Journal of Applied Fluid Mechanics , Vol. 9, No. 1, pp. 487-499, 2016. Available online at www.jafmonline.net, ISSN 1735-3572, EISSN 1735-3645. DOI: 10.18869/acadpub.jafm.68.224.23934 CFD Simulations of Pressure Drop and Velocity Field in a Cyclone Separator with Central Vortex Stabilization Rod J.J.H. Houben 1† , Ch. Weiss 2 , E. Brunnmair 3 1 1 Johannes Kepler University Linz, Altenbergerstrasse 69, 4040 Linz, Austria 2 Montanuniversitaet Leoben, Franz-Josef-Strasse 18, 8700 Leoben, Austria 3 Bublon GmbH, Grazer Straße 19-25, 8200 Gleisdorf, Austria † Corresponding Author Email: [email protected](Received July 8, 2014; accepted December 3, 2014) ABSTRACT A problem of cyclone separators is the low grade efficiency of small particles. Therefore, a high efficiency cyclone separator has been developed and successfully tested in former work. In this cyclone separator, a vortex stabilizer is used to suppress the vortex core precession. In this article, the pressure and flow field in this cyclone separator are calculated by means of computational fluid dynamics using the commercial software Ansys Fluent 13. The position of the vortex core is tracked in these simulations by searching the position of minimal dynamic pressure and the centre of moment of the horizontal velocity components as function of the axial coordinate. The results are compared with experimental data. It is demonstrated that when using a stabilizer, the vortex is kept in position. Furthermore the maximum of the tangential velocity is found to be larger, which is known to have a positive effect on the separation of small particles in the inner solid body rotation vortex. Keywords: Computational Fluid Dynamics; preceeding vortex core; cyclone separator; pressure drop. NOMENCLATURE ¯ p time averaged pressure p 0 time fluctuating pressure C 1ε ; C 2ε ; C μ numerical constants C 1 ; C 2 ; C 0 1 ; C 0 2 numerical constants C ij convection term D diameter D H hydraulic diameter D T,ij turbulent diffusion D L,ij molecular diffusion E empirical constant F ij production term f frequency G k generation of turbulence G ij buoyancy k turbulent kinetic energy L c natural vortex length M velocity moment P ij stress production t time ax axial c cone, centre h horizontal cb cyclone body i counter in inlet o outlet P near wall point r rod rad radial rel relative tan tangential tot total vf vortex finder vfi vortex finder inner I turb turbulent intensity St Strouhal number ε turbulent dissipation rate κ von K´ arm´ an constant μ dynamic viscosity μ t turbulent viscosity ν kinematic viscosity φ ij , φ ij,1 , φ ij,2 , φ ij,w pressure strain terms ρ density τ w wall shear stress and S. Pirker
Transcript
Journal of Applied Fluid Mechanics , Vol. 9, No. 1, pp. 487-499, 2016. Available online at www.jafmonline.net, ISSN 1735-3572, EISSN 1735-3645.DOI: 10.18869/acadpub.jafm.68.224.23934
CFD Simulations of Pressure Drop and Velocity Field in aCyclone Separator with Central Vortex Stabilization Rod
J.J.H. Houben1†, Ch. Weiss2, E. Brunnmair3 1
1 Johannes Kepler University Linz, Altenbergerstrasse 69, 4040 Linz, Austria2 Montanuniversitaet Leoben, Franz-Josef-Strasse 18, 8700 Leoben, Austria
3 Bublon GmbH, Grazer Straße 19-25, 8200 Gleisdorf, Austria
(Received July 8, 2014; accepted December 3, 2014)
ABSTRACT
A problem of cyclone separators is the low grade efficiency of small particles. Therefore, a high efficiencycyclone separator has been developed and successfully tested in former work. In this cyclone separator, avortex stabilizer is used to suppress the vortex core precession. In this article, the pressure and flow fieldin this cyclone separator are calculated by means of computational fluid dynamics using the commercialsoftware Ansys Fluent 13. The position of the vortex core is tracked in these simulations by searching theposition of minimal dynamic pressure and the centre of moment of the horizontal velocity components asfunction of the axial coordinate. The results are compared with experimental data. It is demonstrated thatwhen using a stabilizer, the vortex is kept in position. Furthermore the maximum of the tangential velocityis found to be larger, which is known to have a positive effect on the separation of small particles in theinner solid body rotation vortex.
