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On the failure of a brittle material by high velocity gas jet impact

On the failure of a brittle material by high velocity gas jet impact
On the failure of a brittle material by high velocity gas jet impact

On the failure of a brittle material by high velocity gas jet impact

Andrei Kaliazine *,Morteza Eslamian 1,Honghi N.Tran

Pulp and Paper Centre,Department of Chemical Engineering and Applied Chemistry,University of Toronto,200College Street,Toronto,ON M5S 3E5,Canada

a r t i c l e i n f o

Article history:

Received 17November 2008Received in revised form 12May 2009

Accepted 3June 2009

Available online 12June 2009Keywords:

Kraft recovery boilers Sootblowing

Supersonic jet–solid body interaction Deposit failure

Jet impaction on a surface

a b s t r a c t

Failure of brittle solid bodies due to the impingement of a high velocity air jet on the body surface is studied,experimentally and https://www.doczj.com/doc/5e17836144.html,ing the linear elastic theory and stress distribution analysis,a general criterion for the failure of brittle materials impacted by a gas jet is derived.Several special cases of jet–solid body interaction including failure of thin and thick layers and cylindrical objects immersed in a cross?ow gas stream are investigated and proper material failure criteria are developed.These criteria correlate the minimum jet peak impact pressure (PIP)required to break the material to the material’s tensile strength and Poisson’s ratio.A series of experiments were performed using a laboratory-scale apparatus.Gypsum cast on steel tubes forming cylindrical samples was used as the model brittle material.Experimental data and high-speed breakup movies are employed to understand the gas jet–solid body interaction and to validate the theoretical criteria developed for the material failure.It is deduced that the failure of cylindrical samples impacted by a gas jet is by the formation and propagation of cracks.However,when the impact jet diameter is small,the cracks cannot propagate,and the material is failed due to localized surface pitting.One of the practical applications of this research is in Kraft recovery boilers,where high velocity supersonic steam jets are employed to remove deposits accumu-lated on the outer surfaces of the steam tubes.

ó2009Published by Elsevier Ltd.

1.Introduction

The erosive nature of the high velocity liquid and gas jets makes them attractive for several industrial applications,such as the development of abrasive cutting machines using high power water jets and removal of deposits accumulated on tube surfaces in industrial boilers using supersonic steam jets.Understanding the jet–solid body interaction is important for optimizing nozzle design and operation.Liquid and gas jets interact with solid bodies differ-ently.Because of higher density and incompressibility,liquid jets are able to generate sharp short-duration pressure spikes at the begin-ning of the impact with solid bodies,a phenomenon that elevates the destructive force of the liquid jets in comparison with the gas jets.

The problem of solid body impact by a liquid jet has been studied experimentally and theoretically.Below is a review of the relevant literature.Bowden and Brunton [1]investigated the deformation of solids by supersonic liquid jets.They measured the magnitude and duration of the impact load and developed

a model to predict the deformation of plastic,elastic and brittle materials impacted by liquid jets.Bowden and Field [2]studied the fracture of brittle solid objects by liquid jet impact,and found that the so-called water-hammer pressure can cause substantial damage to the material.Bourne et al.[3]studied possible mecha-nisms of brittle material damage caused by a liquid jet impact,using high-speed photography and the Schlieren visualization technique.In another study,Momber [4]investigated the erosion of tension-softening materials,such as concrete,reinforced ceramics,and rocks due to the liquid jet impaction and found a correlation for the volumetric erosion rate as a function of material brittleness and the characteristic length of the material.

In contrast,very few studies have examined the material failure by high velocity gas jet impact.Kaliazine et al.[5]used a scaled-down laboratory apparatus to simulate the deposit removal formed on outer tube surfaces by air jet impact.They experimentally investigated the effect of jet parameters and deposit strength on the breakup of symmetric gypsum deposits cast around steel tubes.In another study breakup of similar samples was visualized from the front and back simultaneously,and the effects of deposit asymmetry,jet/deposit attack angle,and jet duration and frequency were investigated [6].For each experiment,breakup duration and length were measured.In a complementary study,Eslamian et al.[7]studied the failure of a cylindrical brittle material (gypsum)impacted by a supersonic air jet.The breakup behavior of

*Corresponding author.Tel.:t14169785021.

E-mail address:kaliazi@https://www.doczj.com/doc/5e17836144.html, (A.Kaliazine).1

Present address:Department of Mechanical and Industrial Engineering,University of Toronto,Toronto,Canada.Email:m.eslamian@utoronto.ca (M.

Eslamian).

Contents lists available at ScienceDirect

International Journal of Impact Engineering

journal home page:

https://www.doczj.com/doc/5e17836144.html,/locate/ijimpeng

0734-743X/$–see front matter ó2009Published by Elsevier Ltd.doi:10.1016/j.ijimpeng.2009.06.002

International Journal of Impact Engineering 37(2010)131–140

two deposit sizes,positioned at several distances from the nozzle exit,was visualized and documented using high-speed video imaging.Three deposit failure behaviors/modes were observed:(i )crack formation and propagation along the longitudinal axis of the cylinder,(ii )surface pitting followed by axial crack formation,and (iii )surface pitting followed by spalling.They correlated the failure characteristics to the ratio of jet to deposit diameter,based on a qualitative boundary layer analysis.In the current study we study the same problem,i.e.gas jet interaction with brittle solid deposits,but from the fracture mechanics point of view.The stresses developed within a brittle body,as a result of the impingement of a jet on its surface are formulated and failure criteria for several special cases are derived.These theoretical criteria are then validated against the experimental data obtained in this study and those of Kaliazine et al.[5]and Eslamian et al.[6,7].2.Experimental

2.1.Procedure,materials and methods

In Kraft recovery boilers,sootblowers are employed to remove deposits or fouling formed on the outer tube surfaces,using high velocity steam jets.The main part of a sootblower,called the ‘‘lance’’is a long tube equipped with two opposing nozzles,mounted at its working end.These nozzles,called de Laval nozzles,after Carl G.P.de Laval,have a convergent–divergent shape that is essential to produce a supersonic jet,when a high pressure gas passes through it.The industrial nozzle’s throat diameter varies from 2.22to 3.18cm.The high pressure,high temperature steam introduced into the lance passes through the nozzle and gains high velocities (w 600m/s)at the nozzle exit.In laboratory experiments,high pressure air at room temperature was used as the working ?uid (in lieu of high temperature steam).The key component of the appa-ratus is a scaled-down converging–diverging nozzle,which is geometrically similar to a typical sootblower nozzle used in Kraft recovery boilers;the nozzle throat and exit diameters are 0.45and 0.74cm,respectively.The dimensions of this nozzle are about a quarter of those of an actual nozzle.The apparatus is schematically shown in Fig.1.The nozzle was used to generate a supersonic air jet,directed at a cylindrical tube coated by an arti?cial deposit;the tube was mounted at various distances downstream of the nozzle exit and in-line with the jet https://www.doczj.com/doc/5e17836144.html,pressed air was supplied from a high pressure cylinder at 2MPa (300?5psig);at this pressure,the nozzle generates a supersonic air jet with an exit Mach number of about 2.5.This Mach number is comparable to the operating Mach numbers of the industrial sootblowers.In a de Laval nozzle,

