTàer VTár l

?àr P dàgáx r qtF re33Twhere P d=Pàq gx(with x the position vector)is preferred to the hydrostatic pressure P to avoid large changes in pressure across interfaces.The discrete form of the momentum equation integrated over the volume X of the cell centered at p,and integrated over time using the Euler Implicit scheme is written in the conventional form:

a p V ttD t

p t

X

N

a N V ttD t

N

?S upàe$P dtgáx$qTe34T

where V N is the velocity in the neighboring cells and a p,a N are the diagonal and off-diagonal velocity coef?cients,which account for the central and neighboring cells contributions.S up accounts for uniform source terms,including the source part of the transient term from the Euler Implicit time integration.The equation can be re-arranged to give,having dropped the subscript t+D t for simplicity:

V p?

1

p à

X

N

a N V NtS up

!

à

1

p

e$P dtgáx$qTe35T

The?rst term on the right hand side(r.h.s)of Eq.(35)de?nes the operator H[V]p which contains all matrix coef?cients from cell neighbors multiplied by the corresponding velocities plus all source terms other than the pressure gradient.Eq.(35)is is solved by treating the pressure and density gradients and the source term explicitly using the Gauss Theorem to evaluate the gradients at cell centers from the pressure and density interpolated at the face cen-ters,while all other terms are handled implicitly.In the present study,the system is solved for velocity using the Preconditioned bi-conjugate gradient(PBiCG)algorithm with a Diagonal incom-plete LU(DILU)pre-conditioner and the solution is assumed con-verged when the absolute normalized residual falls below10à6. This is the momentum prediction step of the PISO loop.

The velocity approximation from this momentum prediction step does not satisfy continuity and a pressure correction is derived by coupling the momentum(Eq.(2))and continuity equation.The discretise continuity equation provides a constraint on cell?uxes P

f

S fáq V f?0and V f can be interpolated from Eq.(35):

V f?

1

p

f

H?V

f

à

1

p

f

e$P dtgáx$qTfe36T

Face values(à)f,for all terms in Eq.(36)are evaluated by linear interpolation.The coupling provides an equation for pressure:

X

f

S fá

1

p

f

e$P dTf

"#

?

X

f

1

p

f

S fá?H?V

f

àegáx$qTf e37T

Its solution requires that the operator H[V]is estimated from the velocity approximation of the momentum prediction step.That is the operator is handled explicitly.The pressure solution from Eq.(37)is used to correct the velocity(Eq.(36))and face?uxes F f=S fáV f which are therefore calculated as part of the PISO solu-tion procedure.This step is known as the velocity correction.Since

?H?V

f

àegáx$qTf is treated explicitly in the derivation of Eq.(37), the correction relies entirely on an iterative correction of?uxes from P d,that is the method relies on a single momentum correction step followed by a series of iterative pressure corrections.

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【小技巧】教你如何删除微软Surface恢复系统后,C盘Windows.old文件夹!

【小技巧】教你如何删除微软Surface恢复系统后,C盘Windows.old文件夹! 不知道大家有没有发现,微软Surface在恢复系统设置后(无论是删除,还是不删除文件),在C盘里都会多出来?一个Windows.old文件夹,对Windows比较熟的朋友应该都知道,它是重装前的系统,也就是说Surface恢复系统的效果也就是和覆盖重装系统差不多,这倒不是重点,重点是Windows.old会占宝贵的C盘空间,如果是不删除文件恢复,old文件夹可以占数百M的空间,如果是删除文件恢复,那么old文件夹甚至可以占用数G 的空间。所以我们肯定是要将其删除的,而在文件管理器直接删肯定不行,那该怎么办呢?其实微软早就为我们想好了,Windows中有?一个名为“ 磁盘清理”的工具,直接使用它,就可以删掉old文件夹,非常简单,下面就简单介绍?一下步骤。

磁盘清理工具,在Metro界面下就能找到,不过?一般默认是不显示的,想要将它调出来,先在Surface右侧滑动屏幕(或按Win+c)调出Charm菜单,然后选择设置,再选择“磁铁”,在里面的设置里将“显示管理工具”打开。

然后在Metro界面下,就可以看到做右面多出来?一大堆系统工具,其中就有“磁盘清理”

打开磁盘清理后,会自动跳到桌面模式下打开,选择“清理系统文件”,然后就开始分析C 盘的系统文件,等?一会

分析好后,再次回到工具的主界面,这时会发现原来左下角“清理系统文件”的选项已经没有了,这时只要选择确定,就开始清理删除Windows.old等冗余的系统文件,释放系统空间,耐心等?一会即可!