Although their introduction is more than a cen-tury ago, cyclone separators are still widely usedin industry. This because of their robustness, lowproduction and running costs and high temperatureand pressure resistance. The design should allowa maximal separation efficiency combined with aminimal pressure drop. Also a high selectivity be-tween the over- and underflow is desired. How-ever, particles smaller than roughly 1 µm in diame-ter are still hard to separate with a standard cycloneand other complementary technologies are needed,such as electrostatic precipitators, bag and fiber fil-ters, venturi scrubbers or rotating particle separa-tors (Brouwers (2002)). These technologies arehowever more expensive in both investment and op-eration costs.
From the middle of the last century, many researchhas been performed on (semi)empirical models topredict the velocity distribution, the pressure dropand the separation efficiency in cyclone separa-tors. Pioneering work in this field was performedShephered and Lapple (1939). In the fifties Barth(1956) developed the cut size theory, which pre-dicts the particle diameter that is separated with aprobability of 50%. Barth’s theory was further im-proved for higher solid loadings by Muschelknautz(1970) and Trefz and Muschelknautz (1993) and isnowadays one of the most widely used analyticalmodels (Muschelknautz et al. (1997)). For a re-cent and complete overview of existing models thereader is referred to e.g. Cortes and Gil (2007),which also provides an overall picture of compu-tational fluid dynamics (CFD) used for cyclone sep-arators, starting from Boysan et al. (1982). Froma comparison to laser doppler measurements, it isknown that only the Reynolds Averaged Navier-Stokes Reynolds Stress Model or (lattice Boltz-mann) Large Eddy Simulation give reasonable nu-merical results (e.g. Gronald and Derksen (2011)).Since the latter method has high computationalcosts, the newest developments go into direction ofhybrid models that are able to resolve critical re-gions finer (e.g. Pirker et al. (2013)).
One of the problems in cyclone separator design isthat, in contradiction to most mathematical models,longer cyclones do not automatically have a betterseparation efficiency (Hoffmann and Stein (2007)).In these cases the vortex core does not reach thebottom of the cyclone but will bend before to thewall. This phenomenon is known as the end of thevortex (EOV), where the distance between the en-trance of the vortex finder and the height where thevortex touches the wall is defined as the natural vor-tex length.
Three models from literature to estimate this natu-
ral vortex length are listed in Tab. 2 and are com-pared with the distance available in the test cy-clone, i.e. between the entrance of the vortex finderand the disc near the dust outlet (see Fig. 1(a)).All three models predict a longer natural vortexlength than the distance available in the geometryand therefore no EOV may be expected.
Another character of many cyclone designs is thatthe movement of the vortex’ centre is not station-ary in the cyclone’s axis, which is called the pre-cessing vortex core (PVC) by Derksen and Van denAkker (2000). This non-stationary behaviour in-fluences the cyclone’s pressure drop and separationefficiency in a negative way. The frequency, f , ofthe vortex core may be defined by a dimensionlessStrouhal number, St, as function of the body diame-ter Dc and the inlet velocity vin according to Eq. (1)(Peng et al. (2005)):
St =f Dc
vin. (1)
The St number is known to be more or less inde-pendent of the volume flow rate and can be statedto be a function of the geometry only. In literaturevalues between 0.4 and 0.6 are mentioned (Hoek-stra et al. (1999), Peng et al. (2005)), which wouldgive a PVC-frequency of 8 and 60 Hz for volumeflow rate of 200 and 1500 m3/h respectively for thecyclone geometry in this study.
