# Design Turbulence Model selection 4.4.4. Discrete Phase Modelling 4.5.

Introduction1.1 Overview1.2 Objective of the Study2.    High Efficiency CycloneDesign2.1. Factors influencing theCyclone Separator3.    CFD modelling 4.

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1. Geometry design 4.2. Modelling in Solidworks& ANSYS Workbench 4.

3. Meshing 4.4. Governing Equations4.4.

1. Continuity Equation4.4.2. Momentum Equations4.4.

3. Turbulence Modelselection4.4.4. Discrete PhaseModelling4.

5. Boundary Condition andUser settings 4.    Results and Discussion 5.

1. Results of simulation 5.2. Discussion 5.2.1. The pressure field 5.

2.2. The velocity field 5.2.3. Cut-off Efficiency ofthe cyclone6. Conclusion7.

References 1.   IntroductionIn order to make thegasification and the reduction process of the coal and iron-ore, it necessaryto consider circulating type of fluidized bed. Majority of the papers publishedin the field have mentioned that the reduction process had been done using ironore of particle size of above 150 microns only. Since we propose to utilise thesmaller size particles ranging from 1-176 microns, we propose the usage ofCyclone Separator which is, widely used in Chemical Engineering Industries,capable of collecting fine particles up to 10 microns.

Cyclone Separator is aGas-Solid Separator device which works on the influence of Centrifugal forcesand spirals downward trapping the particles of particular diameter based uponthe objective. The inner vortex, created at the bottom, carries mostly the gas phasespiralling up, with limited number of particles along with the flue gas. Theremoval of solid particles during the reaction processes is quintessentialwhereas in most cases the driving force happens to be gravitational force.

1.1.       OverviewThe Separation processis influenced by the flow parameters such as pressure drop, tangential velocitywhich in turn depend upon the geometric dimensions. The geometricparameters affecting the performance are cyclone inlet dimensions, height andvortex finder diameter, cone tip diameter, cone height.

Decreasingthe vortex finder diameter increases the pressure drop slightly at thebeginning; afterwards the change becomes sharper. Working on these geometricparameters with varying cases would help understand the effect of geometryvariable over the flow field characteristics. Due to the vortexphenomenon, effect of the varying the conical section and dust collectingchamber is critically important though such studies were found to be rare 1.Computational studies that have been performed by varying the dimensions predictthat reliable pressure drop is necessary for theseparation efficacy 1,2,3,4. Maximum tangential velocity is decreased whenthe cyclone inlet dimensions are increased 2 and when the cyclone height isincreased 4,5 which would yielded lower separation efficiency in the studieswhich has been experimentally verified6. When cyclone inlet dimensions areincreased, the pressure drop decreases which has to maintain critical magnitudefor optimum efficiency. Many reported the design aspect of cone bottom is relativelyless important than other geometric parameter even though the computationalstudies done over the bottom cone cyclone dimension were not exactly matchingwith the experiment results in these studies 3,7. For the 100% efficiency ofparticle separation, condition is predicted computationally such that theoverall drag forces acted upon the particles have to be higher than that of thecentrifugal forces 8.

With regard to discrete phase simulation of loadedparticle inside the cyclone separator, it is detailed that when the flow ismacroscopically steady, the pressure drop and the tangential velocity reducedas soon as the solid loading ratio is increased 9. The importance of four-waycoupling and its necessity for high particle loading cases is stressed out aswell 10.  1.2 Objective of the StudyHowever thisstudy concentrates upon studying the effect of varying geometric parameters of proposedcyclone separator designed by standard procedure which is proposed to connectto the outlet of the combustion fluidised bed reactor. The effect of varyinggeometric parameters over the flow field characteristics is involvedconsidering discrete phase calculation which does have effect over the flowfield characteristics and vice versa (Two-way Characteristics) which also playsa prominent role in predicting the separation efficiency. The study wasfollowed after recreating parts of the case study successfully depicting theperformance characteristics and the effect of static pressure over theperformance 1 which involved designing the geometric parameters based uponthe standard cyclone geometry proposed by Stairmand in 1951.

2.     High Efficiency Cyclone Design Stairmand (1951) proposed a standard design of theCyclone separator for higher efficiency specifically, in 1951. The basediameter of the cyclone separator is based upon the volumetric flow rate, andDimensions are derived from the base diameter of the cyclone separator inStairmand Design. Standard Procedure of High Efficiency Stairmand CycloneDesign 11 involves selecting a suitable inlet velocity which shouldpreferably be in the range of 20 to 30 m/sec.2.1.