Microsoft Surface 交互设计规范

第1.0节: 简介 微软的Surface使开发人员和设计人员,为他们的客户提供惊人的,社交的,具有很强的互动体验。来自四面八方的人们可以使用360°接口面对面的协作,合作和建立信任。 开发引人注目的Serface体验需要不同的方法来设计接口。本文提出的设计原则和指导方针,以解决关键方面,包括:互动,视觉,声音,文字,和更多的应用程序界面设计。使用这些原则和惯例为出发点,得到最有效的界面软件和硬件平台的独特功能。 第4.0节: Serface 硬件 本节讨论具体涉及到serface的硬件设计注意事项和指导方针。 第4.1节: 输入法 1.基于视觉的触摸 与serface互动的主要方式是触摸。Serface从一开始就在为触摸设计,它是Surface 应用程序中互动的关键动力。 手指和blobs :serface自动识别区分手指和blobs。当有人将手指放在屏幕上,手指会被识别。他们指出的方向,视觉输入系统会自动检测到手指数目、位置和方向。当其它不认定为手指或者标签的物品被放置在屏幕上时,被列为blobs。提供基本大小的信息并分配一个任意方向。方向值在blobs中通常是没有可靠的手指或者标签。 触摸交互- 表面SDK操作处理器识别三个离散的操作:移动,旋转和调整大小。 事实上,Surface SDK中只有三个操作手势是一个技术性的事实,但是从交互的角度看,有许多不同的触摸交互,一个人可以使用这些操作。下面的插图显示了如何使用一个手指或者几个手指,在各种触摸交互中执行虚拟对象。

点击- 按,然后释放 保持-然后按住 滑动或推- 使用你的手指滑动或推来移动对象

轻击-轻按,迅速滑落,然后释放 触摸并开启- 将你的手指,靠近物体外侧边缘的一块内容,并围绕其中心旋转 自旋- 扭转迅速用两个手指旋转对象

微软Surface-Pro-4平板系统恢复镜像安装图文教程

微软Surface Pro 4平板系统恢复镜像安装图文教程 一:U盘恢复镜像下载 要点1:从官方下载立即下载 要点2:镜像包要跟自己型号匹配,否则无法自动激活 例如:Surface Pro 4 国行专业版i5 8G i256G恢复镜像=SurfacePro4_BMR_45_2.114.0.zip 专业版i5 4G 128G恢复镜像=SurfacePro4_BMR_155_2.114.0 二:制作U盘启动器 步骤1:将FAT32 U 盘插入电脑,U 盘大小最好大于8GB 步骤2:从桌面打开文件资源管理器。 步骤3:点击并按住(或右键单击)U 盘,选择“格式化”。 步骤4:选择“FAT32”作为文件系统,输入一个卷标(如“恢复”)以命名U 盘,开始格式化。 步骤5:双击已下载的恢复映像以打开并解压缩文件。 步骤6:然后将压缩文件夹中的文件拖动到格式化后的U 盘。 三:U盘恢复镜像安装 步骤1:关闭Surface,并插上电源。 步骤2:将制作好的U盘驱动器插入Surface 上的USB 端口。 步骤3:按住音量减键,同时按住电源。 步骤4:出现surface的logo的时候,松开电源,但不要松开音量减。音量减键要持续5秒左右再松开。 步骤5:看到提示后,选择所需的语言(简体中文)和微软键盘布局。 步骤6:点击或单击“疑难解答”,然后点击或单击“从驱动器恢复”。

注意注意注意注意注意注意注意注意注意注意注意注意注意注意注意注意 步骤7:选择“仅删除我的文件”或“完全清理驱动器”点击恢复。(选择“完全清理驱动器”硬盘会从新分区恢复成一个盘,硬盘数据一定要备份到移动硬盘或者别的U盘中) 注意注意注意注意注意注意注意注意注意注意注意注意注意注意注意注意 步骤8:等待恢复完成,弹出TPM Change选择OK即可。 步骤9:漫长的等待很快过去,全新的电脑即将到来。

微软Surface网络营销策划案严雪平

微软S u r f a c e网络营销策划案严雪平 公司内部档案编码:[OPPTR-OPPT28-OPPTL98-OPPNN08]