the ratio of the nozzle exit properties such as pressure,temperature,and density to the corresponding stagnation values are functions of the gas speci?c heat ratio and the Mach number only.The speci?c heat ratios of steam (water vapor)and air are comparable.There-fore,the Mach number is assumed to be the main non-dimensional number that governs this gas dynamic process.As a result,our experiments,in which air is used instead of steam with comparable nozzle exit Mach numbers fairly mimic the actual case.Also,note that the temperature and density of steam,which is used in industrial sootblowers,are greater than those of the compressed air used in our laboratory experiments.Nevertheless,since the entire boiler is operated in an elevated temperature,the thermal stresses generated within the deposits due to the high temperature steam are negligible compared to the stresses generated due to the mechanical loading.As such,our theoretical analysis only includes a mechanical stress analysis,which is believed to be able to adequately simulate the actual case.Having said that,also note that the generation of sudden thermal stresses or thermal shocks in the deposits has an important application in deposit removal in Kraft recovery boilers.During thermal shedding (chill-and-blow)events,due to a sudden decrease in temperature,cracks form within the deposit,often leading to deposit debonding from the surface;this greatly facilitates the deposit removal process.

A solenoid valve (Granzow,Inc.)was used to control the high pressure air ?ow to the nozzle.Two high-speed video cameras (Photron Fastcam-Ultima 1024and MS70K Mega Speed,Canadian Photonics Labs,Inc.)operating at 4000frames/s were used to capture the deposit breakup process.A data acquisition system and the LabVIEW software,both supplied by National Instruments,were used to operate the valve,record pressure measurements,and trigger the cameras.

Gypsum (CaSO 4$2H 2O)was used to prepare the samples.Gypsum was prepared by mixing plaster of Paris (CaSO 4$1/2H 2O)and water.Gypsum is suitable for deposit modeling,because it is easy to cast to any desired shape and also its physical properties,such as fracture strength,can be easily altered by varying the water-to-plaster mass ratio.Gypsum deposits were cast on steel tubes with outer diameters (OD)of either 6.35or 12.70mm.The overall OD of samples varied from 12.0?0.1to 26.0?0.1mm.Deposit layer thicknesses to tube diameter ratios varied in a rather wide range of 0.3?0.1–2.0?0.1.For each deposit failure experiment,a sample was placed at a certain distance from the nozzle exit and impacted by a supersonic jet,while a camera recorded the entire cracking and breakup process for later qualitative and quantitative analyses.Also,in order to establish a correlation between deposit strength and the minimum jet peak impact pressure (PIP)required to break a deposit,two series of experiments were performed;note that the jet PIP is the total pressure of the gas jet that is sensed after the impact and is a measure of the jet breakup power.Firstly,using a Pitot tube connected to a static piezoelectric pressure transducer (Omega),the jet PIP along its centerline was measured as a function of the distance from the nozzle exit to the front surface of the deposit.During these experi-ments,the Pitot tube was slightly vibrating,when it was exposed to the supersonic jet.This vibration together with the effect of the shock wave formation in front of the Pitot tube and possible misalignment of the tube with the direction of ?ow may cause some uncertainties in the measurements of the PIP.Secondly,deposits were moved incrementally (increments of 5?1mm)from a distance toward the nozzle exit until they broke.The breakup is not instan-taneous;therefore,at each location the deposit was exposed to the supersonic jet for several seconds.If a deposit placed at a certain distance from the nozzle exit does not break within the ?rst few seconds,it will not usually break at all.In order to minimize the experimental uncertainties,all deposits were prepared following the same procedure [6,7]and used immediately after preparation.

Yet,

Arificial Fig.1.Schematic of the experimental apparatus.

A.Kaliazine et al./International Journal of Impact Engineering 37(2010)131–140

132

the breakup of the brittle deposits is rather statistical,owing to the differences between the structures of the arti?cial gypsum deposits. Nevertheless,since we have performed a large number of experi-ments,the very few possible inaccurate data will have a minimum in?uence on the conclusions we draw here.More details on the uncertainties and errors associated with the breakup experiments under various conditions may be found in refs.[6,7].

2.2.Modes of solid failure

As outlined by Eslamian et al.[7],analysis of the breakup movies has showed that the breakup mechanism may be correlated with the ratio of the gas jet diameter,measured or estimated at the point of jet interaction with the deposit surface,to deposit diameter.For large gas jet to deposit diameter ratios(>w0.5),the deposit failure mechanism is due to axial crack formation,where breakup starts with the formation and propagation of deep cracks in the axial direction.Fig.2displays a typical sequence of breakup images of a12.7mm deposit OD(cast on6.7mm OD tubes),placed9cm away from the nozzle exit.The distance is measured from the front surface of the deposit to the nozzle exit.This deposit size(12.7mm deposit OD)is referred to as the thin deposit hereafter.Fig.2shows that a crack forms in less than1/4ms,measured from the instant of jet arrival at the surface;since the deposit is thin and weak,the material near the crack then breaks into several pieces and debonds off the tube surface,all within3ms.

An estimate of the effective diameter D eff of a fully expanded free jet as a function of the distance x from the nozzle,may be derived from the fact that for a free jet the?owing gas jet, momentum remains conserved downstream of the jet and equals the momentum of the uniform jet at the nozzle exit[7]:Z N

2p r r x V2x d r?

p D2

x

4

r x V2

x

?

p D2

e

4

r e V2

e

(1)

where r,V,and D are gas density,axial velocity,and jet diameter, respectively,and the integration is taken over radial position r, measured from the centre of the jet,which is assumed to be circular.D eff can then be estimated as follows:

D eff?D x?D e

V e

x

?????r

e

r x

r

(2)

Using the gas dynamic equations,the gas velocity and density at the nozzle exit can be determined knowing the nozzle geometry and the supply pressure.The gas velocity and density of a fully expanded jet at any location x may be obtained from empirical equations[7].Using Eqs.(1)and(2),the effective jet diameter at 9cm from the nozzle exit is estimated to be8mm,and so the jet to the thin deposit diameter ratio is0.63.

For intermediate jet diameter to deposit ratios(w0.4),surface pitting preceded axial crack formation.For instance,Fig.3shows the breakup sequence of a19.1mm deposit OD cast on tubes of 6.7mm OD placed9cm from the nozzle exit.This deposit is referred to as the thick deposit hereafter.First surface pitting is observed before an axial crack forms.In this case,the jet is focused on a smaller area of the deposit compared to the case illustrated in Fig.2.For small jet diameter to deposit ratios(w0.3),which is the case for thick deposits placed near the nozzle exit(w5cm),the breakup mechanism was intense surface pitting,which resulted in the fragmentation of the bulk of material into small pieces,as shown in Fig.4.In this case,no distinct deep crack was formed.