Factorsinfluencing the Cyclone SeparatorWith the above prominent parameters, some of themare constrained considering our conditions of the project objective. Particlessize diameter of 53 ?m iron ore sample is tested for particle sizeanalysis using laser interferometry and the results how that 176 ?m is the maximum particle size diameter with 0.172 ?m is the minimum diameter. 1.806 ?m is found to be the average particle size in thedistribution range. Iron ore particles have the density of 4100 kg/m3 areused for the project objective.

With the above mentioned constraints, theseparation efficiency can be influenced by controlling the inlet velocity andthe base diameter of the cyclone separator. Higher Velocity has to be chosenwith respect to the desired cut-off diameter for cyclone separation. Cut-offdiameter can be defined as the critical diameter of the particle up to which50% Separation efficiency is maintained in the particle size range. Theparticle diameters below cut-off diameter have lower separation efficiencybelow 50%. To find the base diameter of the cyclone, InletVelocity of 22 m/s and maximum flow rate condition of 2000 litre per minutei.e.

, 0.034 m3/s are used.Inlet area =  = 1.5454 * 10-3 m2 1.5454 * 10-3= 0.1 D2 The diameter, D = 0.1243 m i.e.

, 12.43 cm which isapprox. 12.5 cm, is calculated as the base diameter of the cyclone separator.Theoretically, the Cut-off Diameter is calculatedby the following formula Cut-off Diameter =                             = 0.

829 ?mVelocity more than 22 m/s could reduce the cut-offdiameter but also the base diameter (less than 10 cm). Critical diameter ofreactor is 20 cm and at least half of it has to be maintained in cyclone toproper working of cyclone considering particle mass flow rate (0.0015 kg/s) andgas volumetric flow rate (0.034 m3/s).3. CFD ModellingThe geometries attempted inthe paper are modelled using Solidworks and edited using ANSYS Workbench DesignModeler. The detailed description of the geometry is given by Fig.1.

Cyclone separator schematic diagram showing different components3.1. Geometry DesignWith 12.

5 cm as basediameter, the other geometric dimensions of the cyclone separator are definedby the Stairmand Design which is as follows.   Parameters Symbol notations Stairmand Design Proposed Design Inlet height a/D 0.5 0.625 m Inlet width b/D 0.2 0.025 m Outlet diameter (vortex finder diameter) Dx/D 0.48 0.6 m Vortex insertion length S/D 0.

5 0.625 m Cylinder length H/D 1.6 0.200 m Cyclone total height Ht/D 4 0.500 m Solid outlet diameter Bc/D 0.

4 0.50 m  3.2. Modelling in Solidworks and ANSYS WorkbenchDesign ModelerThe geometry is saved in Solidworks editing formatand also in IGES format, which will be used in ANSYS Workbench Design Modelerfor further modelling and modifying the geometry necessary to meet therequirements of the workbench meshing platform for Hexahedral meshing.

Fig.2. Sliced Parts of the Cyclone Geometry and Meshing using ANSYS Workbench  3.3.MeshingThe paper also indicated thegeometry for the particular problem attained grid independence that reassures the mesh data pertaining to the geometrythat have been used to yield a reasonable prediction. The geometry issegregated as 3 blocks and meshed individually. Unstructured Hexahedral gridelements are used.

Total grid elements of 280,450 with 204,483 nodesare utilized in our simulation. Mesh Orthogonal Quality of 0.36 with Mesh Aspect Ratio of 8.36 have been found.3.

4. Governing EquationsUnsteady Lagrangian discrete phase model is utilised withsingle-gaseous phase flow is utilized to study the transient nature ofgas-solid phase physics and flow phenomena. The gas phase is modelled withReynold stress model with discrete phase model where the particles released fromthe CFB reactor are treated as inert particle materials.

The governing Equations utilised in the simulation are as follows3.4.1. Continuity EquationThe continuity equation is quintessential for solving any basicfluid flow computational problem and is based upon the law of conservation ofmass.  For incompressible flow, , where  isthe velocity vector components in the Cartesian co-ordinate dimensions, is the density of the gaseous phase. 3.4.2.

