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Fine dust collection in a rotary flow cyclone
Chdcd
finginceting Slime,
d
1976, Vol. 31, pp. 4%503.
Pergamon Press.
Printed in Great Britain
INE DUST COLLECTION IN A ROTARY FLOW CYCLONE DAVID>
CILIBERTI andBRIAN__ LANCASTER ResearchLaboratories,Pittsburgh,PA 15235,U.S.A.
Chemical &ineering, -house
(Received 25 June 1975;accepted 15September 1975)
Abstract-When collectingfine limestonedust, a rotary flowcycloneperformsconsiderablybelow manufacturer’s expectations. The performance is only slightly worse than predicted from fluid/particle mechanics, up to a particle size of 4 p. Beyond this, complete collection is predicted, but only 90% collection is achieved. INTRODUCTION
Coal gasification combined cycle power plants currently under development require high efficiency dust collectors to protect gas turbine components against erosion [11.The collectors must operate routinely at high temperature and pressure with high reliability. As a consequence, mechanical simplicity is desirable. Rotary flow dust collectors have shown the potential for meeting these requirements[2]. The work described in this paper was carried out to establish the efficiency of rotary flow collectors and develop a model for predicting performance in power plant application. DETERMINATION OF FLOW FIELD
A commercially available rotary flow cyclone rated at 50 cfm was used throughout these investigations [3]. The cyclone consisted of a cylindrical body 4 in. dia. into which two separate gas steams were introduced. A primary flow of 50 cfm entered through a central set of turning vanes, 2 in. dia., located in the base of the unit, while a secondary flow of 30 cfm was introduced through eight tangential jets in the upper section of the cyclone. The cyclone body was 13.5 in. long, inlet to outlet. This unit had a particularly complex flow pattern due to the secondary flow, introduced at eight discreet points. Because of this complexity, it was decided to use experimental velocity data to establish the flow field rather than rely on a simplified model. The velocity data were obtained using a wedge probe which measured the magnitude and direction of flow at points along a traverse. From these data, the axial and tangential components of flow as functions of radial position were obtained at eight positions along the axis of the cyclone. Typical axial and tangential velocity profiles are shown in Fig. 1. The radial component of flow was more diicult to obtain as it was not measured directly but was calculated via the continuity equation. The equation of continuity in cylindrical coordinates is:
For steady, axially symetric flow this reduces to
which can be integrated with respect to r to yield U, assuming constant density.
It is convenient at this point to relate U, to the stream function i&(r,z), since stream function data is of interest by itself. This is accomplished by noting that the stream function is defined by $(r, z) = I,’ 27MU5, z) dE The radial component of gas velocity is then related to $(r, z) by the equation U(r, z) =
($)(+p).
The calculations were carried out by numerically integrating the defining equation for $ at each of the axial traverse positions to yield a table of $(a 4). i = 1,lO; j = 1,8. This table of data was then numerically differentiated, and values of the derivatives at intermediate points were obtained using 4 X8 point double interpolation. Equations
of particle
motion
Formulation of the equations of motion for aerosol particles is relatively straightforward, and in vector form is:
dv cD(R;)App~ Iv - ul(v -u) mai=
+ Fe.,.
For spherical particles with negligible external forces, this equation reduces to:
$=- (~)(~)(~)(CD(Re))Iv-ul(v-u). Transforming this to dimensionless form and writing the vector equation out in components, one obtains
499
500
D. F.
CILIEIERTI and
B. W. LANCASTER
loo r -
A
sO60 -
Radial Position (Inches f,rom Center) Q
Radial Position (Inches from Center)
Fig. 1. Measuredvelocityprofilesin cyclone.(A)axialvelocity;(B)tangentialvelocity.1,34 in. above inlet; 2,8+ in. above inlet; 3,134 in. aboveinlet.
=-
(~)(~)(~)(C~(Re))[(~E)’
t (r*g-uq+ (& uq]“* X
[i,(g-
+i,(g-
rr:>+&(r*g-
U$)
U!)].
