The Particle Attrition With A Convergent Divergent Nozzle Essay

The research work discussed in this thesis deals with experimental and numerical surveies affecting the atom abrasion with a convergent-divergent nose in fluidized beds. The integrated-article format was chosen for the thesis.

In this chapter, a brief description of development of oil littorals and fluid coking upgrading procedure in Canada, which is a major motive for present undertaking, is introduced in first subdivision. In following several subdivisions, a brief debut is presented to the fluidized bed reactors and disruptive jet every bit good as basic theory of the atom abrasion and the application of computational fluid kineticss in simulation of multiphase system. Finally, a reappraisal of recent surveies affecting jet-induced atom abrasion at high temperature and an lineation of research nonsubjective follow.

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Oil littorals and the Fluid coking upgrading procedure
The oil littorals in Canada have become a focal point of intense development in recent decennaries. The oil littorals are a extremely dense and syrupy tar-like signifier of crude oil, a mixture of sand, clay, and bitumen. Most of resource is located in northeasterly Alberta, Canada. The Albertan oil littorals modesty is estimated to transcend 1.8 trillion barrels ; about 300 billion barrels can be recovered by current engineerings, ranking Canada 2nd merely to Saudi Arabia in universe ( Government of Alberta, 2009 ) . In 2009, Alberta wholly produced about 1.35 million bbl/d rough bitumen from oil littorals, stand foring about 70 per centum of Alberta ‘s and 49 per centum of Canada ‘s entire petroleum oil and tantamount production. Meanwhile, oil littorals production has become progressively controversial because of several widely broadcasted environmental and wellness issues. For illustration, 100s of ducks were killed on oil littorals chasing pools at Syncrude in Fort McMuarry, Alberta in 2008.

Oil littorals production is different from conventional oil production. For the resources within about 100 metres of the surface, oil littorals are mined and so processed in installations where the bitumen they contain is extracted. For the deeper sedimentations, the most common engineering of in-situ is steam-assisted gravitation drainage ( SAGD ) . In SAGD, two horizontal Wellss are drilled, where hot steam is pumped into the upper one, doing bitumen to flux into the lower well. The bitumen from either excavation or in situ operations contains 50 – 60 wt % vacuity residues. Vacuum residue is the fraction of crude oil that does non purify under vacuity, and typically has a normal boiling point of over 525A°C ( Gray, 1994 ) . So the bitumen can non be processed in refineries, and the upgrading procedure is indispensable for oil littorals production to change over the bitumen from oil littorals to man-made petroleum oil ( SCO ) . On the one manus, to cut down the viscousness to let cargo by grapevine without adding a dissolver ; on the other manus, the bitumen can be processed to give a petroleum oil replacement of high quality. There are two upgrading attacks, fluid coking procedure and hydrotreating procedure.

In the hydrotreating procedure, H is added to the bitumen to bond with the C in the molecule, making more merchandises while besides taking drosss, such as N, sulfur and hint metals from hydrocarbon molecules.

Thermal and coking procedures have been found to be the most prevailing method to accomplish the carbon-carbon bond breakage in bitumen. Thermal transition does non required the extra accelerator ; and have a mild operation conditions with low force per unit area, low temperature, and low costs ( Gray, 2002 ) . There are two chief types of thermal and coking procedures, delayed coking and fluid coking. Delayed coking has a broad application in handling heavy residues, which uses long reaction times in the liquid stage to change over the residue fraction of the provender to gases, distillations, and coke. The hold coking procedure is a semi-batch procedure that gives rise to the extremely aromatic coke merchandise besides tends to retain S, N and metals ( Gray, 1994 ) . The bitumen is heated to about 500oC through a warming spiral and transportation to a coking membranophone where it is maintained until it is converted into the bluess and coke. The operation is uninterrupted until the coking membranophone is well full of coke.

Once the first membranophone is full of coke, the hold coking reaction is switched to another coking membranophone. The fluid coking procedure foremost developed by Exxon Mobile in 1953. It is a uninterrupted fluid engineering that thermally converts heavy oil such as bitumen extracted from oil littorals or FCC undersides to man-made petroleum oil ( SCO ) . Presently, fluid coking is used commercially in refineries for deep transition and as the resource to upgrade oil littorals bitumen. In fluid coking, the bitumen is sprayed into a fluidized bed of hot coke atoms which are maintained at 20-40 psig and 520-530A°C. The provender bluess are cracked while organizing a liquid movie on the coke atoms. The atoms turn by beds until they are removed and new seed coke atoms are added. Due to its uninterrupted fluid bed procedure, flexibleness, high dependability, and big capacity, the fluid coking procedure has been shown to be better to the delayed coking ( Gray, 1994 ) .