Momentum EquationsThe momentum equations of the three Cartesian co-ordinates areas follows. In the above equation, ?, ui are the density of thegaseous fluid, three components of the velocity in the space co-ordinatesrespectively.Since turbulence is also included in the problem, ReynoldsAveraged Navier Stokes Equation is utilised for predicting the turbulence,  where  isthe time-averaged velocity function used to replace the fluctuating terms. Rij =  is the Reynold stress term that requiresmodelling. The fluctuating terms are considered into the momentum equations forthe Reynolds averaged equation. The interaction betweenthe flow and turbulent fluctuations include Mean pressure stress, mean viscousstress tensor and the Reynolds stress tensor. 3.4.

3. Turbulence EquationsReynolds TurbulenceStress Model (RSM) is used as the turbulence model in order to capture thecomplex flow behaviour developed inside the cyclone and many reported to havebetter results in comparison with the experimental behaviour 1,12.                                                                = production rate of the stresses;  = transport of Rij dueturbulent diffusion;  = dissipation rate;  = pressure straininteractions; ?ij = transport due rotation; 3.4.4.

Discrete Phase Modelling EquationsThe Discrete Phase Modelling in FLUENT follows theEuler-Lagrange approach. The fluid phase is treated as a continuum by solvingthe time-averaged Navier-Stokes equations, while the discrete particle phase issolved by Lagrangian approach while the mainstream equations are solved atregular intervals, here in this case, 20 iterations is the interval in whichDPM equations are solved along with the seven equations of the turbulencemodel. The dispersed phase can exchange momentum, mass, and energy with the fluidphase. It is assumed in the study that discrete particle phase occupies a lowvolume fraction of less than 12%. The particle trajectories are computedindividually at specified intervals during the fluid phase calculation.

Dragcoefficient of spherical particles are calculated considering the relative Reynoldsnumber as working function. FD =  ; Rep = WhereFD = Drag force; CD= Coefficient of drag; Rep= Relative Reynolds number; ?p= Density of the discrete phase; dp= diameter of the discrete phase particles; u = Velocity of the continuous phase; up = Velocity of the discrete phase.Collisions between particles and the walls of thecyclone were assumed to be perfectly elastic neglecting the cohesive forces andinelastic collisions.

The boundary condition assuming that particles were onlycollected by the bottom of the cyclone is reasonable with the experimentalresults 13 but can over predict fine particle collection as there is nore-entrainment from the cone bottom considered14,15,16. Hence the particlesare assumed to be captured when touched the bottom wall were assumed to becollected in this study. 3.5. Boundary conditions anduser settings The simulations wereperformed in ANSYS Fluent 18.2 with implicit solver that uses element basedfinite volume methods to discretise the governing equations in the spatialdomain. Turbulent intensity is 4% and the lengthscale used is 0.

07 times the inlet width in both the case. Part name Boundary conditions Inlet Velocity inlet – 22 m/s where the fluctuations are added on the mean v. Discrete Particles set to reflect. Outlet “Outflow”   Flow weighting ratio = 1 since the flow velocity and pressure are not known prior to solving the flow problem. Discrete Particles set to escape.

Wall-dustbin (Cone bottom) Velocity no-slip boundary condition, V=0. Discrete Particles set to trap. Wall (Surface body except cone-bottom) Velocity no-slip boundary condition, V=0. Discrete Particles set to reflect.

As indicated earlier, discrete phase modelling inFluent involves Eulerian-Lagrangian approach. The individual particles areinjected from the inlet surface with Rosin-Rammler particle size distributionwith zero velocity and mass flow rate of 0.0015 kg/s.

If the size distribution is of the Rosin-Rammler type, the mass fraction ofparticles of diameter greater than d isgiven by Where, yd= Mass fraction of particle diameters greater than d, d = Particle diameter, dmean = meanparticle diameter in the distribution, n= spread diameter.Thesensitivity of the two parameters dmeanand n in the Rosin-Rammlerdistribution shows that higher value of ngives a tight spread for the distribution. The average particle size increasesas dmean increases and sodoes the average particle size. Plot.

1.Mass fraction of particles greater than its diameter (d) along the distributionThe simulation utilised the spread parameter of 3.5which resulted in the peaking in the particle size distribution closer to theaverage diameter (dmean)and the cumulative distribution illustrates the rosin-rammler nomenclature.

Working fluid Air Velocity of fluid 22 m/s Density of fluid 0.6 kg/m3 Viscosity of fluid 1.7e-05 kg/m-s Velocity of particles 0 m/s Density of particles 4100 kg/m3 Mass Flow rate of particles 0.0015 kg/s Maximum diameter of particles 10e-06 m Mean diameter of the particles 1.