微软Surface 3网络营销策划案 文官1401 严雪平 一、策划对象 2015年3月31日,美国,雷德蒙德——微软公司宣布推出 Surface 家族的最新成员:Surface 3。正如 Surface Pro 3 一样,这是一款可以替代笔记本电脑的平板电脑,但它更轻、更薄且价格更实惠。强大而高效的 Surface 3 为运行完整版 Windows 和 Office 进行了优化,并具备长时间的电池续航能力。微软Surface 3是微软推出的一款新款机型机更轻、更薄且价格更实惠的平板电脑。其操作系统为Windows 8.1、网络模式不支持3G网络、具有双摄像头、具有WIFI 无线上网功能、上市时间为2015年5月5日。微软给它的产品定位是笔记本平板电脑。 二、策划背景 无风扇设计和最长支持10 小时视频播放的电池续航,再加上优秀的屏幕、集成一体式支架和采用杜比?音频增强音效的立体声扬声器, Surface 3 随时随地为你提供解放双手的娱乐体验。 完整的 Windows 体验,多种端口以及运行桌面软件的能力,只需扣入 Surface 3 专业键盘盖就能让 Surface 3 成为学习、工作、家用和移动办公的理想高效设备。你还可以通过 Surface 3 扩展坞来提高生 产力。 通过完整的 Windows 8.1,以及免费升级至 Windows 10 的能力,Surface 3 几乎能够兼容所有你最喜爱的软件,并可以同时运行Windows

让我们走近MicrosoftSurface

每当我们在讨论多点触摸的用户界面该如何设计时,往往会不由自主地谈到iPhone/iPad。很多时候,我们会忽略另外一个同样使用多点触摸技术的产品——Microsoft Surface。 相信很多人都看过Microsoft Surface 的宣传视频。大尺寸的触摸屏、多点触摸的技术、实物对象的智能识别等等,这些技术所带来交互方式的改变,还是给我留下了深刻的印象。 Microsoft Surface的身影开始渐渐变得模糊起来,也许是因为我们对这个产品的了解,只能停留在那短短的几分钟宣传视频里。一次偶然的机会,发现微软已经为想深入研究 Surface 的设计师和开发人员准备好了一切。 一、建立Surface 体验/开发环境 Surface在哪里?在美国的 AT&T 专卖店里,虽然可以免费使用,但是路途似乎远了点。 在自己的个人电脑上搭建 Surface 体验的平台,也许是个不错的方法。如果你的操作系统是 Windows Vista 或者是Windows 7,那么恭喜你了; 只需要依次安装微软的三个软件就能模拟 Surface 了。 1、 2、 3、 在SDK 工具包中你能找到这个——Microsoft Surface Simulator。 这个模拟器提供了使用多点触摸的软件模拟工具,即使你没有触摸屏,但是你仍然可以间接地操作基于 Surface 的应用程序。如下图:

二、设计Surface 用户界面 为了建立基于 Surface 的用户体验,我们需要重新考虑以下基本思路: ·选择/完成的闭环操作 ·使用界面隐喻 大多数传统的图形界面中通常使用选择/完成闭环操作设计。用户首先选择一个操作对象,然后再执行针对该对象的某个命令以完成操作。例如:重命名或删除一个文件。基于 Surface 的应用程序可以不使用这个交互闭环。Surface 上可以结合界面隐喻使得操作更加直接些。这种设计需要设计师不断去观察生活,从生活中寻找线索。

Surface 恢复方案

Surface 恢复方案 您可以登 陆https://https://www.360docs.net/doc/275996177.html,/zh-cn/software-download/windows10 下载Windows 10. 1. 点击“立即下载工具”,下载Windows 10创建USB安装工具。 2. 保存并运行下载工具。工具名称:MediaCreationTool.exe 注意:双击程序等待几分钟,请勿多次双击程序。 3. 选择“为另一台电脑创建安装介质”,点击下一步。 4. 选择您自己的surface 对应的正确语言(国外设备选择购买国家的语言),注意:“是否对此设备使用推荐的选项”这句话不要打勾。 注意:如果选择版本错误会导致激活问题,如果不清楚设备型号请联系微软surface售后部门 如果下载镜像的电脑就是此台需要重新安装win10,请在左下角“对这台电脑使用推荐的选项”打上对勾 如果使用其他电脑下载镜像,把“对这台电脑使用推荐的选项”去掉默认的对勾。Surface 3国行个人版选择版本:windows 10 体系:64位 Surface pro 1 2 3 4国行专业版设备版本: windows 10 体系:64位 国外设备语言,请选择购买地的国家语言 Surface pro1 2 3 4 中文版设备请把语言先选择成其他国家.然后返回选择成中文(简体). 之后版本:windows 10 家庭中文版体系:64位 5.选择下一步