To summarize the experimental observations,the pattern of brittle deposit failure depends on the ratio of the jet to

deposit

Fig.2.Typical images of breakup due to axial crack formation,for a12.7mm OD

deposit cast around a6.4mm tube OD,placed9cm from the nozzle exit.Breakup

begins at time t?0.This breakup pattern can be explained best by Section3.2.3,

deposit in

cross?ow.

Fig. 3.Typical images of breakup due to surface pitting followed by axial crack

formation,for a19.1mm OD deposit cast around a6.4mm tube OD,placed9cm from

the nozzle exit.The breakup of this deposit is in the thick mode(Section3.2.2),but it is

switched to the thin mode(Section3.2.1)once some of the deposit is removed.

A.Kaliazine et al./International Journal of Impact Engineering37(2010)131–140133

diameter.For average and large ratios (>w 0.5)a deposit fails due to the formation of axial crack.For smaller ratios,failure starts with surface pitting de?ned as removal of small pieces of material at the area of direct jet impact,which may or may not be followed by the formation of an axial crack.These deposit failure patterns are eluci-dated based on a theoretical analysis presented later in this paper.2.3.Effect of jet peak impact pressure (PIP)

A stronger jet is able to break and remove stronger deposits.The jet peak impact pressure (PIP)is a measure of the jet power;it is the stagnation pressure measured after the formation of a shock wave,when the jet hits a solid body or deposit.Note that here we have correlated the breaking ability of a supersonic air jet with its PIP,which is a static property of the jet.It may be argued that the transient effects and pressure ?uctuations may in?uence the deposit breakup,as well.In a recent publication,we have reported our ?ndings on the effect of dynamic or transient characteristics of the jet on deposit breakup behavior.In that research,we did not observe any signi?cant difference between deposit breakup by a pulsating jet compared to a continuous or steady jet.At the instant of the jet impact on a solid surface,air is highly compressed and a transient peak impact pressure with a magnitude greater than PIP may form.However,due to its short duration,this tran-sient peak pressure was found unable to cause deposit breakup,at least at Mach number of about 2.5.

Breakup of cylindrical gypsum samples of different strengths was examined in order to establish an approximate relationship between the material strength and the minimum jet PIP required for breaking a deposit.In these experiments,the samples were moved incrementally toward the nozzle until they broke.Since the jet spreads and decelerates farther away from the source,its PIP drops sharply with distance from the nozzle.The data points

showing the correlation between the deposit strength and the minimum required distance between the deposit surface and the nozzle exit to guarantee the breakup are shown in Fig.5.The variation of PIP(x )/2with distance from the nozzle exit,which was obtained separately,is superimposed on the deposit strength data points.The estimated air jet diameter with distance from the nozzle exit is also shown (using Eqs.(1)and (2)).One may observe that despite obvious correlation between the jet peak impact pressure (PIP)and tensile strength of broken samples (s t ),i.e.PIP/2?s t ,there is certain difference in minimum PIP required to break thinner and thicker deposits,as well as deviation from the semi-empirical relationship PIP/2?s t for small distances from the nozzle exit.In the following section we will perform a stress analysis on solid materials subjected to the action of an impinging jet.This may help explain the above-mentioned experimental observations and data as well as differences in failure modes observed for samples of different sizes.3.Theoretical

In this section,a general criterion for the failure of brittle materials impinged by a gas jet is developed.It will be shown that the failure criterion depends on how the stresses are developed and distributed within the material.For several simple yet practical cases,the failure criterion is simpli?ed and expressed in terms of the impingement pressure,usually PIP,and material’s properties.3.1.Fracture of solid bodies under tensile stresses and hydraulic pressure

It is well known that brittle materials fail due to propagation of cracks,which act as stress concentrators,i.e.stress attains its maximum value near the crack tips [8].Since it is easier to open a crack by pulling the material apart than by compressing it,the brittle materials fail easier under the tensile stress than under other modes of loading.With some simpli?cation,it may be stated that a brittle material fails when the tensile stress experienced within the material (s t )exceeds the material’s tensile strength (s t ),i.e.s t >s t .However,there is a substantial difference between the stresses applied by a mechanical loading and a ?uid ?ow,such as a gas jet,especially when one considers the failure conditions on the material’s surface.When a ?uid ?ow impinges on the surface of a solid body,the ?uid penetrates the surface micro-cracks

and

Fig.4.Typical images of breakup due to surface pitting and spalling,for a 19.1mm OD deposit cast around a 6.4mm tube OD,placed 5cm from the nozzle exit.This pattern can be explained best by Section 3.2.2,thick deposits.

10

20

30

40

50

Jet diameter, mm

D e p o s i t S t r e n g t h o r P I P /2, M P a

Distance from nozzle, mm

Fig.5.Failure data points showing a correlation between the gypsum deposit strength and the minimum required distance from the nozzle exit to guarantee the breakup.The curve of PIP/2,half of the peak impact pressure,which was obtained separately,is superimposed on the deposit strength data points.The estimated air jet diameter with distance from the nozzle exit is also shown.

A.Kaliazine et al./International Journal of Impact Engineering 37(2010)131–140

134

pores and produces pressure on the inner walls of the cracks;this pressure tends to open the cracks similar to the tensile stress applied to the body by mechanical loading.Therefore,the normal pressure generated by a jet applied on a surface,inside the cracks acts as a tensile stress applied in the tangential direction (Fig.6).Hence,for the surface of a brittle body under the action of a ?uid ?ow,the total stress concentration at the tips of the surface cracks is caused by both the ?ow stagnation pressure and the induced stress s t .Therefore,the failure criterion for the surface should be modi?ed to the following form:

P ts t >s t

or

P >às t ts t

(3)

where P is the pressure generated inside the cracks and s t is the tensile stress induced and developed due to the action of the pressure on the body.Pressure P usually equals the jet PIP,but since PIP is a terminology used in sootblowers of Kraft recovery boilers,in stress analysis we use a more general symbol P for this pressure.The induced stress s t depends on the conditions of jet impingement and the geometry of the problem.Therefore,for practical imple-mentation of the general criterion (3)to a speci?c case,a separate analysis of stress distribution within the body is essential.In the following sections several cases of jet–deposit interaction will be considered and appropriate criteria for deposit failure are derived.These cases include thin and thick deposit layers impinged by a gas jet and a deposit (either thin or thick)immersed in a cross?ow gas stream.In the ?rst two cases,the jet diameter with respect to the deposit layer frontal surface area is small,whereas in deposit in cross?ow,the deposit is essentially surrounded by the jet plume.