Figure 1.1 Flow diagram of the fluid coking procedure ( House, 2007 )

As shown in Figure 1.1 ( House, 2007 ) , unstable coking utilizations two chief vass, a reactor and a burner. The reactors cokers are the primary measure in the upgrading of bitumen to man-made petroleum oil, which can be divided into three subdivisions: scrubber subdivision, reaction subdivision, and stripper subdivision. The coker contains a bed of fluidized coke atoms and steam is introduced at the underside of the reactor country, the stripper, to fluidize the coke bed. Feed is atomized and sprayed into the reactor dense coke bed through a figure of high efficiency liquid-gas noses. It is of import that the provender heavy oil can be rapidly and uniformly distributed over the single atoms of the bed to accomplish a stable and optimized reaction rate. The provender vaporizes in the bed and leaves behind a gluey residue on the coke to organize a new bed of coke. Vapor merchandises leave the reactor, base on balls through a figure of cyclones, and enter the scrubber, while, the cyclones take much of the entrained coke atoms from the bluess prior to come ining the scrubber.

The volume of vapour additions increasingly up through the reactor dense bed due to the formation of cracked vapour merchandises. In the reactor, the coke atoms flow downwards through the dense bed into the stripping subdivision at the underside of vas. The gases and bluess, including fluidizing and depriving steam and bluess and gases formed by coking of the provender, rise upwards to keep a disruptive fluidized status. Depriving steam is besides used to displace the hydrocarbon merchandise bluess contained between the coke atoms. To keep fluidization and consequence the desired denudation, the mean superficial speed of the lifting gases is sooner kept at 0.3-1.0 m/s depending upon the sized of coke doing up the bed ( Pfeiffer et al. , 1959 ) . The coking zone is maintained at the coveted coking temperature by circulation of solids coke through a burner. About 15 % to 25 % of the coke is burned with air to fulfill procedure heat demands. The rate of circulation of solids between the coker and burner is controlled to provide the needed heat for the coking procedure and will depend upon the difference in temperature between the vass.

Syncrude Canada, a taking maker in Canada ‘s oil littorals industries, has a productive capacity equivalent to over 15 per centum of the state ‘s rough oil production. In the first nine months of 2010, Syncrude produced 78 barrels or about 286,000 barrels per twenty-four hours of sweet rough oil ( Canadian oil sands trust, 2011 ) . For about 350 KB/D productive capacity, Syncrude has three of largest Fluid Cokers operating in the universe. In unstable coking operation at Syncrude, the oil littorals bitumen is preheated and entered the fluid coker reactor through provender noses. These spray provender noses use 600 psig steam to atomise the reactor provender and spray the droplets into the reactor dense coke bed. The bitumen feed at about 350oC is thermally cracked utilizing the heat provided by hot coke atoms. In the fluid coking procedure, a stable scope of atom size distribution is really of import parametric quantity for operation control.

If the atom size distribution deviates from the scope, for illustration, excessively many all right atoms less than 50 i?­m or big atom more than 600I?m, the fluidized bed behaviour is fickle or can get down to defluidize. Then coke circulation rate, the flow rate of coke between reactor and burner, is besides difficult to keep. Furthermore, some agglomerates are formed by several coke atoms lodging together. Therefore, coke atom size is controlled by the usage of a series of abrasion noses that use high force per unit area and supersonic superheated steam as shown in Figure 1.2. The abrasion nose is a type of convergent-divergent nose, which can speed up the superheated steam to supersonic velocities which fractures the coke atoms by impact.

Figure 1.2 place of abrasion jet in fluid coking procedure

Motivation for research
The motive for the research comes from the Fluid coking procedure, which is popularly used in upgrading procedure of heavy oil. The fluid coking procedure uses thermic checking reactions to upgrade heavy oils and bitumen from oil littorals. Fluid coking utilizations coke atoms to supply the heat for the endothermal snap reactions that convert the provender into vapour merchandises and coke. To keep a good fluidized bed and a satisfied reaction rate, it is desirable to maintain the coke atom size distribution at a needed scope, since atoms that are excessively big or all right will ensue in slugging or hapless fluidization. In fluid cokers, a series of abrasion noses are used to command coke atom size, with high force per unit area, superheated steam. Due to high force per unit area and superheated temperature, abrasion noses consume a great of steam, accounting for 40 % of the entire steam use in fluid coking reactors. To better the efficiency of the abrasion noses would cut down energy ingestion, addition reactor throughput, and cut down rancid effluent production upon its condensation.