8e-06 m Minimum diameter of particles 0.172e-06 m Particle diameter distribution Rosin-Rammler Distribution Max number of time steps (DPM) 100,000 Type of the particle Iron Ore  SIMPLEC (Semi-Implicit Methodfor Pressure linked equation – consistent) is used for the pressure velocitycoupling solver. QUICK scheme (Quadratic Upwind interpolation for Chemicalkinetics) is used to discretise and solve the surface variables of the domain.As for Pressure, staggered grid approach which is widely known in fluent as”PRESTO!” is used. Standard initialization is done before the start of thesimulation using the data from velocity inlet boundary condition. Time stepsize of 0.001 has been used upto 10000 time steps accounting for the first 10seconds with maximum 30 iterations per each time step.

4. Results & DiscussionThe contour plots of the solved variablesare taken into account for analysis and inferring the effect of the designparameters and the overall performance.4.1. Results of simulation  Fig.3. Time averaged flow of static pressure and Turbulence intensity at Z =0 and Sections from bottom, Y = 0; 150; 300; 400; 500; 77.5 (all in mm) with v = 22 m/s   Fig.

4. Time averaged flow of Tangential and axial velocities at Z=0 and Sections from bottom, Y= 0; 150; 300; 400; 500; 77.5 (all in mm) with v= 22 m/s4.2. Discussion Fig.5 shows the time-averagedstatic pressure contours plots.

The static pressure decreases radially from thewall to the centre. A negative pressure zone appears in the forced vortexregion due to high swirling velocity. The cyclonic flow can be considered not exactlysymmetrical from the low-pressure zone at the cyclone centre. The ratio of themagnitude of the high pressure zone and low pressure zone is found to be around7. A drastic change in the pressure drop has been avoided using standard design.Turbulent intensity hinders and disrupts the motion of secondary phaseparticles. Higher Turbulence intensity inhibits the performance of separationwhich is lower at centre around the position of vortex finder walls.

Turbulenceintensity is less intense on the outer walls compared to the vortex finder wallswhich are a good sign as most of the particles get separated from outer wallsif disturbed by less turbulence. The axial and tangential velocities contoursindicate the existence of two flow streams. The axial velocity equals minimumat the cyclone body walls and maximum close to the position of vortex finderwalls.

4.2.1. Cut-off Efficiency of the cycloneIn order to calculatethe cut-off diameter, 4200 particles were injected from the inlet surface withzero velocity and with the mass flow rate of 0.

0015 kg/s.  Post processing the discrete phase data isdone using CFD Post v18.2 after exporting from Fluent Solver. Out of 4200particles, 3439 particles are trapped in the cone bottom whereas 489 particlesare escaped through the gas outlet.

280 particles are set to incomplete as thecalculation must have been taken more than the allowed maximum number of timesteps i.e., 100,000. Plot.2.Separation efficiency of various particle size diameters involved in thesimulationFora given ash content, separation efficiency is plotted versus particle diameter distributionin Plot.

2 from which it can be concluded that the efficiency is little higherfor a larger particle diameters. The plot makes sense with the theory. By theory the particles smaller than the criticalparticle size should be able to escape the influence of the forces developed inthe cyclone separator and exit via dust discharge hole, and the particles largerthan the critical particle are captured.With the given dataset,particles larger than the diameter 0.9 ?m has more than 50% probability ofbeing captured in which particles larger than 1.4 ?m have more than 80% chancesof being captured by the cyclone.

In chapter 2, the cut-off diameter istheoretically calculated to be 0.839?m whereas the results almost match withthe computational prediction. Hence 0.9 ?m is the cut-off diameter (d50)whereas 1.8057 ?m is the mean diameter of the size distribution. Since thecut-off diameter is smaller than the mean diameter, it can be predicted thatmost of the particles in the distribution tend to undergo better separation processefficacy. Plot.

3. Particle distribution involved in thesimulation and the calculated cut-off diameter.5.   ConclusionsReynolds stress modelhas been used to study the effect of using the Stairmand design of cyclone for flowfield and performance characteristics good enough to be used along with the Combustionfluidized bed for separating the larger size particles from the flue gas and recirculatethe non-magnetized particles back to the reactor bed via magnetic separator. The results obtainedfrom the simulation make sense with the theoretical understanding andcalculations done previously upon the Cyclone Separator with respect to theapplication on the CFB process. Hence this Standard Design of the Cyclone isproposed for the manufacturing for fulfilling the objective. 6.     References1.

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