3.2.Special cases

3.2.1.Thin deposits

The case of a thin layer deposit is a relatively simple example of jet–deposit interaction;therefore,we start our analysis with this case.Deposit layer of thickness h is considered as thin if h is substantially smaller than both the tube diameter Dt and the jet diameter d j (see Fig.7):

h (Dt ;

h (d j

(4)

Condition (4)also signi?es that the area on which the jet pres-sure is applied is large compared to the layer thickness.To further simplify the problem,consider a ?at layer of brittle deposit of thickness h ,attached to a non-deformable solid surface;also assume that the jet exerts pressure P ?P (x ,y )on a certain portion of the layer,where x ,y are the axes of a Cartesian coordinate system on the plane of the deposit layer.If the layer is suf?ciently thin,for given x and y coordinates,the stress applied in the direction perpendicular to xy plane remains constant throughout the layer

thickness and,therefore is a function of the tangential coordinates x and y only;thus one may write

s z ?P ex ;y T

(5)

Solid surface supporting the layer from the back prevents it from deformation in the tangential directions x and y ;therefore the tangential strain components are zero:

3x ?3y ?0

(6)

On the other hand,according to Hook’s law,the strains in x and y directions may be expressed in terms of the stresses in x and y directions as follows (e.g.[9]):

3x ?1E

?

s x àn às y ts z á?3y ?

1?

s y àn es x ts z T?e7T

By combining Eqs.(6)and (7)the stress components in x and y directions,s x and s y ,can be expressed in terms of the stress component in z direction,s z .Also,note that according to Eq.(5),s z ?P (where P (x ,y )has been replaced by P for simplicity);therefore one may write

s x ?s y ?

n

1àn

s z ?

n

1àn

P (8)

Note that s t ,the tensile stress developed within the body as a result of jet impaction (Eq.(3)),is equivalent to às x and às y in Eq.(8).This is because since the deposit is adhered to the tube surface and cannot elongate in x and y directions,application of pressure results in the development of compressive tangential stresses (Eq.(8))within the material.By combining Eqs.(3)and (8)and setting s t ?às x ?às y ,the criterion for the failure of a thin deposit impacted by a gas jet is obtained as follows:

P >

1àn

1à2n

s t

(9)

As long as condition (4)is satis?ed,one may apply the local tangential coordinates to any point on the deposit surface and arrive at Eq.(9).Therefore,the criterion (9)may be used for thin brittle deposits not only on ?at surfaces but also on curved tube surfaces,as well.

If the deposit is not well attached to the underlying surface,it may slide along it and therefore condition (6)will be violated.When there is no adhesion between the deposit and the surface,no tangential stresses are applied to the deposit layer and therefore:

s x ?s y ?0

(10)

Therefore,s t ?0and criterion (3)is reduced to

P >s t (11)

Comparison of criteria (9)and (11)for well-attached and unat-tached deposit layers reveals that good adhesion makes the

deposit

a b

Fig.6.Opening of surface cracks:(a)by jet pressure;(b)by mechanical

loading.

a b

Fig.7.(a)Jet impingement on a thin deposit;(b)pressure distribution on the surface.

A.Kaliazine et al./International Journal of Impact Engineering 37(2010)131–140135

breakup more dif?cult,requiring a higher jet peak impact pressure to fracture the deposit.However,the condition of no adhesion between the tube and the surface may not be realistic,because even if there are no bonds between the deposit layer and the underlying surface (tube),the jet pressure pushes the deposit against the surface,and therefore the friction force prevents the deposit from sliding against the underlying surface.

3.2.2.Thick deposit

The purpose of this section is to establish a criterion for the failure of a brittle deposit layer that is large enough so that the deposit characteristic lengths,such as its thickness compared to the jet diameter is suf?ciently large,but the jet does not surround the deposit peripheries (see Fig.8a):

h [d j

(12)

As an ideal case,consider a semi-in?nite elastic body,occupying the half space z <0(see Fig.8b).The body is impinged by a gas jet,generating a normal pressure P on its surface (at stagnation condition,P equals the jet PIP).Prior to the employment of criterion (3),the stress distribution on the surface of the body has to be determined.The solution for this problem may be found as a superposition of solutions for a point force applied on a small area,which is a well-established problem (see Appendix ).Analysis of stresses in this case is more complicated than that of a thin deposit,but the result is simple:thick brittle deposit begins to crack if the maximum pressure P at the impact point exceeds a certain value that depends on the deposit tensile strength and the Poisson’s ratio:

P !

2

1à2n

s t

(13)

Note that in a thick deposit,stresses drop quickly away from the point of the jet impact.When the jet pressure exceeds the limit de?ned by Eq.(13),the surface starts to crack only locally near the point of impact.Since the stresses suf?cient for crack propagation do not exist away from the point of impact,the cracks cannot grow in?nitely;this prevents the failure of the body.Instead,the impacted local area is eroded,i.e.small pieces of material are removed from the body,causing growing of a ‘‘pit’’at the point of impact.This was observed in the experiments,when the jet diameter was about 0.4of the deposit diameter or less (see Figs.3and 4).

3.2.3.Cylindrical deposits in cross?ow

When the nozzle exit diameter is large,or when the distance between the nozzle and a cylindrical body such as a deposit formed on a tube surface is large,the jet spreads wide and completely surrounds the body.For this case,the problem can be modeled by considering a solid cylinder immersed into a uniform cross?ow gas

stream (Fig.9).It is dif?cult to obtain an analytical solution for this problem because of (i )the complicated pressure distribution on a cylinder,and (ii )presence of the tube inside the cylindrical layer of brittle deposit.Pressure distribution on a cylinder immersed into cross?ow is affected by several parameters:Reynolds number,Mach number,?ow turbulence,surface roughness,etc.Generally,pressure is greater at the front side and smaller at the rear side of the cylinder;the pressure may have local maxima/minima,depending on the above-mentioned parameters.The steel tube within the deposit layer affects the deposit breakup conditions in a complicated manner,depending on the tube/deposit diameter ratio.All these factors make the analytical approach rather complex and of restricted practical use.Therefore,several cases of cylinder in cross?ow were studied analytically,assuming simpli?ed pressure distributions on the cylinder surface.Fig.10shows the distribution of angular stress generated within a cylindrical deposit,

assuming

a b

Fig.8.(a)Jet impingement on a thick deposit;(b)pressure distribution on the

surface.

a b

Fig.9.(a)A cylindrical deposit formed on a tube in cross?ow,(b)the typical pressure distribution on a cylinder.

Dd

Dt

Jet

00.2

0.4

0.6

0.81

1.2

45

90

135

180

Angle from front point, θ

T a n g e n t i a l s u r f a c e s t r e s s σθ /P o

a

b

Fig.10.Distribution of tangential stress (s q )on a cylinder circumference for different ratios of deposit diameter to tube diameter Dd/Dt.P 0is equivalent to the jet PIP.

A.Kaliazine et al./International Journal of Impact Engineering 37(2010)131–140

136

pressure distribution on the cylinder surface is approximated as follows:

P eq T?