Equating vector components gives rise to a set of three nonlinear, coupled, second order differential equations for the particle motion. It is not possible to find analytical solutions to these equations without making the assumptions that the Reynolds number is in the region where Stokes Law holds, and that an analytical expression for
the gas flow exists that is simple enough to allow a solution to be found. The equations are amenable to numerical solution without simplification, with gas velocities known only in tabular form, and using empirical correlations for C, as a function of Reynolds number. Several techniques are available, and the one chosen for this case is a fourth order Runge-Kutta, Gill modtied method. While it is not the most efficient method, it does have the advantages of being self starting and is easy to program. Solution results To establish particle trajectories through the cyclone the equations were integrated subject to the initial conditions that the particle had the same axial and tangential velocity as the gas at the starting point, and a zero initial radial velocity. The initial conditions were:
Fine dust collectionin a rotaryflowcyclone r*(o) =
rf
VT(O)= 0 e*(o) = 0 V%(O)= U%(r$,oyrt z*(o)=0 Vi(O) = Ui(rZ, 0). This scheme worked very well for points up to about 3/4 of distance to the wall but, at points closer to the secondary flow inlet jets, the numerically obtained values of radial gas velocity were not accurate. This posed a problem for calculating complete trajectories of captured particles, although it was not a problem in determining if a particle would be caught. This is due to the fact that the radius of the outlet of the cylone was one half that of cyclone body so that particles only have to reach a radius of R/2 or greater at the cyclone exit to be caught. This was well within the region of accurate data. It was found that negative radial gas velocities existed in the unit and these inward radial flows could indeed overcome the centrifugal forces on small particles and drag them toward the axis. The resulting negative radial particle velocities were small, however, and the distances traveled inward toward the axis were never greater than O*l& so that a suitable criterion for particle capture was; if the particle reached a radius greater than 0.6R0, it would be caught. Thus, the determination of capture could be accomplished before the particle reached the outer radial positions where the data were not reliable. To determine whether a particle will be captured as it passes through the cyclone, it is necessary to know at what point the particle enters the cyclone. For example, a particle which enters near the cyclone axis must move further radially to be captured than one which enters close to inlet wall. For any given particle size, there is an inlet radius such that all particles which enter inside the radius will pass through the cyclone uncollected, while all those which enter at a greater radial position will be captured. Consequently, for a uniform distribution of particles at the inlet, the collection efficiency for a given particle size is: Q,~ = ~r(Dt - (2r,)*)/4A (Fig. 2).
Turning and Hub
r Chosen Such that tte FIw Thmqh Al is XI of the Tdal Flaw
Annular Area Between Tumi Vane Hub and Inlet Wall
Fig. 2. Diagram of scheme used to determine grade efficiency CUNC.
-0
1
2 Particle
By defining r, to give the desired value of Q,,, and then using the computer program to do a binary search to determine the corresponding value of D,,, collection efficiency, particle size data has been assembled and grade efficiency curves constructed. The calculated grade efficiency curve for the cyclone operating at the test conditions (50 cfm primary, 30 cfm secondary) on a limestone dust is shown in Fig. 3. The curve implies zero collection efficiency at a particle size of approximately 1.7 CL.For particles smaller than this, the centrifugal forces are insufficient to overcome the drag force imposed on the particle by the radial flow of gas which is directed towards the cyclone axis. Consequently, the particle is unable to escape from the cyclone core and is conveyed from the unit with the exhaust gas. CES Vol. 31, No. b.4
3
4
5
6
DP (II) Size
(Microns1
Fig. 3. Experimentaland predicted grade efficiency curves for rotary flow cyclone. 1, manufacturers curve; 2, predicted curve; 3, experimental curve. + , this study; 0, form Dunson [5]. EXPERIMENTAL DATA
The performance of the rotary flow cyclone was determined using a test dust of - 6 p ground limestone dispersed in air. Dust was dispersed by a moditied “Harvard” dry dust disperser [6] which gave a controlled dust loading of approximately 0.5 gift’. Dust samples were taken isokinetically at sampling points located at least 20 pipe diameters from the nearest upstream flow disturbance (Fig. 4). Overall efficiencies were determined gravimetrically using conventional thimble sampling techniques. Particle size distributions were measured
502
D. F.
CIL~BERTIand
B. W.
LANCASTER Exhaust
,ff
4
Dust
1
‘--ondary
Line
Dust DispensingMetering Unit
qrKxrPressure
Injector Air
Fig. 4. Schematic of experimental equipment.
99.
,
,
,
,
I
I
,
,
i
TJ -
0 0
I
1
‘I’(”
I
,
,I1111
Sedimentation Cascade Impador
w-
mY
10 rd
52
0.2
1 0 I #81,l a5
1.0 2.0 Particle Size (micron)
5.0
10.0
Our predicted grade efficiency curve shows the same form as the curve produced experimentally, but anticipates a better performance than was attained with the limestone test dust. The two curves correspond reasonably well up to a three micron particle size. Beyond 3.75 CL, the prediction is for complete collection, whereas only 90-95% collection was attained experimentally. This has serious implications for turbine applications, where essentially complete removal of larger particles is required. The experimental results correspond closely to those developed by Dunson[S] using a talc test dust in a nominal 2OOcfm test unit. This tends to contirm the manufacturer’s claim that unit performance is not a function of unit size. Our experimental results have consistently shown collection efficiencies of around 30% at O-25CL(Fig. 3). We have no satisfactory explanation for this.