Fundamentalss of atom abrasion
Particle abrasion is an of import issue for a figure of industrial applications such as crystallisation, granulation, crunching and milling, Fluid catalytic snap, and Fluid coking procedures. The breakage of atoms can be required or unwanted dependent upon the applications. For illustration, the grinding or milling procedure is aimed to highest abrasion rate. On the other manus, in most fluidized bed procedures, the breakage occurred with inter-particle hits or particle-wall interactions has a damaging consequence on the operation of fluidized bed reactors because of mulcts. The coevals of mulcts would cut down the efficiency of any reaction happening in the bed reactor and besides increase the natural stuff ingestion due to loss of mulcts. Meanwhile, the mulcts produced in fluidized bed reactors would increase the cost of downstream processing in order to run into environmental ordinances. For case, in unstable coking procedure, a series of abrasion noses are introduced to interrupt atom for maintaining atom size at an ideal scope, where atom breakage is wanted. Whatever the atom abrasion is required or unwanted, a better apprehension of atom breakage is utile for commanding atom breakage during industrial applications as desired.

Particle abrasion in Fluidized bed procedure
Fluidized bed reactors have a widely applications in a figure of industrial countries due to first-class abilities of heat exchange and contacting among multiphase. The vigorous gesture of bed atom consequences to fluidized Attrition going a critical job in the design and operation of the fluidized bed reactors. Forsythe and Hertwig ( 1949 ) foremost developed a research lab accelerated abrasion trial method to find the accelerator abrasion in a fluid-catalytic snap unit. A specific abrasion setup with a high-velocity air jet was designed to prove the abrasion opposition of a land accelerator. The abrasion rate is calculated by gathered mulcts from systems. Vaux and Keairns ( 1980 ) suggested that the mechanisms for atom abrasion in fluidized beds include thermic, chemical, kinetic and inactive mechanical emphasiss. In the instance of bubbling fluidized beds, beginnings of atom abrasion were identified as grid jets abrasion, gas bubbles and cyclones. Zenz and Kelleher ( 1980 ) detailed the most common abrasion could happen in the fluidized beds:

At the grid jets where fluidization gas enters into the fluidized bed

Within the bed where atoms rub against each other as they flow into the lifting bubbles or they move in mass down a standpipe

At the cyclone entrances or in downward coiling way

At the conveying line, such as cubitus or similar directional alteration.

In the fluidized bed burning or hot fluidized bed, the thermic daze and calcination are another chief resource of atom abrasion. Bemrose and Bridgwater ( 1987 ) stated that atom abrasion is affected by a great many variables, largely influenced by atom and fluidized beds belongingss. Gwyn ( 1969 ) reported that both the mean atom size and the spread of the initial atom size distribution affect the abrasion rate. Patel et Al. ( 1986 ) grouped into two chief classs that affect the abrasion procedure in a fluidized bed:

Atom belongingss, such as size, form, surface raggedness, and strength ;

Properties of the environment ; such as the fluidization speed, runing temperature, and force per unit area.

In add-on, material features such as the break strength, and distortion behaviour besides play critical functions in atom breakage. The break strength

Material belongingss
Particle size and population balance
Although it is undoubted that atom size and size population distribution have an intensive influence on atom abrasion, the apprehensions of influence of atom size vary with breakage mechanism. For illustration, Gwyn ( 1969 ) reported that both the mean atom size and the spread of the initial atom size distribution affect the abrasion rate. When Arena et Al. ( 1983 ) studied the coal abrasion in a mixture with sand at high temperature ; they found that a larger size of sand would significantly better the abrasion rate of coal. Ray and Jiang ( 1987a ) believe that all atoms portion the breakage energy proportional to their surface countries. The analysis by Zhang and Kavetsky ( 1993 ) demonstrates that the breakage distribution map correlates to material belongings and atom size, and the breakage rate map besides changes with stuff type and with atom size distribution. Lin ( 2005 ) argued that atom abrasion increased with decreasing mean atom size. They suggested that is because that all right atoms have a larger figure of atoms for the same weight footing with a larger surface country, which increases the chance of hit.

Particle break energy
The atom break energy corresponds to the strain energy stored in the atom up the blink of an eye of failure ( Tavares, 2007 ) . The specific atom break energy can be measured straight with conditions of slow compaction.

The break chance describes the likeliness at which atoms of a given stuff and size show characteristic breakage events as a map of the stressing strength.

Particle strength, hardness, and snap
These belongingss of solids can alter the atom breakage significantly.

Bed belongingss
Solid speed
The speed of solid is an of import factor in bring forthing the mechanical emphasis by inter-particle hit and particle-wall interaction. The kinetic of solid is the most resource to present the atom breakage. More inside informations would be discussed in ulterior subdivisions.

Operation temperature
Thermal daze, atom belongingss, gas belongingss, those facts can act upon the atom abrasion dramatically, would be changed by the temperature. For illustration, atom belongingss such as strength, hardness, and snap may besides be affected by the temperature. For gas belongingss, the effects of the temperature largely concentrate on the denseness and viscousness.