P 0

2

ecos q t1T(14)

where P 0is the maximum pressure occurring at q ?0;therefore,P 0equals the jet PIP.Analysis of this and other similar cases shows that when the deposit layer is not very thin compared to the tube diameter (the case of thin deposit layer was studied in Section 3.2.1),the interaction of the cross?ow with the cylinder leads to the development of compressive stresses within the cylinder,with the maximum value at the front stagnation point (q ?0)close to s q ?àP 0/2(see Fig.10).Note that the developed tensile stress in this case s t is equal to s q ,and one may write s t ?s q ?àP 0/2,or simply às t ?P /2(P 0has been replaced by P ,and P in fact equals the jet PIP).Finally,criterion (3)for the special case of deposit in cross?ow is reduced to the following form:

P >2s t (15)

where P is the peak impact pressure at the front point.A crack forms near the point q ?0and propagates in the axial direction,because of the effective opening stress applied in the angular direction (see Fig.2).Criterion (15)is in fact the experimental correlation we obtained from Fig.5.

4.Discussion

4.1.Experimental observations

The theoretical criteria obtained for the failure of thin and thick brittle deposits,Eqs.(9)and (13),are functions of tensile strength and the Poisson’s ratio of the deposit material.The criterion for the failure of deposits in cross?ow as shown by Eq.(15)is a function of the peak impact pressure only.It has been shown that,for porous materials composed of elongated crystals,like gypsum,with the increase of porosity,the Poisson’s ratio approaches 0.2[10,11].Also,the Poisson’s ratio for hard,non-porous gypsum is 0.33[10].For the conditions of this study,where porous gypsum is used,a value of 0.2is assumed for the Poison’s ratio.

Figs.11–13compare the prediction of the theoretical criteria for the failure of brittle materials with the experimental data.The ordinate shows the measured applied peak impact pressure sensed on the deposits and the abscissa shows the measured or estimated [7]tensile strength of the sample deposits.The theoretical failure criteria are represented by the straight lines.To better observe and comprehend the trends,the data points corresponding to different deposit sizes are demonstrated by different symbols.

Fig.11shows the data points for the thin deposits along with the criteria for the failure of thin deposits when the deposit is perfectly bonded to the tube surface (Eq.(9))and when the bonding between the tube and the deposit is negligible (Eq.(11)).Note that for sample deposits with low tensile strengths,the criteria for the failure of thin deposits (Eqs.(9)and (11))are in good agreement with the experimental data.For stronger deposits,however,the required peak impact pressure for breakup is greater than that predicted by the theory.This may be attributed to the variations in the experimental conditions:stronger deposits could be broken only when placed close to the nozzle,where jet diameter was rather small.In the development of the theoretical criteria for the thin layer geometry (Eq.(9)or (11)),it is implied that the area on

0.20.40.60.8

11.2

P I P , M P a

Sample tensile strength, MPa

Fig.11.Deposit removal data for thin deposits.Eqs.(9)and (11)show the failure criteria for thin deposits assuming perfect bonds between the deposit and the tube and negligible bonding,respectively.Eq.(15)shows the failure criterion for deposits immersed in cross?ow.A thin deposit has a deposit layer thickness much smaller than the tube and the jet diameters (Eq.(4)).The thickness of a thick deposit is substantially greater than the jet diameter (Eq.(12)).An immersed deposit in cross?ow could be thin or thick but is completely surrounded by the jet.

0.20.40.60.8

1.2P I P , M P a

Samples tensile strength, MPa

Fig.12.Deposit removal data for relatively thick deposits.Eq.(13)shows the failure criterion for thick deposits.Eq.(15)shows the failure criterion for deposits immersed in cross?ow.The thickness of a thick deposit is substantially greater than the jet diameter (Eq.(12)).An immersed deposit in cross?ow could be either thin or thick but is completely surrounded by the jet.

0.2

0.40.60.8

1.2P I P , M P a

Samples tensile strength, MPa

Fig.13.Deposit removal data for all sample deposits along with the relevant theo-retical failure criteria.A thin deposit has a thickness much smaller than the tube and the jet diameters (Eq.(4)).The thickness of a thick deposit is substantially greater than the jet diameter (Eq.(12)).An immersed deposit in cross?ow could be thin or thick but is completely surrounded by the jet.

A.Kaliazine et al./International Journal of Impact Engineering 37(2010)131–140137

which the jet pressure is applied has to be large compared to the layer thickness.In Fig.11,deposits that failed only at a distance close to the nozzle exit have experienced a jet with a small diameter acting on a small area of the deposit;therefore,the conditions for the theoretical criteria are shifted from‘‘thin layer’’to concentrated force in‘‘thick layer’’mode.Asymptotic behavior of this case described by Eq.(13),which is the criterion for the failure of thick deposits,is also plotted in Fig.11.In addition,the statistical nature of the breakup of brittle materials along with the experimental uncertainties may be responsible for some of the discrepancies between the experimental data and the theory.

Similarly,Fig.12shows the experimental data and the failure criteria for failure of thick deposits and deposits in cross?ow.The experimental data generally follow the criteria for the failure of deposits in cross?ow,with obvious deviation for stronger deposits. These deviations are similar to the ones observed for thin deposits and may be explained in the same way.

There is a certain difference between the failure of‘‘thin’’and ‘‘thick’’deposits,as seen in Fig.13,which includes all experimental data and the theoretical failure criteria.According to criteria(9)and (11),for Poisson’s ratio of0.2,the minimum pressure required to break the‘‘thin’’deposits is P?1.33s t for deposits bonded to the surface,and P?s t for deposits with loose connection with the surface,which are,respectively,about40%and30%of the pressure required for the failure of the‘‘thick’’deposits.Thick deposits require a minimum failure peak impact pressure of P?3.33s t.The minimum peak impact pressure for the failure of thin deposits for?rmly bonded and loosely bonded deposits are,respectively,0.67%and50% of the pressure required for the breakup of deposits immersed in cross?ow,for which P?2s t.It is evident that all experimental data points are bounded between the lines representative of the criteria for thin and thick deposits.

The theoretical analysis and the failure criteria developed here may be used to interpret the breakup movies shown in Figs.2–4. For deposits placed far from the nozzle exit,the deposit failure mechanism is by axial crack formation where breakup starts with the formation and propagation of cracks in the axial direction (Fig.2).The thin deposit of Fig.2placed far enough from the nozzle exit may be considered as immersed into a cross?ow or traverse air jet.In this case,the effective tensile stress is applied in the angular direction with the maximum value near the front point.For this reason,a crack starts around the front point,i.e.q?0,and develops in the axial direction.

On the other hand,for the deposit of Fig.3,which relative to the deposit of Fig.2is placed closer to the nozzle exit,?rst surface pitting is observed before an axial crack forms.In this case,the jet is focused on a smaller area of the deposit compared to the case illustrated in Fig.2,and the condition for material failure exists only in this area.As the small pits created by the jet grow in size and depth,the jet penetrates deeper inside the sample,?nally being able to blow it from the inside.