Fig. 5. Particle size distribution of inlet dust.
before and after the cyclone with Sierra cascade impactors[4]. The size of dust particles collected on the cascade impactor stages were checked using a scanning electron microscope and shown to correspond to the ranges expected from the impactor calibration. Particle size distributions (Fig. 5) indicated virtually complete dispersion of the test dust, and it was assumed that no agglomeration occurred within the inlet duct. Grade efficiency curves constructed from this data are shown in Fig. 3 for the cyclone operating with a 5Ocfm primary flow and a 30cfm secondary flow.
DISCUSSION
A comparison of the manufacturer’s grade efficiency curve with those obtained in this study, and with independent results obtained by Dunson[S], is given in Fig. 3. This shows a large discrepancy between the claimed and measured performance, especially in the l-4 CLrange.
NOTATION
A
cyclone inlet area
AD projected area of particle CO drag coefficient, a function of Reynolds number
4
particle diameter cyclone inlet diameter FCX, external force vector particle mass cyclone radius : 6 critical radius at inlet for particle capture radius r: rlR, Re Reynolds number Dp . pg.Iv - 111/p t time t* (U:/%)f u gas velocity u; axial gas velocity at t = 0 U* VI u,” II gas velocity vector
4
V
particle velocity vector
Fine dust collection in a rotary flow cyclone
z z* pp pP p 19 O*
I)
axial distance z/R gas density particle density gas viscosity angle
e stream function
503 REFERENCES
[l] ArcherD. H. and LemezisS., WestinghouseEngineer 197333 119. [2] Klein Heimich., Staub 1%3 23 501. [3] Aerodyne Development Co., Cleveland, Ohio. [4] Sierra Instrument Co., Minneapolis, Minn. [51 Dunson, Jr. J. B., Paper SE, AIChE 63rd Annqal Meeting, Chicago, Ill., Nov. 1970. [6] Ciliberti D. F. and Lancaster B. W., Reu. Sci. Inst.197546 929.
finginceting Slime,
d
1976, Vol. 31, pp. 4%503.
Pergamon Press.
Printed in Great Britain
INE DUST COLLECTION IN A ROTARY FLOW CYCLONE DAVID>
CILIBERTI andBRIAN__ LANCASTER ResearchLaboratories,Pittsburgh,PA 15235,U.S.A.
Chemical &ineering, -house
(Received 25 June 1975;accepted 15September 1975)
Abstract-When collectingfine limestonedust, a rotary flowcycloneperformsconsiderablybelow manufacturer’s expectations. The performance is only slightly worse than predicted from fluid/particle mechanics, up to a particle size of 4 p. Beyond this, complete collection is predicted, but only 90% collection is achieved. INTRODUCTION
Coal gasification combined cycle power plants currently under development require high efficiency dust collectors to protect gas turbine components against erosion [11.The collectors must operate routinely at high temperature and pressure with high reliability. As a consequence, mechanical simplicity is desirable. Rotary flow dust collectors have shown the potential for meeting these requirements[2]. The work described in this paper was carried out to establish the efficiency of rotary flow collectors and develop a model for predicting performance in power plant application. DETERMINATION OF FLOW FIELD
A commercially available rotary flow cyclone rated at 50 cfm was used throughout these investigations [3]. The cyclone consisted of a cylindrical body 4 in. dia. into which two separate gas steams were introduced. A primary flow of 50 cfm entered through a central set of turning vanes, 2 in. dia., located in the base of the unit, while a secondary flow of 30 cfm was introduced through eight tangential jets in the upper section of the cyclone. The cyclone body was 13.5 in. long, inlet to outlet. This unit had a particularly complex flow pattern due to the secondary flow, introduced at eight discreet points. Because of this complexity, it was decided to use experimental velocity data to establish the flow field rather than rely on a simplified model. The velocity data were obtained using a wedge probe which measured the magnitude and direction of flow at points along a traverse. From these data, the axial and tangential components of flow as functions of radial position were obtained at eight positions along the axis of the cyclone. Typical axial and tangential velocity profiles are shown in Fig. 1. The radial component of flow was more diicult to obtain as it was not measured directly but was calculated via the continuity equation. The equation of continuity in cylindrical coordinates is:
For steady, axially symetric flow this reduces to
which can be integrated with respect to r to yield U, assuming constant density.