Operation force per unit area
The operation force per unit area of system has a small influence on the atom abrasion. In contrast to operation force per unit area, the force per unit area of abrasion gas plays an of import function in atom abrasion.

Chemical reaction

Chemical reactions of particulate stuff may bring forth emphasis within the atom taking to break.

Jet-induced atom abrasion
Air jet milling, which is a most popular commercial application of jet-induced atom abrasion, uses high speed jets of gas to impact atom for size decrease. In 1882, Goessling foremost invented a modern jet factory to crunch stuffs, with a jet and a grinding chamber. During the procedure of air jet milling, the high force per unit area fluid is converted to either sonic or supersonic jet watercourses as it expands to the lower force per unit area in the factory. Two common types of nose are used in jet milling, disconnected type nose and the convergent-divergent nose ( Albus, 1964 ) . In convergent-divergent nose, a supersonic can be reached due to gas expand to the full in the divergent subdivision. A typical type of jet Millss is fluidized bed opposed jet Millss. In fluidized bed opposed jet Millss, air jets are used to give high-energy impacts between atoms which are in suspension in a fluidized bed ( Chamayou and Dodds, 2007 ) . For these types factory, atoms are fed in the factory by a screw feeder and the mercantile establishment of the factory is attached at the top by agencies of an built-in centrifugal classifier. The velocity of rotary motion of the classifier defines the upper size of the atoms which can go forth the grinding chamber.

Figure 1.3 Fluidized bed opposed jet factory ( Hosokawa Alpine )

There are more concerns about jet-induced abrasion in fluidized beds for design and development of new fluidized bed reactors, because the abrasion rate at grid jets country is significantly higher than that of occurred in cyclone and bubble countries. A figure of surveies have been performed to concentrate on the jet-induced atom abrasion in fluidized bed, utilizing subsonic jets.

De Michele et Al. ( 1976 ) developed the turbulent gushing part and jet theoretical account for axisymmetric jets in beds, which is based on the extension of theory of turbulent, submerged jets to the injection of gas in fluidized beds. Merry suggested a strategy of the atom paths in the locality of the jet, shown in Figure 1, with the bulk of entrainment happening near the nozzle tip in the possible zone part ( Merry, 1971 ) . Bentham et Al. ( 2004 ) further described that the breakage mechanism of subsonic jets involves the entrainment of atoms from the dense stage part into the jet pit country, where atoms are accelerated by the high speed gas and collide with each other every bit good as impact on the dense stage on the top of jet.

A figure of surveies have been carried out on the effects of abrasion gas belongingss on jet-induced abrasion in fluidized beds. In research by Chen et Al. ( 1980 ) , the jet abrasion was assumed as an lone resource of abrasion in fluidized bed. They found that the jet would lose much of its high initial speed as a consequence of enlargement. They farther developed a abrasion theoretical account in which the abrasion rate is relative to shoot energy of abrasion gas and the extra surface country of atom. Werther and Xi ( 1993 ) found that high-velocity gas jets produce high abrasion rates. In add-on, they developed an abrasion theoretical account in which the abrasion rate, defined as the mass of attrited mulcts per unit clip produced by a individual jet, is relative to ( jet gas denseness, opening diameter, and jet issue speed severally ) . Ghadiri et Al. ( 1992, 1994 ) confirmed that the abrasion rate is relative to the opening speed up to the power 5. A sum-up of the correlativities of abrasion rate for subsonic horizontal jets is list in Table 1.1.

Table 1.1 Correlations to foretell atom abrasion rate with subsonic jets

Model equation

Operating conditions


( 1.1 )

= 25-300 m/s, 142-274Aµm

Fe ore, 3940kg/m3 ;

lignite char, 1250 kg/m3

Chen et al. , 1980

( 1.2 )

=25-100 m/s ;

FCC: 106Aµm, 1500 kg/m3 ;

accelerator HA-HPV: 125 Aµm, 650 kg/m3.