6.请选择 U盘(U盘需要提前格式化,选择文件储存格式为FAT32,U盘一定要大于等于16GB)或者选择 ISO文件 (最好选择ISO文件 ) 选择下一步选择保存到桌面,下载好了把ISO文件包解压 7.下载过程较为缓慢,请您接上电源保持网络正常连接,耐心等待下载完成。完成后桌面上会有文件 windows 10 iso. 8. 创建恢复驱动器将清除 U 盘中存储的所有内容。使用U 盘创建 Surface USB 恢复驱动器之前,请确保将U 盘中的所有重要数据转移到其他存储设备。 步骤 1: 将 FAT32 U 盘插入 Surface 或电脑的 USB 端口。对于 Surface 平板电脑 和 Surface 2 平板电脑,您的 U 盘大小至少应为 8GB。对于 Surface Pro 中文版/专业版型号和 Surface 3平板电脑,您的 U 盘至少应为 16GB。 步骤 2: 从桌面打开文件资源管理器。 步骤 3: 点击并按住(或右键单击)U 盘,然后选择“格式化”。 步骤 4: 选择“FAT32”作为文件系统,输入一个卷标(如“恢复”)以命名 U 盘,然后点击或单击“开始”。 步骤 5: 点击或单击“确定”清除 U 盘的内容。 步骤 6: 格式化完成后点击或单击“确定”。

让Surface Pro有更多可用存储空间

让Surface Pro有更多可用存储空间 在Surface Pro 北美上市之时,微软官方已经就Surface Pro 存储空间进行了说明: 初看这张表格,你可能认为Surface Pro 64GB 版的存储容量太小。但事实上,你可以做一些简单的工作来释放一些Windows8存储空间 – 其中最有效的,便是删除Windows 8 保留的恢复空间。接下来具体介绍方法: “磁盘管理”来删除系统恢复空间

1.释放系统恢复工具的空间,最简单的方法是:前往“控制面板”->“管理工具”->“计算机管理”-> 左侧“磁盘管理”-> 右侧选择容量为约7.8 GB 的恢复分区(而不是 600MB 的),对其右键选择“删除卷”; 2.右键单击 C:,选择“扩展卷”,直接点击“下一步”直至完成。 然而,这样做的问题是:如果你的系统遇到问题,你希望通过Windows 8 自带的“刷新和重置”快速恢复系统,由于恢复分区已经被删除,系统会要求你插入恢复介质才能使用“刷新和重置”。 Surface Pro 团队在Reddit 有问必答环节中谈到,为何不提供Surface Pro 恢复优盘,而选择预置硬盘恢复分区的原因是: “我们本可以这么做(指提供恢复盘),但你有可能会遗失这个恢复优盘。因此我们给你选择,可以通过工具释放存储空间,并制作一个新的恢复驱动器。” “创建恢复驱动器”来删除系统恢复空间

接下来介绍的删除Surface Pro 恢复分区方法将更加保险,但前提需要准备至少 8GB 的优盘,而且其数据将全部格式化: 1.Windows 8 开始屏幕或按Win+W 键盘快捷键,“设置”中搜索“Recovery”或“恢复”,找到“创建一个恢复驱动器”,运行; 2.勾选“将恢复分区从电脑复制到恢复驱动器”,下一步; 3.选择用于保存恢复分区的驱动器,下一步; 4.整个格式化加复制恢复分区的过程需要 15 分钟左右; 5.完成后,恢复驱动器将询问是否“删除恢复分区”,点击底部的“删除恢复分区”,并在接下来的界面点击“删除”,即可释放约7.8GB 存储空

教你看懂微软Surface配置

Surface(中文名:奢飞思)是美国微软公司推出的全新硬件品牌,微软公司于2012年6月19日发布了Surface 系列平板电脑。这款平板电脑采用镁合金机身,10.6英寸显示屏,配备USB 2.0或3.0接口,使用Windows 8操作系统。微软官网将其称为“全高清显示屏”,屏幕比例为16:9。这款产品分为两个版本:一个使用Windows 8专为ARM设计的版本Windows RT;另一个使用英特尔Core i5 Ivy Bridge 处理器,使用Windows 8 Pro 。2012年10月26日,中国市场由苏宁全球同步首发微软Surface。 相关知识点: ARM是微处理器行业的一家知名企业,设计了大量高性能、廉价、耗能低的RISC处理器、相关技术及软件。技术