It is convenient at this point to relate U, to the stream function i&(r,z), since stream function data is of interest by itself. This is accomplished by noting that the stream function is defined by $(r, z) = I,’ 27MU5, z) dE The radial component of gas velocity is then related to $(r, z) by the equation U(r, z) =
($)(+p).
The calculations were carried out by numerically integrating the defining equation for $ at each of the axial traverse positions to yield a table of $(a 4). i = 1,lO; j = 1,8. This table of data was then numerically differentiated, and values of the derivatives at intermediate points were obtained using 4 X8 point double interpolation. Equations
of particle
motion
Formulation of the equations of motion for aerosol particles is relatively straightforward, and in vector form is:
dv cD(R;)App~ Iv - ul(v -u) mai=
+ Fe.,.
For spherical particles with negligible external forces, this equation reduces to:
$=- (~)(~)(~)(CD(Re))Iv-ul(v-u). Transforming this to dimensionless form and writing the vector equation out in components, one obtains
499
500
D. F.
CILIEIERTI and
B. W. LANCASTER
loo r -
A
sO60 -
Radial Position (Inches f,rom Center) Q
Radial Position (Inches from Center)
Fig. 1. Measuredvelocityprofilesin cyclone.(A)axialvelocity;(B)tangentialvelocity.1,34 in. above inlet; 2,8+ in. above inlet; 3,134 in. aboveinlet.
=-
(~)(~)(~)(C~(Re))[(~E)’
t (r*g-uq+ (& uq]“* X
[i,(g-
+i,(g-
rr:>+&(r*g-
U$)
U!)].
Equating vector components gives rise to a set of three nonlinear, coupled, second order differential equations for the particle motion. It is not possible to find analytical solutions to these equations without making the assumptions that the Reynolds number is in the region where Stokes Law holds, and that an analytical expression for
the gas flow exists that is simple enough to allow a solution to be found. The equations are amenable to numerical solution without simplification, with gas velocities known only in tabular form, and using empirical correlations for C, as a function of Reynolds number. Several techniques are available, and the one chosen for this case is a fourth order Runge-Kutta, Gill modtied method. While it is not the most efficient method, it does have the advantages of being self starting and is easy to program. Solution results To establish particle trajectories through the cyclone the equations were integrated subject to the initial conditions that the particle had the same axial and tangential velocity as the gas at the starting point, and a zero initial radial velocity. The initial conditions were:
Fine dust collectionin a rotaryflowcyclone r*(o) =
rf
VT(O)= 0 e*(o) = 0 V%(O)= U%(r$,oyrt z*(o)=0 Vi(O) = Ui(rZ, 0). This scheme worked very well for points up to about 3/4 of distance to the wall but, at points closer to the secondary flow inlet jets, the numerically obtained values of radial gas velocity were not accurate. This posed a problem for calculating complete trajectories of captured particles, although it was not a problem in determining if a particle would be caught. This is due to the fact that the radius of the outlet of the cylone was one half that of cyclone body so that particles only have to reach a radius of R/2 or greater at the cyclone exit to be caught. This was well within the region of accurate data. It was found that negative radial gas velocities existed in the unit and these inward radial flows could indeed overcome the centrifugal forces on small particles and drag them toward the axis. The resulting negative radial particle velocities were small, however, and the distances traveled inward toward the axis were never greater than O*l& so that a suitable criterion for particle capture was; if the particle reached a radius greater than 0.6R0, it would be caught. Thus, the determination of capture could be accomplished before the particle reached the outer radial positions where the data were not reliable. To determine whether a particle will be captured as it passes through the cyclone, it is necessary to know at what point the particle enters the cyclone. For example, a particle which enters near the cyclone axis must move further radially to be captured than one which enters close to inlet wall. For any given particle size, there is an inlet radius such that all particles which enter inside the radius will pass through the cyclone uncollected, while all those which enter at a greater radial position will be captured. Consequently, for a uniform distribution of particles at the inlet, the collection efficiency for a given particle size is: Q,~ = ~r(Dt - (2r,)*)/4A (Fig. 2).
Turning and Hub
r Chosen Such that tte FIw Thmqh Al is XI of the Tdal Flaw
Annular Area Between Tumi Vane Hub and Inlet Wall
Fig. 2. Diagram of scheme used to determine grade efficiency CUNC.