Werther and Xi, 1993

( 1.3 )

Ns: 0.6-0.76 for FCC ; 0.44-1.11 for NaCl

m: 3.31 for FCC ; 5.1 for NaCl

=25-125 m/s ;

Federal communications commissions: 425-600 Aµm

NaCl: 90-106 Aµm

Ghadiri et al. , 1994

( 1.4 )

=33-303 m/s,

Silica-Alumina FCC Catalyst

Zenz and Kelleher, 1980

McMillan et Al. ( 2007a ) studied the public presentation of supersonic jets in atom abrasion procedure. They proposed a new standard for qualifying atom abrasion, and defined a grinding efficiency, which was defined as the sum of new surface country created per mass of abrasion gas used. Based on experimental consequences with supersonic jets, an empirical correlativity was developed to foretell the grinding efficiency of solids ( McMillan et al. , 2007a ) :

( 1.5 )

where I± and I? are coefficients that depend on atoms belongingss and nozzle geometry, severally. Harmonizing to another survey of McMillan et Al. ( 2007b ) , the high speed gas jet publishing from an abrasion nose entrains bed atoms and accelerates them to a high velocity ; due to their inactiveness, these atoms slam on slow traveling bed atoms near the jet tip, doing breakage and cut downing the atom size. Typically, convergent-divergent noses are more efficient than regular noses, i.e. they require less steam to accomplish the same abrasion rate ( McMillan et al. , 2007a ) .

Particle breakage manners
The two types of breakage mechanism scratch and atomization have been proposed by Blinicheve et Al. ( 1968 ) . Abrasion indicates that atoms of a much smaller size interrupt off from the original atom. The atomization of atom is a procedure of atom breakage into similarly sizes girl atoms. Ray and Jiang ( 1987 ) argue that the breakage mechanism in a fluidized bed depends upon the atom strength and the breakage force. They farther noted that the breakage manner can alter from scratch to atomization with increasing force.

Pis et Al. ( 1991 ) suggested that the two abrasion manners have different effects on the atom size distribution, as shown in Fig. 1.2. If abrasion is dominated by an scratchy type mechanism, there will be non intermediate size atoms between boy atoms and the mulcts produced, in contrast to atomization mechanism.

Figure 1.4 Attrition manners and the effects on the atom size distribution ( retrieved from Pis et al. , 1991 )

In rule, atomization can be understood as the large-scale break where the clefts are generated due to high degree emphasis, and so develop through the whole volume of the atom. Ghadiri et Al. ( 2002 ) through their probes indicates that indenture break, a critical size of indenture above which break is induced, is given by

( 1.6 )

where I± ‘ is a changeless, E denotes Young ‘s modulus, I“ is the break surface energy and Y is the output emphasis. They farther analyzed the impact harm to big marks by the quasi-static indenture of half-space specimens, and an equation was developed to depict abrasion leaning of particulate solids:

( 1.7 )

Features of abrasion noses in fluidized bed
Convergent-divergent noses
Convergent-divergent noses have been widely applied to assorted fluidized bed procedures, such as the production of pharmaceutical pulverizations, fluid catalytic snap procedure, jet milling, and unstable coking procedure. As a type of abrasion noses used in jet-induced abrasion procedure, the convergent-divergent nose has distinguish physical features of the nose as country ratio ( the ratio of the issue country to the pharynx country ) , and force per unit area ratio ( the ratio of the stagnancy force per unit area to the ambient force per unit area ) . In supersonic noses, the fluid reaches the sonic speed at the pharynx, and supersonic speed is obtained in the divergent subdivision ( Smith, 2005 ) . The cross-sectional country, force per unit area and temperature vary with Mach figure along the converging-diverging flow way harmonizing to ( Liepmann, 1957, and Perry, 2008 ) :

( 1.8 )

( 1.9 )

( 1.10 )

The sonic mass flux through the pharynx is given by:

( 1.11 )

If A is set equal to the nozzle issue country, the issue Mach figure, force per unit area, and temperature may be calculated. The relation between country and any other flow informations can be obtained through the Mach figure, as shown in Fig. 1.5.

Figure 1.5 Convergent-divergent abrasion nose

Figure 1.6Effect of country ratio on the Mach figure and force per unit area ratio in a convergent-divergent nose

Figure 1.7 Operating manners for convergent-divergent nose ( Adapted from Zucker and Biblarz, 2002 )

For a nose with a specific geometry, the operating force per unit area ratio determines the location and strength of the daze. Figure 1.6 list three critical points. The first critical point represents gas flow that is subsonic in both the convergent and divergent subdivisions but is choked with a Mach figure of 1.0 in pharynx. The 3rd critical point represents gas flow with subsonic flow in the convergence subdivision and supersonic flow in the full diverging subdivision. Expansion will be uncomplete if the issue force per unit area exceeds the ambient discharge force per unit area ; in this instance, daze moving ridges will happen downstream of the nose. If the deliberate issue force per unit area is less than the ambient discharge force per unit area, the nose is over expanded and compaction dazes will happen within the spread outing subdivision of the nose. Fig. 1.5 shows the convergent-divergent nozzle abrasion noses used in present research, which was located inside the bed at a 0.2 m tallness above the fluidizing gas sparger.

Jet belongingss
A convergent-divergent nose injected horizontally in a fluidized bed with sonic or supersonic speed can be assumed to act as a submersed jet, similar to a disruptive jet distributing through a liquid medium at remainder. If a nose with a unvarying speed of U0 inject into a big dead mass of the same fluid, the size of boundary of speed shows in Figure 1.7.