具有性能高、成本低和能耗省的特点。适用于多种领域,比如嵌入控制、消费/教育类多媒体、DSP和移动式应用等。 RISC的英文全称为:ReducedInstructionSetComputing,中文即“精简指令集”,它的指令系统相对简单,它只要求硬件执行很有限且最常用的那部分指令,大部分复杂的操作则使用成熟的编译技术,由简单指令合成。在中高档服务器中普遍采用这一指令系统的CPU,特别是高档服务器全都采用RISC指令系统的CPU。在中高档服务器中采用RISC指令的CPU主要有Compaq(康柏,即新惠普)公司的Alpha、HP 公司的PA-RISC、IBM公司的PowerPC、MIPS公司的MIPS和SUN公司的Spare。 DSP数字信号处理(Digital Signal Processing,简称DSP)是一门涉及许多学科而又广泛应用于许多领域的新兴学科。20世纪60年代以来,随着计算机和信息技术的飞速发展,数字信号处理技术应运而生并得到迅速的发展。数字信号处理是一种通过使用数学技巧执行转换或提取信息,来处理现实信号的方法,这些信号由数字序列表示。在过去的二十多年时间里,数字信号处理已经在通信等领域得到极为广泛的应用。德州仪器、Freescale等半导体厂商在这一领域拥有很强的实力。 Windows 8 有三个版本,分别是Windows 8、Windows 8 Pro、Win8企业版和ARM 版的Windows 8 RT。Windows8 Pro

广告案例介绍Surface

一、广告案例介绍 这个产品是微软发布的第一个实体产品,广告开始通过一个学生到公园里使用surface,带有平板和键盘的一体机,在键盘和平板结束时候所发出的特殊的声响,接着是引发了所有人的surface的交换使用,表现的是键盘和平板可以随意搭配,风格迥异。在随后的出现的使用人群中有老人、小孩、学生、上班族以及一些时尚人士,也展现了surface受用的广泛性。并在后面有一段机械舞舞蹈表演也想表现的是surface的性能高。 二、企业介绍 微软(Microsoft,NASDAQ:MSFT,HKEx: 4338)公司是世界PC(Personal Computer,个人计算机)机软件开发的先导,由比尔·盖茨与保罗·艾伦创始于1975年,总部设在华盛顿州的雷德蒙市(Redmond,邻近西雅图)。目前是全球最大的电脑软件提供商。微软公司现有雇员6.4万人,2005年营业额368亿美元,其主要产品为Windows操作系统、Internet Explorer网页浏览器及Microsoft Office办公软件套件。1999年推出了MSN Messenger网络即时信息客户程序;2001年推出Xbox游戏机,参与游戏终端机市场竞争。2012年8月23日,微软25年以来首次更换公司Logo。 三、产品介绍 微软于2012年6月19日发布了Surface系列平板电脑。其采用镁合金机身,10.6英寸显示屏,配备标准USB 2.0接口,搭载Windows操作系统。这款产品分为两个版本:一个使用Windows 8专为ARM设计的版本Windows RT,名为Surface RT;另一个使用英特尔Core i5 Ivy Bridge 处理器,搭载Windows 8操作系统,名为Surface Pro。 四、广告发布背景介绍 微软发布产品主要是在针对于超级本和苹果IPAD的之间的兼容性较差,超级本偏向于办公设计,而IPD则偏向于游戏设计,玩游戏的性能很好,微软看到了市场间的空隙,开发了一款集游戏办公办公一体化的机子,surface,屏幕尺寸为10.6寸,属于平板电脑的一类,办公、游戏,携带很方便,外观时尚,并配有高性能键盘,合起来就是保护膜。 五、企业广告战略分析 微软采用的广告战略是单一媒介战略。Surface的使用人群虽然不受年龄限制,但是还是局限在使用网络的人群中,所以surface的广告几乎都是在网络上展开营销。所聘请的演员并不是很大牌的明星,像肯德基一样的广告的演员是年轻时尚一族的。Surface也一样,这样给人感觉更有亲和性,也可以表现出surface是适用于任何一个人的,所传递的时尚、性能配置都是很有诱惑力,尤其是新一代网民的选择,休闲,携带方便,超长使用时间,随处都可以办公游戏。 六、企业广告策略分析 1.调研策略:surface利用微软强大的品牌优势,几乎在所有的电脑中都会有微软所开发的软件,微软自身的强大品牌力也为surface打下了良好了基础,在win7技术很成熟的情况下,微软开发的win8最新软件系统也是和surface一道面世,并配备在surface系统里面。在中国市场下,微软和苏宁达成协议,独家大力销售,利用苏宁这些年的强大发展势头,稳定你给的顾客群,强大的品牌效应,在苏宁电器、苏宁易购、LAOX同步销售。 2.创意策略:在整个广告中,surface所有使用的人群包括,老人、小孩、学生、上班族等各类人群,并通过其中的部门夸张的舞蹈,表现surface所带给人的震撼力。 3.媒介策略:surface的发布只通过网络媒体做宣传,因为她的主要目标人群是网络的使用者。在国内还通过苏宁电器、苏宁易购、LAOX,三种方式宣传。