Brunnmair et al. (2009) developed a new typeof cyclone with a higher separation efficiency forsmall particles, which was successfully tested in ex-periments. Features of this cyclone are the highand small logarithmic inlet and the central rod(described for the first time by Staudinger et al.(1992)), which stabilises the inner vortex and pre-vents it from precessing. Due to the last, the sep-aration zone is divided into one for large particles,located at the outer wall, and a second one in thecyclone’s centre around the rod separating smallerparticles. The tangential velocity component ofthe vortices in these two regions is described withEq. (2)
vtan · rn = const, (2)
where n takes the value -1 to describe the solid in-ner vortex and ca. 0.7-0.8 for the outer free Rank-ine vortex (Meißner and Loffler (1978), Hoffmannet al. (2001)). Brunnmair et al. (2009) found themaximal tangential velocity to be higher with theuse of a rod. This higher tangential velocity would
Fig. 1. Cyclone dimensions and measurement levels.
Table 1. Cyclone dimensions as sketched in Fig. 1(a).
quantity symbol value unit
inlet width ain 0.022 minlet height bin 0.400 moutlet width ao 0.120 moutlet height bo 0.120 mcone top diameter Dc 0.400 mvortex finder diamter Dvf 0.130 mrod diamter Dr 0.030 mdisc diamter Dd 0.286 mcone heigth Hc 0.350 mvortex finder total length Hvf 0.222 mvortex finder inner length Hvfi 0.185 mdisc height Hd 0.002 mdust outlet gap s 0.020 m
Table 2. Models to calculate the natural vortex length, Lc, and its values for the test cyclone’s geometrywith: Dvf, the vortex finder diameter, Dcb, the diameter of the cyclone body (without spiral inlet) andain and bin, the width and height of the inlet respectively. The vertical distance between the bottomof the vortex finder and the disc near the dust outlet equals 0.563 m (further cyclone dimensions aredefined in Fig. 1(a)).
Author Equation Lc [m]
Alexander 1949 (Hoffmann et al. (1995)) LcDcb
= 2.3 DvfDcb
(D2
cbainbin
)1/3
0.786
Bryant et al. 1983 (Qian and Zhang (2005)) LcDcb
= 2.26(
DvfDcb
)−1( D2cb
ainbin
)−0.50.652
Zhongli et al. 1991 (Hoffmann et al. (1995)) LcDcb
Fig. 2. The cyclones computational grid topview (left) and front view (right).
cause higher centrifugal forces on smaller particlesand therefore a higher total separation efficiency.
In this article the effect of the use of such a stabili-sation rod is demonstrated by comparing the resultsof CFD-simulations with pitot tube and manometermeasurements of Brunnmair (2010). Furthermoreresults of the simulations provide a closer look tothe vortex precession which gives insights that havenot been noticed during the experiments.
The mesh shown in Fig. 2, was created in Gam-bit and consists of hexahedral and polyhedral cells.The 235 640 polyhedral cells were converted froma paved mesh. They are only present in the sec-ond half of the outlet spiral, located downstream,because of the geometry of this outlet spiral. Themesh of the lower part of the cyclone is structured.For the mesh of the geometry without rod, the cellsin the centre axis form a cuboid, which preventshighly skewed cells. The total number of cells is759 470 for the geometry with and 852 910 withoutrod.
2.2 Conservative laws
The considered fluid velocities in the experimentsof Brunnmair et al. (2009) are much smaller (max-imal < 100 ms−1) than the speed of sound of thisfluid under the same conditions (≈ 340 ms−1), i.e.pressure and temperature. Therefore the Mach-number is much smaller than unity (Ma≈ 0.3, andthe flow can be treated as incompressible (Nieuw-stadt (1998)). The equations for continuity then be-
comes:
∂ui
∂xi= 0. (3)
Since the medium considered to be incompressibleand is known to be a Newtonian fluid, for momen-tum the Navier-Stokes equations have been taken asbasis:
ρ∂ui
∂t+ρuj
∂ui
∂xj= ρgi−
∂p∂xi
+µ∂2ui
∂x2j. (4)
The fluid velocity components ui and uj are knownto be turbulent and fluctuating in time for the flow incyclone separators (Gronald and Derksen (2011))and Eq. (4) is therefore solved using Reynolds Av-eraged Navier Stokes (RANS) modelling describedin the sections below.
Energy conservation laws are further not taken intoaccount since the experiments of Brunnmair (2010)were carried at ambient conditions, without anyheat fluxes due to temperature gradients.