Figure 1.8 the speed profile of round turbulent jet ( adapted from Rajaratnam, 1976 )

In a free turbulent jet, the cosmopolitan jet axial speed profile is expressed ( Abramovich, 1963 ) :

( 1.12 )


( 1.13 )

The dimensionless speed profiles at different cross subdivisions of a jet boundary bed B can be represented in the equation:

( 1.14 )

where ub is the interstitial jet speed on the thickness of boundary bed B.

De Michele et Al. ( 1976 ) developed the turbulent gushing part and jet theoretical account for axisymmetric jets in beds, which is based on the extension of theory of turbulent, submerged jets to the injection of gas in fluidized beds. In the initial part of jet, as shown in Figure 1.7, there exists a nucleus part is known as the potency nucleus where possible flow issues and where the turbulency has non been penetrated. Davies ( 1972 ) suggests that the length of possible nucleus is about 6.4 jet diameters, followed by a passage nucleus of about 8 jet diameters. An equation was developed by De Michele et Al. ( 1976 ) to cipher the length of possible nucleus:

( 1.15 )

As for disruptive jets in conventional fluids, jets in fluidized beds have a “ possible ” nucleus within which gas impulse, temperature and composing are the same as at the oral cavity of the opening. Merry suggested a strategy of the atom paths in the locality of the jet, shown in Figure 1.8, with the bulk of entrainment happening near the nozzle tip in the possible zone part [ Merry, 1971 ] .

Figure 1.9 Solid entrainment path in the injection part ( adapted from Merry, 1971 )

Bentham et Al. ( 2004 ) further described that the breakage mechanism of subsonic jets involves the entrainment of atoms from the dense stage part into the jet pit country, and in where, atoms were accelerated by the high speed gas and collide with each other every bit good as impacting on the dense stage on the top of jet. McMillan et Al. ( 2007b ) suggest the high speed gas jet publishing from an abrasion nose entrains bed atoms and accelerates them to a high velocity ; due to their inactiveness, these atoms slam on slow traveling bed atoms near the jet tip, doing breakage and cut downing the atom size. Typically, convergent-divergent noses are more efficient than regular noses, i.e. they require less steam to accomplish the same abrasion rate ( McMillan et al. , 2007a ) .

Jet incursion
The incursion length of abrasion nose is a critical belongings for survey of abrasion mechanism in fluidized bed. Table 1 provides illustrations of published correlativities for jet incursion length. The jet incursion length additions with increasing gas denseness and gas speed. However, all these correlativities were developed from informations obtained with nozzle runing at subsonic speeds. Furthermore, the definitions of incursion length are assorted. Massimilla ( 1985 ) compared all of the bing empirical and semi-empirical correlativities for Lj. The survey found that immense disagreements existed between the predicted values for Lj by each correlativity, and their predicted effects of system variables on Lj.

Table 2 Correlations for jet incursion length



( 1.16 )

Shakhova ( 1968 )

( 1.17 )

Zenz ( 1968 )

( 1.18 )

Merry ( 1971 )

( 1.19 )

Yang and Keairns ( 1978 )

( 1.20 )

Hong ( 1997 )

( 1.21 )

Benjelloun ( 1991 )

( 1.22 )

Yates ( 1991 )

The incursion length of jet depends on the jet impulse dissipation. Yang and Keairns ( 1981 ) provided the undermentioned relation for perpendicular jets to cipher jet impulse dissipation:

( 1.23 )

Sing the influences of the distance from the nose, the gas inject speed, the fluidization speed and nozzle form on the gas speed profile, Xuereb et Al. ( 1991 ) proposed a correlativity for horizontal jets:

( 1.24 )

On the other manus, Yang and Keairns ( 1978 ) foremost suggested that a two-phase Froude figure, defined as ( , could be used to foretell the jet incursion length. Yang ( 1998 ) further proposed that the dependance of jet incursion on the two-phase Froude figure can be derived theoretically from the perkiness theory of Turner ( 1973 ) .

The impulse flux at the jet, M is given by

( 1.25 )

The perkiness flux at the opening, J, can be expressed as:

( 1.26 )

The characteristic length graduated table L, assumed here to be the jet incursion length, is derived by Turner ( 1973 ) for a floaty jet to be:

( 1.27 )

Benjelloun et Al. ( 1991 ) used a new dimensionless to depict the relationship between the jet impulse and the forces of gravitation moving on the jet:

( 1.28 )

Sing that the volume of the jet is relative to Ld02, the relationship between these forces can eventually be written:

( 1.29 )

( 1.30 )

where the Froude figure of the system characteristic biphasic gas-particles.