买前须知!Surface RT必须了解的小细节

微软Windows 8正式发布,旗下Surface平板电脑也正式开卖,被寄予厚望的“真平板”终于和大家见面了。通过一段时间的使用,我们对微软的Surface RT有了较为深入的了解,并总结了一些日常使用中所用到的一些问题或者困惑,希望能够帮助到近期有购买计划的朋友。 过于“私人化”的平板电脑 微软Surface RT的第一印象是它对个人隐私的处理不是很好,也许是微软为了标榜其互联网服务的全面,因此Surface RT上所有功能和应用都必须建立在每个人的微软私人账户之上,而用户一旦登录,自己的个人头像、私人照片、所有的信息和邮件,甚至云里存储的内容都会在屏幕上一目了然。 当然,对于iPad、Android而言,输入个人账户也是必须的,但是当拿到一台iPad或者Android时,除非刻意寻找,否则很难发现用户因为登录账户而产生的的个人信息。而在Surface RT上,屏幕的右上角

就有你的个人头像,订在桌面的图片“瓷砖”上轮换显示着本地和云空间里的照片,进入SkyDrive不需要输入密码,日历里的会议邀请也是在桌面上一目了然。 那可不可以不登录个人账户直接使用Surface呢?当然不可以,Surface RT在首次开机时会让用户输入微软的个人账户,否则系统将无法开启,而之后的软件下载、云服务、消息功能都和个人账户进行了绑定;而且Surface RT不支持删除用户,因此一旦用设置过自己的账户,除非重装系统,个人信息将在这台平板上永久保存。 当然,Surface RT支持添加多用户,但是需要注意的是,所添加的用户同样不支持删除,一旦添加,也是永久性存在于你的平板上。这意味着Surface RT几乎不能外借,如果有朋友借这款平板用两天,只有三种选择:1、任由别人查看自己的云空间、个人照片、邮件、日历信息、MSN信息……2、让朋友添加新用户,但是要做好这个用户将一直跟随自己的心理准备(账户之间应用不能互用,新用户软件需要重新下载);3、干脆不借。 史上最高深莫测的平板操作系统 Surface RT所采用的Windows RT系统,界面多样,变化丰富,简直就是平板操作系统中的变形金刚,但由于Surface RT的操作系统的操作方式之前没有先例,而系统的各种操作、动作又比较繁杂,因此造成了Windows RT的上手非常困难,即使是一位接触过很多数码产品的达人,要想玩转Surface RT也需要一定的时间。

Windows 8和Surface常见故障解决方案

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2019年微软surface平板电脑如何-推荐word版 (1页)