For the deposit placed closest to the nozzle exit(Fig.4),the intense surface pitting resulted in deposit fragmentation into small pieces.The deposit was close to the nozzle exit,and the jet impacted only on a relatively small area of the deposit surface.The stresses in this case are distributed isotropically,but drop quickly away from the point of impact.For this reason,the cracks could develop in any direction,but they could not grow in?nitely beyond the point of impact.Instead,small pieces of the material are chipped off,causing the growth of a hole at the jet impact area.

4.2.Practical implications

In the lower superheater region near the screen tubes,the?ue gas temperature is usually high.The deposit surface is?uid and the PIP is dampened as the jet impacts on the tube/deposit surface.This makes it dif?cult for cracks or pits to form in the deposit.As a result, the sootblowing ef?ciency in this region is low.In the upper superheater region and at the generating bank inlet of the recovery boiler,the?ue gas temperature is typically lower than the deposit ?rst melting temperature.The deposit is brittle and the results of this work are applicable to this region.In this region,the deposit may be removed only when it is thin.However,if it is allowed to grow thicker,it may not be removed by a single blow and may need repeated blowing to crack and breakup.The effectiveness of a sootblower jet in removing a deposit depends greatly on the peak impact pressure of the jet,the strength and thickness of the deposit, and the exposure time of the deposit to the jet.Since the jet is constantly moving and rotating,the exposure time is short(typi-cally around100ms,depending on the linear and angular speed of the sootblower).

As it was shown here,the PIP required to break a thick gypsum deposit is2.5times larger than that of a thin deposit.Also,note that due to the formation and propagation of cracks,a large amount of deposit layer is removed,when the deposit is thin.Breakup of thick deposits is more localized and little amount of deposit may be removed in this case.Therefore,the frequency and speed of soot-blowing should be optimized such that the largest amount of thin deposits is removed easily with minimum steam consumption.

5.Conclusions

High-speed imaging was employed to study the breakup of brittle cylindrical deposits impinged by a high velocity air jet. General trends and some details of failure patterns were explained on the basis of stress analysis,adapted for the case of hydraulic loading(loading by means of the jet?ow).Failure criteria suitable for the breakup of thin deposits,thick deposits,and deposits entirely immersed in cross?ow were developed.The predictions of the failure criteria are in a good agreement with the experimental data.The theory explains why thin samples break easier than thick samples of the same strength,and also qualitatively explains observed variations in the patterns of failure for samples of different sizes.

For samples placed far from the nozzle exit the breakup mecha-nism is by the formation of axial cracks.These samples may be considered as immersed into a cross?ow or traverse air jet,where the tensile stress is applied in the angular direction with the maximum value near the front point.As a result,a crack starts around the front point and develops in the axial direction and the deposit is removed quickly.On the other hand,for samples placed close to the nozzle exit,the jet diameter compared to deposit diameter is small and the stresses are concentrated on a small area; therefore,the fracture is rather localized with limited possibility of crack propagation;consequently,failure occurs by erosion or pitting of the material in a longer process compared to axial crack formation.

The application and implications of our results in Kraft recovery boilers were also discussed.It is concluded that the frequency and speed of sootblowing and the steam?ow rate should be optimized such that the largest amount of thin deposits is removed easily with minimum steam consumption.

Acknowledgements

This work was generously funded by the members of the research consortium on‘‘Increasing Energy and Chemical Recovery in the Kraft Pulping Process’’at the Pulp and Paper Centre,University of Toronto.The authors wish to thank Professors Donald E.Cormack and Markus Bussmann of the University of Toronto for their suggestions and Ameya Pophali for his help with the experiments.

A.Kaliazine et al./International Journal of Impact Engineering37(2010)131–140 138

Appendix

Consider a semi-in?nite elastic body occupying the half space z <0(see Fig.14a).The body is impinged by a gas jet,generating normal pressure P ?P (x ,y )on its surface.The stress distribution may be found as a superposition of the solutions for an elementary force,applied at a point,which is a well-established problem [12,13].If a force P is applied to an arbitrary point normal to the surface of a semi-in?nite solid body (see Fig.14a),then the stress components in cylindrical coordinates may be presented as follows:

s r ?P 2p &à1à2n á

1r 2àz r 2

àr 2tz

2áà1=2

à3r 2

z àr 2tz 2

áà5=2'

(A1)

s z ?à

3P 2p

z 3àr 2

tz 2áà5=2(A2)

s q ?P

p

e1à2n T

&

à1r tz r

à

r 2tz 2áà1=2tz àr 2tz 2áà3=2'

(A3)

where r is the radial distance from the z-axis.These equations describe stresses at any point of the body,caused by the action of a normal point force/pressure.The stress generated by the jet pressure is found by integration over the surface,provided the normal pressure distribution P is known.

Assume that the force applied to the surface of the body is not concentrated,but distributed over a portion of the surface of the body,not necessarily uniformly,as in the case of a jet exerting certain normal pressure on the surface at the point of the jet impact.In addition,assume M is an arbitrary point on the surface of the body and x and y are the tangential directions at this point (see Fig.14b).Stress components at point M at z ?0may be found using the principle of superposition as:

s x ?Z Z à

s r es ;q T,cos 2q ts q es ;q T,sin 2q á

s d s d q (A4)s y ?

Z Z

à

s r es ;q T,sin 2q ts q es ;q T,cos 2q á

s d s d q

(A5)

Note that as z /0,the integrand functions in Eqs.(A1)and (A3)become inde?nite.Therefore,we split functions (A1)and (A3)into two parts ‘‘local’’part having z as a multiplier and the rest,which we call ‘‘distributed’’part.Below are the ‘‘local’’stresses:

s loc r ?

P 2p &à1à2n á àz r 2àr 2tz 2áà1=2 à3r 2z àr 2tz 2áà5=2

'(A6)s loc q

?P 2p e1à2n T&

tz r

2àr 2tz 2áà1=2tz àr 2tz 2áà3=2

'(A7)

Careful inspection of Eqs.(A6)and (A7)reveals that at very small

z ,the right-hand side of these equations are very small everywhere except for a small circle (small s )around point M .But within this circle,pressure P is nearly constant and equal to its magnitude at point M .In this case,s r and s q are independent of q and,therefore,Eqs.(A4)and (A5)after taking the integration with respect to q are transformed to the following form:

s x ?s y ?P M p Z

h

àe1à2n T3r 2z às 2tz 2

áà5=2p tz às 2tz

2áà3=2

p i s d s (A8)

Taking the integral of Eq.(A8)with respect to s over a small

circle of radius ‘‘a ’’results in the following equation:

s x ?s y ?P M àe1t2n Tt2e1tn Tz ????????????????a 2tz 2p à z

????????????????

a 2tz 2

p 3!(A9)

Taking the limit of Eq.(A9)as z approaches zero we ?nally arrive

at the following equation:

s x ;loc ?s y ;loc ?à

P M

2

e1t2n T(A10)

The contribution of non-local stress components are as follows:

s 0x

?