2.3 Turbulence modelling
Since the flow in a cyclone is strongly swirled,the Reynolds stress model (RSM) is used to ac-count for anisotropic turbulence. The RSM modelis known to give reasonable results for industrialapplications (Gronald and Derksen (2011), Talbiet al. (2011)). However, in order to get stable fi-nal RSM-simulation results the standard k−ε modelwas used for the first iteration steps.
2.31 Standard k− ε model
In the standard k− ε model, two differential equa-tions for the turbulent kinetic energy k and the tur-bulent dissipation rate ε are considered, having thefollowing general form (Fluent (2005)):
is the turbulent viscosity. The generation of turbu-lence is calculated as follows:
Gk =−ρu′iu′j
∂uj
∂xi. (7)
The generation of turbulent energy due to buoy-ancy Gb is not taken into account for isothermalflows such as the dilatation dissipation YM, which isonly important for flows with higher Ma-numbers,and any user-defined source terms Sk and Sε forthe turbulent kinetic energy and dissipation rate re-spectively. The constants in Eq. (5) have the fol-lowing numerical values in this study: C1ε = 1.44,C2ε = 1.92, Cµ = 0.09, σk = 1.0, σε = 1.3, the lattertwo being the turbulent Prandtl number for k and ε
respectively.
2.32 Reynolds stress model RSM
The transport equations of the Reynolds stressesρu′iu
′j are written in the following general form:
∂
∂t
(ρu′iu
′j
)+Cij =
DT,ij +DL,ij +Pij +Gij +φij− εij +Fij,
(8)
representing the following terms from left to right:local time derivative; Cij: convection; DT,ij: turbu-lent diffusion; DL,ij: molecular diffusion; Pij stressproduction: Gij buoyancy; φij: pressure strain; εij:dissipation; Fij: production by system rotation. Nomodeling is needed for the convection, the molecu-lar diffusion, the stress production and the produc-tion by system rotation, whereas the buoyancy pro-duction equals zero for isothermal flow. The re-maining terms are closed by the following equa-tions (Fluent (2005)):
DT,ij =∂
∂xk
(µt
σk
∂u′iu′j
∂xk,
)(9)
where σk = 0,82 (Lien and Leschziner (1994)).The pressure strain is modelled linear using the fol-lowing decomposition:
φij = φij,1 +φij,2 +φij,w (10)
with, when ignoring system rotation and buoyancy:
φij,1 =−C1ρε
k
[u′iu′j−
23
δijk], (11a)
φij,2 =−C2
[(Pij +−Cij
)− 2
3δij (P−C)
], (11b)
φij,w =C′1ε
k
(u′ku′mnknmδij−
32
u′iu′knjnk
−32
u′ju′knink
)Clk
3/2
εd
+C′2
(φkm,2nknmδij−
32
φik,2njnk
−32
φjk,2nink
)Clk
3/2
εd(11c)
The constants in Eq. (11) have the following numer-ical values: C1 = 1.8; C2 = 0.6; C′1 = 0.5; C′2 = 0.3and κ = 0.4187 the von Karman constant. nk is thexk component of the unit normal to the wall, d is thenormal distance to the wall. Furthermore P = 1
2 Pkk,
C = 12Ckk and Cl =C
3/4µ /κ.
2.4 Boundary conditions
In the CFD simulations the following boundary con-ditions were set in Fluent Ansys (Fluent (2005)):
• inlet: velocity inlet
• outlet: pressure outlet
• wall: standard wall function
The details of these boundary conditions are dis-cussed in the sections below.
2.41 Inlet
The velocity of the fluid is assumed to have a blockprofile with a magnitude of the ratio of the volumeflow rate and the area of the inlet. Turbulence is cal-culated by the hydraulic diameter DH and the tur-bulent intensity, which is calculated with (Houben(2011)):
Iturb = 0.16ReH−1/8 (12)
with the Reynolds number based on the hydraulicdiameter
ReH =vinDH
ν. (13)
For the Reynolds stress specification method k orthe turbulent intensity are used.
Since the outlet in the experiments of Brunnmair(2010) is of the spiral type, no problems with backflow into the domain were expected, which wasconfirmed during simulations. Therefore, no geom-etry adaption was made, e.g. of the type of the disc(e.g Derksen (2003)). Back flow turbulent intensitywas put on zero to avoid turbulence to flow backinto the domain.