Sing the term of ( 1-Iµ ) in the correlativity does non better because Iµ different porousnesss beds are really similar. So, they developed a new simple correlativity with Froude figure to foretell the incursion length of a horizontal nose.

( 1.31 )

A figure of techniques have been developed to mensurate jet incursion in fluidized beds. Ocular observation of the jet public presentation in the beds is a most common method to mensurate jet incursion length. Assorted investigation techniques such as the radiation densitometer, Pitot tubing investigation, optical investigation, and electrical capacity investigation are besides employed to mensurate the jet tallness ( Raghunathan et al. , 1988 ) . Vaccaro et Al. ( 1997 ) analyzed and classified the assorted techniques into two chief groups: the first group ( ocular observations of the phenomenon, photographic or high-velocity movie analysis, optical investigations, electrical capacity investigations, and X-ray image analysis ) , and the 2nd group ( Pitot tubing investigations and I?-ray emanation by radioactive isotope ) .

Vaccaro et Al. ( 1997 ) developed a fresh measurement technique based on the comparing of the fluctuations of the inactive force per unit area at the bed side wall and on the jet axis. In the survey by Hong et Al. ( 1997 ) , a high-velocity picture was used for measuring of incursion length. Zhu et Al. ( 2000 ) foremost use a thermocouple to mensurate jet incursion length in survey of liquid jets in gas-solid system. This technique was adapted and developed to qualify liquid-gas jet in a fluidized bed ( Ariyapadi et. , 2005 ; McMillan et al. , 2005 ) . Dawe et Al. ( 2008 ) developed a triboelectric technique to mensurate gas jet boundaries in fluidized beds. In their work, the incursion length and enlargement angle of jets have been successfully measured by triboelectric technique. Once a atom comes into contact with a metal surface, clash occurs, and charges are exchanged between the metal surface and the atom. The triboelectric consequence refers to this charge transportation, and if the metal surface is grounded, a triboelectric current arises.

Solid entrainment
The jet speed is much higher than the superficial gas speed. Previous surveies have found that the transverse gas and solids speed profiles in horizontal jets in fluidized beds are of the Schlichting or Tollmien type, as for homogenous jets ( Shakhova, 1968 ; Donadono et al. , 1980 ; Filla et al. , 1983 ; De Michele et al. , 1976 ) . Hence, the theory of turbulent gas jets developed by Abramovich ( 1963 ) can be applied to solids entrainment with supersonic jets. Shakhova ( 1968 ) suggested that a pure gas zone and a gas-solid zone are exited in a turbulent jet in a fluidized. The boundaries of zones are determined by the gas speed and voidage of dense bed country.

The solids entrainment shows upper limit at the possible nucleus of the jet, finally diminishing as the distance from the nose additions ( Felli, 2002 ; Xuereb et al. , 1991 ) . De Michele et Al. ( 1976 ) developed a modified theoretical account of the submersed turbulent theory to construe mass transportation associated with gas injection, horizontal injection and big temperature differences between the bed and injected gases of assorted thermic belongingss. Yang and Keriarns ( 1982 ) proposed a mathematical theoretical account for solid entrainment into a flame-like jet in a fluidized bed. With their probe of solid entrainment into jet, the speed of solid entrainment into jet was found to increase with additions in distance from the jet nose, to increase with additions in jet speed and to diminish with additions in solid burden in the gas-solid, two-phase jet. The solid entrainment rate into a jet in a fluidized bed can be calculated by Yang-Keairns Model, as expressed below:

( 1.32 )

where Lj is the jet incursion length, voidage outside of jeti??and C1 and C2 are two empirical invariables.

Xuareb et Al. ( 1992 ) proposed a theoretical account to foretell the solids entrainment and suggested the most of solid entrainment occurred near the tip of the nose. They besides found that increasing gas flowrate through jet leads to a important addition in particle speed on the jet axis.

( 1.33 )

In old surveies by Briens et Al. ( 2008 ) and Hulet et Al. ( 2008a ) , a particular technique was employed to mensurate the solids entrainment into submerged gas and gas-liquid jets.

Literatures study
Many surveies have been conducted on atom abrasion in fluidized beds. The mechanisms proposed for atom abrasion in fluidized beds include thermic, chemical, kinetic and inactive mechanical emphasiss ( Vaux and Keairns, 1980 ) . In the instance of bubbling fluidized beds, beginnings of atom abrasion were identified as grid jets abrasion, gas bubbles and cyclones. Bemrose and Bridgwater ( 1987 ) stated that atom abrasion is affected by a great many variables, largely influenced by atom and fluidized beds belongingss. Earlier surveies have revealed that the operating temperature has a important influence on the atom abrasion in fluidized beds, because it affects material strength, Young ‘ modulus of the solid, and thermic diffusivity of the gas with temperature.