às 0y

?1

p

e1à2n TZ Z

à

P ex ;y Ts àcos

2

q àsin 2q ás d s d q (A11)

r

z

P

x

y M

s

θ

A

B

Fig.14.Application of pressure on a thick deposit;(a)force P is applied to an arbitrary point normal to the surface of a semi-in?nite solid body;(b)M is an arbitrary point on the surface of the body and x and y are the tangential directions at this point.

A.Kaliazine et al./International Journal of Impact Engineering 37(2010)131–140139

Non-local stresses depend on overall distribution of the jet pressure over the surface of the body and generally can be evalu-ated only numerically if the pressure distribution P (x ,y )is available.However,the contribution of the second terms is relatively small.In fact,if pressure distribution is symmetrical,as in the case of a round jet,contribution of non-local stresses in the centre point (where pressure P reaches maximum)is exactly zero.To illustrate this,consider the following example.Assume that the normal pressure distribution is given as follows:

P ?P 0exp ààr 2=R 2

á

(A12)

Fig.15provides the numerical solution of the non-dimensional local and non-local components of the tangential stress on the surface as a function of the dimensionless distance r /R from the jet axis.It is observed that the ‘‘non-local’’stresses not only are numerically smaller than the ‘‘local’’stresses,but they also vanish as r /0,where the pressure is at maximum and the failure most probably occurs at this point.In fact,this is true for any axially

symmetric pressure distribution.For this reason,the effect of non-local stresses on failure criterion is neglected.Taking into account only the ‘‘local’’stresses,the failure criterion (3)combined with Eq.(A10)which relates the tensile stress of the material on the surface,to the applied jet pressure and the material’s Poisson ratio,we obtain the following criterion for the failure of thick deposits:

P !

2

1à2n

s t

(A13)

where P M in Eq.(A10)has been replaced by P for simplicity.Eq.(A13)is the same as Eq.(13)introduced earlier in Section 3.2.2.

References

[1]Bowden FP,Brunton JH.The deformation of solids by liquid impact at

supersonic speeds.Proceedings of the Royal Society of London.Series A,Mathematics and Physical Sciences 1961;263(1315):433–50.

[2]Bowden FP,Field JE.The brittle fracture of solids by liquid impact,by solid

impact,and by shock.Proceedings of the Royal Society of London.Series A,Mathematics and Physical Sciences 1964;282(1390):331–52.

[3]Bourne NK,Obara T,Field JE.High speed photography and stress gauge studies

of jet impact upon surfaces.Philosophical Transactions of the Royal Society of London,Series A 1997;355:607–23.

[4]Momber AW.Fluid jet erosion of tension-softening materials.International

Journal of Fracture 2001;112:99–109.

[5]Kaliazine A,Piroozmand F,Cormack DE,Tran HN.Sootblower optimization –

part 2:deposit sootblower interaction.TAPPI Journal 1997;80(11):201–7.

[6]Eslamian M,Pophali A,Bussmann M,Tran HN.Effect of processing conditions

on removal of brittle deposits formed on tube surfaces by a supersonic air jet.International Journal of Impact Engineering 2009;36:199–209.

[7]Eslamian M,Pophali A,Bussmann M,Cormack D,Tran HN.Failure of brittle

cylindrical deposits impacted by a supersonic air jet.ASME Journal of Engi-neering Materials and Technology 2008;130(3):031002.

[8]Broek David.Elementary engineering fracture mechanics.The Netherlands:

Sijthoff and Noordhoff International Publishers B.V.;1978.

[9]Shames IH.Mechanics of deformable solids.In:Prentice-Hall,Inc;1964.

[10]Haussuhl S.Elastische und thermoelastische eingenschaften von CaSO 4$2H 2O

(Gips).Zeitschrift fur Kristallographie 1960;122:311–4.

[11]Meille S,Garboczi EJ.Linear elastic properties of 2-D and 3-D models of porous

materials made from elongated objects.Modelling and Simulation in Materials Science and Engineering 2001;9(5):371–90.

[12]Boussinesq J.Application des Potentiels a l’Etude et du Mouvement des Solids

Elastiques.Paris:Gauthier-Villars;1885.

[13]Timoshenko SP,Goodier JN.Theory of elasticity.In:McGraw-Hill Company;

1970.

0.2

0.4

0.6

0.8

1

1

2

3

4

5

6

Distance from axis, r/R

P r e s s u r e , s t r e s s s /P 0

Fig.15.Distribution of surface stresses for a semi-in?nite body.Applied pressure P ?P 0exp(àr 2/R 2).

A.Kaliazine et al./International Journal of Impact Engineering 37(2010)131–140

140

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M A: Has the case been closed yet? B: No, the magistrate still needs to decide the outcome. magistrate n.地方行政官,地方法官,治安官 A: I am unable to read the small print in the book. B: It seems you need to magnify it. magnify vt.1.放大,扩大;2.夸大,夸张 A: That was a terrible storm. B: Indeed, but it is too early to determine the magnitude of the damage. magnitude n.1.重要性,重大;2.巨大,广大 A: A young fair maiden like you shouldn’t be single. B: That is because I am a young fair independent maiden. maiden n.少女,年轻姑娘,未婚女子 a.首次的,初次的 A: You look majestic sitting on that high chair. B: Yes, I am pretending to be the king! majestic a.雄伟的,壮丽的,庄严的,高贵的 A: Please cook me dinner now. B: Yes, your majesty, I’m at your service. majesty n.1.[M-]陛下(对帝王,王后的尊称);2.雄伟,壮丽,庄严 A: Doctor, I traveled to Africa and I think I caught malaria. B: Did you take any medicine as a precaution? malaria n.疟疾 A: I hate you! B: Why are you so full of malice? malice n.恶意,怨恨 A: I’m afraid that the test results have come back and your lump is malignant. B: That means it’s serious, doesn’t it, doctor? malignant a.1.恶性的,致命的;2.恶意的,恶毒的 A: I’m going shopping in the mall this afternoon, want to join me? B: No, thanks, I have plans already. mall n.(由许多商店组成的)购物中心 A: That child looks very unhealthy. B: Yes, he does not have enough to eat. He is suffering from malnutrition.

base on的例句

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英语造句大全

英语造句大全English sentence 在句子中,更好的记忆单词! 1、(1)、able adj. 能 句子:We are able to live under the sea in the future. (2)、ability n. 能力 句子:Most school care for children of different abilities. (3)、enable v. 使。。。能句子:This pass enables me to travel half-price on trains. 2、(1)、accurate adj. 精确的句子:We must have the accurate calculation. (2)、accurately adv. 精确地 句子:His calculation is accurately. 3、(1)、act v. 扮演 句子:He act the interesting character. (2)、actor n. 演员 句子:He was a famous actor. (3)、actress n. 女演员 句子:She was a famous actress. (4)、active adj. 积极的 句子:He is an active boy. 4、add v. 加 句子:He adds a little sugar in the milk. 5、advantage n. 优势 句子:His advantage is fight. 6、age 年龄n. 句子:His age is 15. 7、amusing 娱人的adj. 句子:This story is amusing. 8、angry 生气的adj. 句子:He is angry. 9、America 美国n.