2.43 Wall
Standard wall functions were applied where themean velocity is calculated with:
U∗ =1κ
ln(Ey∗) for y∗ > 11.225 (14a)
U∗ = y∗ for y∗ < 11.225 (14b)
in which the dimensionless velocity U∗ and the di-mensionless wall distance y∗ are defined as:
U∗ =UPC
1/4µ k
1/4P
τw/ρ(15a)
y∗ =ρC
1/4µ k
1/2P yP
µ, (15b)
where UP, kP and yP are the mean fluid velocity,turbulent kinetic energy at the near wall point P andthe distance from this near wall point to the wall re-spectively. Furthermore, E is an empirical constantwith the value of 9.793.
The wall boundary condition from the k-equationapplied meaning that
∂k∂n
= 0. (16)
For the production of k and the turbulent dissipationrate the following equations are used:
Gk =τ2
w
κρC1/4µ k
1/2P yP
(17a)
ε =C
3/4k3/2P
µ
κyP. (17b)
2.5 Discretization schemes
The velocity-pressure coupling was performed withthe SIMPLE algorithm with the PRESTO! pressurediscretization scheme, whereas the discretizationof momentum, turbulent kinetic energy, dissipationrate and Reynolds stresses were achieved with theQUICK scheme.
2.6 Vortex core tracking
During the same time the centre of the vortex isdetermined by dividing the cylindrical and conicalpart into 11 levels of axial coordinate. For savingcomputational effort and for achieving a high res-olution, the velocities were only tracked on circleswith diameters twice as large as that of the vortexfinder. The resolution of the x and y-velocity sam-pling data was 5.2 mm in both x and y directions.The moment of inertia by these two velocity com-ponents around the cyclone’s vertical axis is com-puted with:
Mu =N
∑i=1
ui · yi (18a)
Mv =N
∑i=1
vi · xi, (18b)
where ui and vi are the velocity components in xand y direction respectively and xi and yi the coor-dinates for each local grid point, with index i. Thecentre of the vortex is then determined to the point(xc,yc) where the cumulative sum the moment ofinertia of both velocity components is half of thetotal moment of inertia of these velocities:
x=xc
∑i=1
vi · xi = Mv,c =Mv
2, (19a)
y=yc
∑i=1
ui · yi = Mu,c =Mu
2. (19b)
Also the position of the vortex core was calculated,where the absolute value of the horizontal velocitieshas a minimum value:
vh =√
v2x + v2
y. (20)
Under the assumption that the z-velocity remainsconstant in the observed area, this point corre-sponds with the point of minimal dynamic pressure,
pdyn =12
ρ(u2 + v2 +w2) (21)
and therefore with the vortex core.
2.7 Computational time and convergence
Calculations were started with the smallest volumeflow rate of 200 m3/h and k−ε as turbulence modelusing 3 of 4 available CPU’s. For checking conver-gence, the statical pressures on the in- and outletof the cyclone separator as well on the lower and
upper cross sectional area of the vortex finder weremonitored. After 1 000 iteration steps and approx-imately 1 hour real time, monitored pressures be-came stable and the turbulence model was changedto RSM, for which another 9 000 iteration stepswere performed taking approx. 15 hours real time.Then the solver mode was changed from steady tounsteady using a time step of 0.01 s and maximal 50iterations per time step. After 100 time steps, takingcirca 8 hours, pressure monitors results were writ-ten during another 100 time steps. During another100 equal time steps, the velocity components andpressure monitors were averaged during 1 s flowtime.
The vortex core tracking was achieved using onesingle CPU and using 11 user defined functions, i.e.one for each horizontal cross sectional area. Timefor achieving 0.01 s real time and writing out thedata for after 50 iterations was 10 and 5 minutesrespectively. I.e. collecting data for 1 s real timetook 25 h in total.
Quasi steady state solutions for larger volume flowrates were reached in the same starting from thesteady state RSM-solution of the next smaller vol-ume flow rate, leaving all other further steps un-changed.