2019年微软surface平板电脑如何-推荐word版 本文部分内容来自网络整理,本司不为其真实性负责,如有异议或侵权请及时联系,本司将立即删除! == 本文为word格式,下载后可方便编辑和修改! == 微软surface平板电脑如何 1975年比尔盖茨和保罗艾伦一起合作创办了这家后来闻名全球的科技公司,在其所有的科技产品中最有名的就是他们独立开发的Windows操作系统和Microsoft office(微软办公)系统。那么,微软surface平板电脑怎么样呢?下面和jy135小编一起来看看吧! 微软surface平板电脑如何 1.微软surface的发展 微软的surface系类产品是在201X年6月左右公布,10月左右入驻中国 市场,随后发展出了第二代、第三代产品。第二代产品包括surface2和 surface Pro2两个系列,这两者的差别主要体现在配置上,处理器的性能、内 存大小上均有区别,总体来说surface Pro是surface的升级版。 现在的第三代surface产品包括surface3、surface Pro3和surface Pro4这三个系列。除了在二代的基础上升级换代,不仅作为平板使用功能更加 强大甚至超过笔记本电脑,且在重量方面做了精简使携带更加轻便,屏幕的 分辨率也有所提高,电池的续航能力也进行了优化。 2.微软surface的配置 在了解了surface系类的发展历史后,我们来看一下他们的各自配置是怎 么样的。以最新的第三代产品为例,我们介绍下surface Pro3和Pro4的配置 参数,两个产品都分为64G、128G、256G存储空间这三个版本,运行内存分为 4G和8G两个版本 surface Pro3:除了以上介绍的共同点之外,Pro3的屏幕为12英寸,支 持多点触控,电池持续续航时间为10小时,待机时间为15-20天。采用英特尔四代酷睿处理器分别有i3、i5、i7三个版本,前后置摄像头均为500万像素,配置中带有surface触控笔。 surface Pro4:Pro4的屏幕大小为12.5英寸,屏幕为支持多点触控的电 容屏,电池续航时间上差别和Pro3并不大,处理器采用了英特尔第六代skylake酷睿i5处理器,像素也有所提升前置仍是500万像素,后置提升至 800万像素,更为轻便的机身还能执行PC电脑软件。

微软surfacepro4平板系统恢复镜像安装图文教程

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微软将通过售后解决Surface键盘开裂问题

微软将通过售后解决Surface键盘开裂问题 近期在Zdnet的论坛上,一些首批Surface RT用户爆出,同Surface RT一起购买的Touch Cover 键盘保护套出现了问题,在与设备的连接处容易开裂,除此之外还有部分用户在抱怨关于Touch Cover 键盘保护套的边缘出现褶皱和松动的现象。 尽管开售仅仅两周,但是在Zdnet的论坛上已经有不少的用户都表示他们的Touch Cover出现这样的情况, 对于这样的情况,微软已经发出声明: 微软一直在尽全力保证我们的消费者可以使用高质量产品。我们正积极与售后服务联系,并会注意这些材料开裂的情况。 除了声明之外,微软还建议,所有的用户若是遇到Touch Cover本身存在质量问题,可以同微软售后服务联系,微软将会尽量帮助大家解决这一问题。 事实上,出现这样的情况也并非微软独此一家,有购买iPad的SmartCover的朋友或许知道,SmartCover时常出现边缘开裂、褶皱和磁性吸附处松动的情况,

除了这些之外,iPad和iPhone频频爆出的相机门、信号门等等情况,但是苹果官方不论是对于附件上还是机器本身的态度却没有微软来的诚恳。许多时候由于SmartCover毕竟只是一个保护套,而Touch Cover则是充当了键盘的角色,用户对二者的关注度不同,当然二者之间的售价也不能够相提并论。 Surface键盘开裂仅仅是一部分用户出现的问题,大部分用户手上的键盘都是好的。当大家对于一个产品拥有很高的期望值时,就希望这款产品十分的完美,没有任何的缺憾,实际上,不论是从产品本身还是从生产过程上看,没有一个厂家敢声称自己的产品完美无缺。 原文来源wp8新锋网:https://www.360docs.net/doc/275996177.html,/

微软Surface叫板苹果iPad的六大优势

微软Surface叫板苹果iPad的六大优势 (首发:爱比妮pba https://www.360docs.net/doc/275996177.html,/ ) 微软Surface平板将于10月26日发布,定在苹果iPad mini发布会三天之后。Surface平板电脑搭载的是最新Windows 8操作系统,售价上分为不同档次,基本上与苹果The New iPad相同。从定位和设计上,我们可以判断出该产品也正是冲着The New iPad而来。虽然这两款平板电脑基于不同的操作系统,搭载不同的硬件,但是依然具有很多可比之处。Surface前途几何,它能否具备足够的实力与 iPad抗衡?目前业内评价褒贬不一。下面是我们总结出的Surface可以对抗苹果iPad的六大优势。 一、更先进的Touch cover保护盖 微软Surface配备了一款名为“Touch cover”的保护盖。Touch cover有点类似苹果iPad Smart Cover的平板保护罩,不过在功能上更为强大,采用Polartec 材料制作,可以通过磁性技术和Surface平板电脑连接。最特别之处在于,它含有完整的Windows触控键盘,为显示屏上的虚拟键盘节省了空间。 Touch Cover有两种类型,触敏型和触觉型。触敏型拥有让人惊艳的3mm厚度,而触觉型也仅为6mm。触敏型键盘主要是由于它在一片薄膜上采用了可触摸的电容式电阻,并不需要为键盘提供额外的空间,拆开Touch Cover之后我们可以