(完整版)主谓造句

主语+谓语 1. 理解主谓结构 1) The students arrived. The students arrived at the park. 2) They are listening. They are listening to the music. 3) The disaster happened. 2.体会状语的位置 1) Tom always works hard. 2) Sometimes I go to the park at weekends.. 3) The girl cries very often. 4) We seldom come here. The disaster happened to the poor family. 3. 多个状语的排列次序 1) He works. 2) He works hard. 3) He always works hard. 4) He always works hard in the company. 5) He always works hard in the company recently. 6) He always works hard in the company recently because he wants to get promoted. 4. 写作常用不及物动词 1. ache My head aches. I’m aching all over. 2. agree agree with sb. about sth. agree to do sth. 3. apologize to sb. for sth. 4. appear (at the meeting, on the screen) 5. arrive at / in 6. belong to 7. chat with sb. about sth. 8. come (to …) 9. cry 10. dance 11. depend on /upon 12. die 13. fall 14. go to … 15. graduate from 16. … happen 17. laugh 18. listen to... 19. live 20. rise 21. sit 22. smile 23. swim 24. stay (at home / in a hotel) 25. work 26. wait for 汉译英: 1.昨天我去了电影院。 2.我能用英语跟外国人自由交谈。 3.晚上7点我们到达了机场。 4.暑假就要到了。 5.现在很多老人独自居住。 6.老师同意了。 7.刚才发生了一场车祸。 8.课上我们应该认真听讲。9. 我们的态度很重要。 10. 能否成功取决于你的态度。 11. 能取得多大进步取决于你付出多少努力。 12. 这个木桶能盛多少水取决于最短的一块板子的长度。

初中英语造句

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翻译加造句

一、翻译 1. The idea of consciously seeking out a special title was new to me., but not without appeal. 让我自己挑选自己最喜欢的书籍这个有意思的想法真的对我具有吸引力。 2.I was plunged into the aching tragedy of the Holocaust, the extraordinary clash of good, represented by the one decent man, and evil. 我陷入到大屠杀悲剧的痛苦之中,一个体面的人所代表的善与恶的猛烈冲击之中。 3.I was astonished by the the great power a novel could contain. I lacked the vocabulary to translate my feelings into words. 我被这部小说所包含的巨大能量感到震惊。我无法用语言来表达我的感情(心情)。 4,make sth. long to short长话短说 5.I learned that summer that reading was not the innocent(简单的) pastime(消遣) I have assumed it to be., not a breezy, instantly forgettable escape in the hammock(吊床),( though I’ ve enjoyed many of those too ). I discovered that a book, if it arrives at the right moment, in the proper season, will change the course of all that follows. 那年夏天,我懂得了读书不是我认为的简单的娱乐消遣,也不只是躺在吊床上,一阵风吹过就忘记的消遣。我发现如果在适宜的时间、合适的季节读一本书的话,他将能改变一个人以后的人生道路。 二、词组造句 1. on purpose 特意,故意 This is especially true here, and it was ~. (这一点在这里尤其准确,并且他是故意的) 2.think up 虚构,编造,想出 She has thought up a good idea. 她想出了一个好的主意。 His story was thought up. 他的故事是编出来的。 3. in the meantime 与此同时 助记:in advance 事前in the meantime 与此同时in place 适当地... In the meantime, what can you do? 在这期间您能做什么呢? In the meantime, we may not know how it works, but we know that it works. 在此期间,我们不知道它是如何工作的,但我们知道,它的确在发挥作用。 4.as though 好像,仿佛 It sounds as though you enjoyed Great wall. 这听起来好像你喜欢长城。 5. plunge into 使陷入 He plunged the room into darkness by switching off the light. 他把灯一关,房

改写句子练习2标准答案

The effective sentences:(improve the sentences!) 1.She hopes to spend this holiday either in Shanghai or in Suzhou. 2.Showing/to show sincerity and to keep/keeping promises are the basic requirements of a real friend. 3.I want to know the space of this house and when it was built. I want to know how big this house is and when it was built. I want to know the space of this house and the building time of the house. 4.In the past ten years,Mr.Smith has been a waiter,a tour guide,and taught English. In the past ten years,Mr.Smith has been a waiter,a tour guide,and an English teacher. 5.They are sweeping the floor wearing masks. They are sweeping the floor by wearing masks. wearing masks,They are sweeping the floor. 6.the drivers are told to drive carefully on the radio. the drivers are told on the radio to drive carefully 7.I almost spent two hours on this exercises. I spent almost two hours on this exercises. 8.Checking carefully,a serious mistake was found in the design. Checking carefully,I found a serious mistake in the design.

用以下短语造句

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英语造句

English sentence 1、(1)、able adj. 能 句子:We are able to live under the sea in the future. (2)、ability n. 能力 句子:Most school care for children of different abilities. (3)、enable v. 使。。。能 句子:This pass enables me to travel half-price on trains. 2、(1)、accurate adj. 精确的 句子:We must have the accurate calculation. (2)、accurately adv. 精确地 句子:His calculation is accurately. 3、(1)、act v. 扮演 句子:He act the interesting character.(2)、actor n. 演员 句子:He was a famous actor. (3)、actress n. 女演员 句子:She was a famous actress. (4)、active adj. 积极的 句子:He is an active boy. 4、add v. 加 句子:He adds a little sugar in the milk. 5、advantage n. 优势 句子:His advantage is fight. 6、age 年龄n. 句子:His age is 15. 7、amusing 娱人的adj. 句子:This story is amusing. 8、angry 生气的adj. 句子:He is angry. 9、America 美国n. 句子:He is in America. 10、appear 出现v. He appears in this place. 11. artist 艺术家n. He is an artist. 12. attract 吸引 He attracts the dog. 13. Australia 澳大利亚 He is in Australia. 14.base 基地 She is in the base now. 15.basket 篮子 His basket is nice. 16.beautiful 美丽的 She is very beautiful. 17.begin 开始 He begins writing. 18.black 黑色的 He is black. 19.bright 明亮的 His eyes are bright. 20.good 好的 He is good at basketball. 21.British 英国人 He is British. 22.building 建造物 The building is highest in this city 23.busy 忙的 He is busy now. 24.calculate 计算 He calculates this test well. 25.Canada 加拿大 He borns in Canada. 26.care 照顾 He cared she yesterday. 27.certain 无疑的 They are certain to succeed. 28.change 改变 He changes the system. 29.chemical 化学药品

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