3. RESULTS & DISCUSSION
The pressure drop and flow velocities are comparedto experimental data of Brunnmair (2010). Theexistence of the precessing vortex core is demon-strated with the help of the methods as described inSec. 2.
3.1 Pressure (drop)
The total pressure, i.e. the sum of static and dy-namic pressure, with and without rod are shown inFig. 3 and are compared with experimental data.The individual pressure levels have been monitoredat the inlet, the entrance and exit of the vortex finderand the exit of the spiral outlet (see Fig. 1).
The pressure drop between the inlet and the en-trance of the vortex finder is slightly underpredictedin the simulations (Fig. 3(a)). Furthermore, thenumerical results do not show the reduction of thepressure drop by the rod, which has been noticedduring the experiments.
In the vortex finder itself, the pressure drop furtherincreases by the high swirl in the flow (3(b)). How-ever the increase in pressure drop is seen to be muchhigher during the experiments than in the simula-tions. The value with and without stabilisation roddo not differ very much, although also here a littletendency for a higher pressure drop when using therod is visible in the numerical results.
After the spiral outlet the biggest difference be-tween experimental and numerical results are no-ticed (Fig. 3(c)). Whereas the experimental resultsshow a decrease in pressure drop, in the simulationsthe total pressure drop raises. The stabilisation rodhas a comparable effect on the mean pressure dropas for the case without a spiral outlet. An expla-nation for the large differences between the simu-lations and the experimental results is the difficultyto measure a time averaged pressure due to the highturbulence induced by the trailing edge of the vor-tex finder and the change in flow direction.
The relative pressure drop fluctuation, defined as
p′rel =
∫ tendt=0
√(p− p)2dt∫ tend
t=0 pdt(22)
p =
∫ tendt=0 pdt
tend(23)
is shown in Fig 3(d) for a volume flow rate of 500m3/h. It is clearly noticed that the pressure fluc-tuates much less when a rod is used: whereas therelative fluctuating pressure without a rod is in therange of 5-8%, this value decreases to only 0-3%which indicated the vortex stabilising effect of therod.
3.2 Flow field
The three velocity components are shown in Fig.4 as function of the radial coordinate from the cy-clones centre to the opposite of the inlet. The ra-dial and tangential velocities are made dimension-less with the mean inlet velocity and the axial ve-locity with the mean axial velocity through the vor-tex finder. Because of the vortex core precession(Derksen and Van den Akker (2000)) the velocitycomponents strongly fluctuate in time. This move-ment is due to the unsteady character of the flow,not due to turbulence. Therefore, the shown pro-files are mean values for a simulation time of onesecond, which corresponds to approximately 20 cy-cles of fluctuating pressure drop for the simulatedvolume flow rate of 500 m3/h acc. to Eq. (1).
For the tangential velocity a clear difference be-tween the inner and outer zone is visible. The in-ner vortex is represented by a solid body rotationwhereas the outer region represents a potential vor-tex. The maximal tangential velocity is found ata radial coordinate slightly smaller than the vor-tex finder diameter as observed in experiments byBrunnmair et al. (2009). As in the experimentsa larger maximum for the tangential velocity is no-ticed in case a rod is used, which is assumed to have
Fig. 3. Comparison of experimental and computational results of total pressure drops for the cycloneseparator with and without stabilisation rod. The levels are according to Fig. 1(b).
a positive effect on the separation of fine particlesin the inner vortex.
Also the axial velocity has a maximum between thestabilisation rod and the vortex finder. In the outerregion the velocity in general points downwards al-though close the vortex finder it may also point up-wards. The drop in the axial velocity below thevortex finder is also noticed in the simulations ofDerksen et al. (2006). The agreement between ex-periments and simulations would be better in casemass loading effects are considered in stead of us-ing one-way coupling. At the two lower levels inthe cyclone, the correspondence of the experimen-tal to the numerical values becomes less.
Close to the stabilisation rod the radial velocitypoints towards the centre. It becomes smaller andeven negative with a minimum at the same radius ofthe vortex finder. This phenomena is known as lipleakage (Hoffmann and Stein (2007)) and vanishesfurther downwards in the cyclone. Curious is thepeak of the radial velocity at the level just beneaththe vortex finder, which is pointed outwards. Thepeak is about 4 times larger when a rod is used andcould force particles outward again after they havebecome entrained in the secondary flow.