-0
1
2 Particle
By defining r, to give the desired value of Q,,, and then using the computer program to do a binary search to determine the corresponding value of D,,, collection efficiency, particle size data has been assembled and grade efficiency curves constructed. The calculated grade efficiency curve for the cyclone operating at the test conditions (50 cfm primary, 30 cfm secondary) on a limestone dust is shown in Fig. 3. The curve implies zero collection efficiency at a particle size of approximately 1.7 CL.For particles smaller than this, the centrifugal forces are insufficient to overcome the drag force imposed on the particle by the radial flow of gas which is directed towards the cyclone axis. Consequently, the particle is unable to escape from the cyclone core and is conveyed from the unit with the exhaust gas. CES Vol. 31, No. b.4
3
4
5
6
DP (II) Size
(Microns1
Fig. 3. Experimentaland predicted grade efficiency curves for rotary flow cyclone. 1, manufacturers curve; 2, predicted curve; 3, experimental curve. + , this study; 0, form Dunson [5]. EXPERIMENTAL DATA
The performance of the rotary flow cyclone was determined using a test dust of - 6 p ground limestone dispersed in air. Dust was dispersed by a moditied “Harvard” dry dust disperser [6] which gave a controlled dust loading of approximately 0.5 gift’. Dust samples were taken isokinetically at sampling points located at least 20 pipe diameters from the nearest upstream flow disturbance (Fig. 4). Overall efficiencies were determined gravimetrically using conventional thimble sampling techniques. Particle size distributions were measured
502
D. F.
CIL~BERTIand
B. W.
LANCASTER Exhaust
,ff
4
Dust
1
‘--ondary
Line
Dust DispensingMetering Unit
qrKxrPressure
Injector Air
Fig. 4. Schematic of experimental equipment.
99.
,
,
,
,
I
I
,
,
i
TJ -
0 0
I
1
‘I’(”
I
,
,I1111
Sedimentation Cascade Impador
w-
mY
10 rd
52
0.2
1 0 I #81,l a5
1.0 2.0 Particle Size (micron)
5.0
10.0
Our predicted grade efficiency curve shows the same form as the curve produced experimentally, but anticipates a better performance than was attained with the limestone test dust. The two curves correspond reasonably well up to a three micron particle size. Beyond 3.75 CL, the prediction is for complete collection, whereas only 90-95% collection was attained experimentally. This has serious implications for turbine applications, where essentially complete removal of larger particles is required. The experimental results correspond closely to those developed by Dunson[S] using a talc test dust in a nominal 2OOcfm test unit. This tends to contirm the manufacturer’s claim that unit performance is not a function of unit size. Our experimental results have consistently shown collection efficiencies of around 30% at O-25CL(Fig. 3). We have no satisfactory explanation for this.
Fig. 5. Particle size distribution of inlet dust.
before and after the cyclone with Sierra cascade impactors[4]. The size of dust particles collected on the cascade impactor stages were checked using a scanning electron microscope and shown to correspond to the ranges expected from the impactor calibration. Particle size distributions (Fig. 5) indicated virtually complete dispersion of the test dust, and it was assumed that no agglomeration occurred within the inlet duct. Grade efficiency curves constructed from this data are shown in Fig. 3 for the cyclone operating with a 5Ocfm primary flow and a 30cfm secondary flow.
DISCUSSION
A comparison of the manufacturer’s grade efficiency curve with those obtained in this study, and with independent results obtained by Dunson[S], is given in Fig. 3. This shows a large discrepancy between the claimed and measured performance, especially in the l-4 CLrange.
NOTATION
A
cyclone inlet area
AD projected area of particle CO drag coefficient, a function of Reynolds number
4
particle diameter cyclone inlet diameter FCX, external force vector particle mass cyclone radius : 6 critical radius at inlet for particle capture radius r: rlR, Re Reynolds number Dp . pg.Iv - 111/p t time t* (U:/%)f u gas velocity u; axial gas velocity at t = 0 U* VI u,” II gas velocity vector
4
V
particle velocity vector
Fine dust collection in a rotary flow cyclone
z z* pp pP p 19 O*
I)
axial distance z/R gas density particle density gas viscosity angle
e stream function
503 REFERENCES
[l] ArcherD. H. and LemezisS., WestinghouseEngineer 197333 119. [2] Klein Heimich., Staub 1%3 23 501. [3] Aerodyne Development Co., Cleveland, Ohio. [4] Sierra Instrument Co., Minneapolis, Minn. [51 Dunson, Jr. J. B., Paper SE, AIChE 63rd Annqal Meeting, Chicago, Ill., Nov. 1970. [6] Ciliberti D. F. and Lancaster B. W., Reu. Sci. Inst.197546 929.