发现有个很薄的电路板,同时结合了加速计和一定的柔韧性,能够实现180度的自由旋转。这样的厚度和设计也非常方便携带。 二、带有USB接口,扩展性强大 虽然Surface厚度仅为9.4mm,但依然还是配备了一个全尺寸的USB端口,这样的设计非常不易,对平时应用来说更加方便。用户可以通过它外接一个移动硬盘或者U盘等移动存储器,还可以连接鼠标、键盘等,如果觉得不够用,买个USB HUB扩展器,这样就可以接入更多周边设备了。如此一来,Surface的功能是不是就要强大很多了呢? 相比Surface的竞争对手,iPad目前还停留在30针接口上,未来虽然可能会采用更小的闪电接口,但是周边配件却远远不如Surface多,这也是微软从电脑时代保留下来的优势。 三、更自由的应用程序体验 Surface分两种版本,ARM版和X86版。X86版理论上可以兼容目前Windows桌面系统下的所有程序,这样一来程序的数量和用户自由度就比封闭的iPad好得多。为了便于管理,苹果iPad目前只能从苹果官方商店内下载应用,用户的可选择范围就大打折扣(虽然可以越狱实现目的,但步骤的繁琐和其他限制并不是所有用户都可以自由使用,另外越狱有风险,我们建议使用正版程序)。

微软对SurfacePro的定位是超级本而非平板

微软配置了键盘,用户可像笔记本电脑一样使用该款电脑.这项在平板电脑上地新设计可能源于微软硬件产品越来越多采用“自己动手”设计. 地价格、应用程序兼容性、整体性能可能表明其更像是一款“乔装”地超级本.不过如果作为一款超级本,又面临着一个不利因素即电池寿命.微软近日证实地电池寿命约为搭载系统地平板电脑电池寿命地一半,据估计版平板电脑地电池寿命在至小时之间.这意味着地电池寿命大约在至小时,因为该款电脑配置地处理器电源需求较高.文档来自于网络搜索 超级本地一个关键卖点便是较长地电池寿命,通常在至小时,在某些情况下甚至达到小时.除了电池寿命之外,显然微软对其地定位是一种触屏超级本,顾客可选择是否要键盘防尘罩. 地分析师安德鲁( )表示,随着产能地提高,地价格很可能会在明年地某个时间出现下降,这将会增加该款电脑对企业地吸引力.文档来自于网络搜索 超频总是被人们说得神秘兮兮地,说白了,超频就是提高电脑各部件运行地频率,让电脑得到更好地性能,超频这事儿这样说白了,真地很简单! 可以说,初中以上文化程度,看两篇超频地过程文章都会超频,当然,能小超一下很简单,想成为超频高手也不是那么简单地,但如果知道几点超频地关键,想成为一个准高手也是很简单地. 要想成为超频准高手,首先我们应该明白电脑是一个有机地整体,牵一发而动全身,在调高地同时,不仅仅是地频率上去了,内存地频率、其他诸如、、和总线地频率也都会上去,而这些东西在很多时候都会成为影响超频成败地关键因素. 听起来很复杂吧,嘿嘿,其实很简单,现在地主板一般最多需要锁定总线频率,动手调一下内存频率,而其他都是自动地. 以我个人地小经验来说,在整个超频过程中,主板和地超频体质是固定地,能不能超到地极限频率,很多时候我们得用心调好内存,内存地调整是很关键地步骤! 应该也正是因为这样,现在市面上有一些专门为超频而推出地内存,比如金士顿系列地超频内存. 下面以一个列子详细地说一下具体地步歘与细节: 机器主要配置为: 不同地主板设置项不太一样,详细请参考自己地主板说明书找到下面对应地选项: 开机按进入设置: 主要需要关注地有如下几个项,一般都类似 设置系统日期时间以及软硬盘规格等. 设置开机磁盘顺序进阶功能.开机显示装置选择

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