3.3 Precessing vortex core
In Fig. 5 the results of calculated position of thevortex core as function of the dimensionless verti-cal coordinate z = z+Hc+Hd
Hc+biare shown. The radial
position of the vortex core r is made dimension-less by the diameter of the rod Dr = 30 mm. Itis calculated by solving Eq. (18) and Eq. (19) forFig. 5(a), 5(c) and 5(e) and by searching the point,where the velocity in the horizontal plane has anabsolute minimum according to Eq. (20) for Fig.5(b), 5(d) and 5(f). For obtaining the data, the ve-locities on 11 planes were tracked during 100 timesteps of 0.01 s and 50 iterations per time step. Aspost processing from the simulation the mean ve-locity components at the radial position and theirstandard deviation were calculated for an averagingtime interval of one second.
The use of a stabilisation rod does not seem to havemuch influence on the centre of moment for vol-ume flow rates of 200 and 1500 m3/h: the curvesin both Fig. 5(a) and 5(e) intersect more than once.However, at a volume flow rate of 500 m3/h thisdoes not occur and the use of the rod has a positiveeffect on the symmetry of the vortex (Fig. 5(c)).
Fig. 5(b), 5(d) and 5(f) show that the centre of min-imal pressure of the vortex does not drift away fromthe radius of the stabilisation rod, although it mayrotate around it. The smaller deviations at the vol-ume flow rates of 500 and 1500 m3/h are due tonumerical errors of the finite grid size. Without the
rod the vortex is observed to precess. However, thisprecession is within a fluid volume smaller than thatof the rod and from this point of view the rod’s di-ameter seems to be over-dimensioned.
4. CONCLUSIONS AND RECOMMENDA-TIONS
A new type of cyclone separator has been success-fully simulated by means of computational fluiddynamics and the results of this study have beencompared with data from former experiments. Thenew type uses a central rod, which stabilises thevortex and prevents it from precessing around thecyclone’s axis and from prematurely ending at thewall. Effects of the rod are:
• A more constant pressure drop, which is no-ticed from the numerical results. An absolutereduction in pressure drop as seen during ex-periments is not confirmed by the simulations.One possible reason for this could be the largerfrictional area of a cyclone separator with arod and the difficulty of experimentally mea-suring a time mean pressure drop in turbulentflow.
• A higher maximum of the tangential velocityprofile, both noticed in experiments and sim-ulations. The location of this maximum is ata radius a little smaller than half the vortexfinder’s diameter. This higher tangential ve-locity is assumed to have a positive effect onthe separation of smaller particles in the sec-ondary flow beneath the vortex finder.
• A decrease of the vortex core precessing.When using a stabilisation rod, the vortexcore, i.e. the place of minimal dynamic pres-sure, is not seen to precess. However, with-out a rod this precession is in an area smallerthan the rod’s cross sectional area. This meansthat the diameter of the rod most probably hasbeen oversized and a smaller rod could havethe same positive effect on the PVC withoutthe negative results on the pressure drop.
Recommendations on future work are:
• A more sophisticated turbulence model coulddescribe the velocity profiles more realisti-cally. This turbulence model could be used asa hybrid model where the better model is onlyused locally where a (much) higher resolutionis desired.
Recommendations for improving the cyclone de-sign are:
Fig. 5. Comparison of the vortex core equated from the moment of inertia (left) and minimum ofdynamic pressure in the horizontal plane (right) for volume flow rates of 200, 500 and 1500 m3/h. Theradial position of the vortex core r is made dimensionless by half the diameter of the rod (Dr = 30mm).
• The use of a thinner rod, which lowers thepressure drop due to wall friction without los-ing the effect of stabilising the vortex.
• For a longer cyclone design the rod could evenhave a more positive effect since it would notonly stabilise the PVC but could also elongatethe natural vortex length.
• A rotating rod would raise the maximum ofthe tangential velocity and therefore improvethe separation efficiency. Such a rotating rodcould be combined with a rotating particleseparator mounted on it.
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