Arena et Al. ( 1983 ) suggested that bed temperature affects straight the mechanism of coevals of C mulcts. With the survey of the consequence of thermal daze, Vaux and Keairns ( 1980 ) suggested that the atom abrasion rate increased with increasing temperature difference between the atoms and the surrounding gas. Lin and Wei ( 2005 ) reported that the abrasion rate additions with increasing temperature, decreases with atom size, and increase with fluidization speed. Chirone et Al. ( 1985 ) and Lee et Al. ( 2002 ) claimed that a higher temperature causes a higher interior force per unit area and a higher thermic emphasis, ensuing in enhanced atom atomization. So far, most of these surveies on jet abrasion in fluidized beds have used subsonic noses or have been conducted at ambient temperature.

Research aims
The chief aim of the present research is to analyze the mechanism of atom abrasion, better atom crunching efficiency, and eventually cut down the steam ingestion in the abrasion procedure, with supersonic noses in fluidized beds at high temperature.

Study of solids entrainment into abrasion jets in fluidized beds
Supersonic noses are applied to assorted fluidized bed procedures, such as the production of pharmaceutical pulverizations, fluid catalytic snap, and fluid coking. In applications such as jet milling, it is indispensable to entrain a maximal flow-rate of solids from the fluidized bed into the jet pit. Surveies of solid entrainment rate into gas jets have been largely conducted with subsonic jets and none with convergent-divergent noses. The intent of this research is to analyze solids entrainment into jets publishing from supersonic convergent-divergent noses, and peculiarly the effects of nozzle size, nozzle mass flow-rate, injection gas belongingss and fluidization speed. A fresh accurate technique is developed to mensurate solids entrainment into jets.

Penetration of high speed horizontal gas jets into a fluidized bed at high temperature
High speed horizontal gas jets are applied to assorted industrial procedures. In this work, a new thermal technique has been developed to mensurate the incursion length of horizontal gas jets. Experiments were conducted in a fluidized bed with a tallness of 1.23m and a rectangular cross subdivision of 0.10m A- 0.50m. The fluidized bed atoms, which were either crude oil coke or sand, were heated by an in-bed electrical warmer to temperatures between 300A°C and 500A°C. Cold gases, such as He, N, C dioxide, were injected into the hot fluidized bed via a horizontal nose operating over a scope of speeds. Based on the experimental consequences, a new empirical correlativity was developed to foretell the incursion length of jets publishing from the horizontal sonic nose at high temperature.

Particle abrasion with supersonic noses in a fluidized bed at high temperature
Fluidized beds are used for a assortment of procedures such as nutrient, pharmaceutical, petrochemical and energy production. The fluid coking procedure, a typical application of fluidized beds, uses thermic checking reactions to upgrade heavy oils and bitumen from oil littorals. Supersonic noses shooting steam are used in the fluid coking procedure to command coke atom size, which is indispensable to keep a well-fluidized bed and a satisfactory reaction rate. Keeping a high abrasion rate with a lower steam flowrate would cut down energy ingestion, addition reactor throughput, and cut down rancid effluent production. The aim of the present research is, hence, to analyze atom abrasion with supersonic convergent-divergent noses in a fluidized bed at high temperatures, under status such as these encountered in the fluid coking procedure. Harmonizing to the experimental consequences, the grinding efficiency is significantly affected by fluidized bed temperature, abrasion gas belongingss, and nozzle size. The experimental information further suggest that, with supersonic noses at high temperature, atom atomization is the dominant abrasion procedure.

Modeling of horizontal jet incursion in fluidized beds at high temperature
Numeric simulation of atom abrasion with a convergent divergent nose in fluidized beds at high temperature
Attrition procedure is a critical measure in fluid coking procedure to command atom size distribution in system. Cherished survey has shown some chief belongingss of atoms and environment affect the jet-induced atom breakage in a fluidized bed. Because the multiphase interaction and the complex flow behaviour in bed and jet system, it is desirable to develop a numerical theoretical account uniting theoretical and experimental techniques for abrasion procedure.

Therefore, a jet-induced abrasion theoretical account in fluidized beds at high temperature has been proposed and developed. The theoretical account is coupled Eulerian-Eulerian multiphase theoretical account with population balance method. Furthermore, particle-particle interactions are described with the kinetic theory of farinaceous flow. The theoretical account is solved utilizing the distinct method and the quadrature method of minutes. The critical adjustable parametric quantities of theoretical account were determined by the experimental information. It is found that the best anticipation was obtained utilizing Ghadiri breakage meat, Diemer-Austin generalized girl size distribution map, and distinct solution method.


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