Nuray Kayakol, Darmstadt University of Technology, Germany
This study describes development of 3D numerical modelling to simulate the complex flow structure of coal pulverizers. The internal geometry of this equipment is very complicated and has not been investigated in detail.
The 3D singlephase swirling turbulent flow field inside a bowlmill coal pulverizer is calculated using Computational Fluid Dynamics (CFD) techniques, taking full account of the internal geometrical features.
In this first part of the study clean airflow without coal particles in the coal pulverizer is numerically simulated by the CFD software FLUENT. Clean airflow structure analysis is important to understand imbalance in the coal/air mixture flow. The CFD results can be used to examine a range of geometry and flow options and increase the performance of the pulverizer.
In pulverized coal fired utility boilers, control of coal fineness, and uniform distribution of coal flow from pulverizers to burners, lead directly to better control and performance of the firing system. Finer coal particles burn quickly and more efficiently, reducing carbon in the fly ash while maintaining low NOx emissions and increasing boiler efficiency.
However, nonuniform pulverized coal flow distribution to the burners is a wellknown problem. This results in lower combustion efficiency due to different air/fuel ratios in the burners which can cause higher fly ash unburnt carbon and unstable combustion with higher carbon monoxide (CO) emissions.
The generally poor combustion conditions also require increased levels of excess air à‚— with the expected negative impact on NOx emissions, capacity and heat rate. Therefore, the improvement of pulverizer performance can play a dominant role on the boiler efficiency and emission control.
The function of a modern pulverizer system is to dry and grind the power station’s coal supply and distribute it to the burners. In a bowlmill coal pulverizer, raw coal, which is fed through a central coal pipe at the top of coal pulverizer, falls by gravity to a rotating grinding table where it is pulverized between grinding rollers.
Hot primary air, for drying and coal transport, enters from the primary air inlet, flows upward through a ring section with multiple sloped nozzles fixed to the surrounding grinding table. The developed swirl airflow induces larger particles to return to the grinding table.
During this first stage of classification, fine particles are carried upward from the grinding zone into the classifier zone in the stream of air, and coarser particles fall back to the table for regrinding. In the next stage of classification, the velocity in the classifier zone decreases and larger particles drop out. Fine particles are carried to the classifiers. Oversized coarse coal particles return for regrinding.
The last stage of classification takes place in the rotating and stationary classifiers located at the top of the pulverizer. An arrangement of circumferentially angled vanes spin the air stream so that the coarser particles are thrown out and return to the grinding zone, while the finer particles pass on with the air stream.
The classification is dependent on the velocity of the primary air, rotation speed of the classifier, position of blades and the cyclonic action of the primary air/coal mixture. Fine pulverized coal exits the outlet section typically through four discharge coal pipes leading to the burners.
Coal pulverizers rely on a uniform airflow distribution to entrain the varying sizes of pulverized coal particles. If the primary airflow is poorly distributed excess air in some regions of the pulverizer carries large coal particles that are not properly pulverized.
This can lead to the blocking of the pulverizer at the classifier, reducing the total pulverizer output. If airflow through the pulverizer is too low, pulverized coal can stagnate in ducts or irregular sections inside the pulverizer, therefore giving rise to fire or explosion risk. Thus, it is important to ensure proper air distribution in the pulverizer.
CFD has a great potential to predict the flow field characteristics and particle trajectories through the coal pulverizer as well as the pressure drop. The complicated swirling turbulent flow in the coal pulverizer places great demands on the numerical techniques and turbulence models employed in the CFD codes.
Generally, CFD predicts turbulent flows through three approaches: direct numerical simulation (DNS), largeeddy simulation (LES), and Reynoldsaveraged NavierStokes (RANS) equation simulation with turbulence models.1 DNS and LES provide detailed information on instantaneous airflow and turbulence with the cost of considerable computing time.
For the design and study of air distributions in enclosed environments, the mean air parameters are more useful than instantaneous turbulentflow parameters. Thus, there is more interest in solving the RANS equations with turbulence models which can quickly predict air distributions.
The RANS approach calculates statistically averaged (Reynoldsaveraged) variables for both steadystate and dynamic flows, and simulates the turbulence fluctuation effect on the mean airflow by using different turbulence models, namely standard kàŽµ, RNG (Renormalization Group Method) kàŽµ and Reynolds Stress Model (RSM).
The highlevel turbulence model, Reynolds Stress Model (RSM) which takes into account the high swirl effects that occur in this type of equipment, is used to get more accurate results.
In recent years there have been several studies published for the prediction of twophase (air/coal) flow in cyclones and coal pulverizers that have swirl flows. The results show that the quality of the numerical solutions depends on the type of turbulence model used for the continuous phase flow.
The aim of this study was to understand the flow structures within the coal pulverizer. CFD analysis of the pulverizer is carried out only for a 3D singlephase flow (cold clean air) employing FLUENT 6.3.2 Although twophase flow (coal/air mixture) was excluded, clean airflow structure analysis is important to understand possible imbalances in the coal airflow.3
Mathematical ModelLing
Reynoldsaveraged equations of continuity and momentum can be written as follows:

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where p and àŽ¼ are the density and viscosity of the fluid; Ui and ui are xi components of the mean and the fluctuating fluid velocities; p is pressure; and g is gravity acceleration and

are the components of turbulent moment flux, known as “Reynolds stress”.
Turbulence Model
The RSM is a higherlevel turbulence model than the standard kàŽµ family of models. The standard kàŽµ model assumes isotropic turbulence and does not have any correction for swirl flow. RSM incorporates anisotropy arising from swirling.
It involves solving the transport equations for the individual stresses of

appearing in the above equation, together with an equation for the turbulence energy dissipation rate.
This means that seven equations are required for threedimensional flows. Therefore, it is computationally more expensive than the standard kàŽµ model, which is known as the twoequation model. The equations of RSM can be written as:

with

being turbulent diffusion, àŽ¦ij the pressurestrain term, àŽµij the dissipation term, and Pij the production term. These quantities are given by the equations below.

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Meshing and Solution Procedure
Governing equations are solved numerically employing the finite volume based code, FLUENT. The SIMPLE (Semi Implicit Method on Pressure Linked Equations)4 method is used for pressurevelocity coupling. Due to difficulty in reaching convergence in simulations, the first order upwind scheme was applied for discretization of Reynold stresses and other flow variables.
The threedimensional model was set up in GAMBIT using an unstructured grid with tetrahedral cells. The geometry was created considering the actual dimensions and thus no scaling was involved.
All the geometric details of the equipment, such as air inlet duct, blades of air nozzle ring, grinding rollers, loading frame holding rollers, stationary and rotating blades of the mill and pulverized coal outlets, are considered. The number of cells, 1.56 million, is sufficient to obtain a gridindependent solution.
Figure 2 gives boundary conditions for the coal pulverizer. It has one air inlet and four pulverized coal outlets. The coal pulverizer is a commercial scale. Airflow rate at the inlet is 18.9 kg/s. The speed of the rotating classifier is 88.2 rpm and the bowl (grinding table) rotates at 24.9 rpm.
Figure 2. Velocity vectors (m/s) at the pulverizer. 
Both of them rotate in a clockwise direction. The number of blades in the stationary and rotating classifiers is 60, and the number of blades in air nozzle ring is 42. At the walls, a noslip boundary condition was applied for velocity, and near wall treatment is achieved by using nonequilibrium wall functions, which includes pressure gradient effects.
“Governing equations are solved numerically employing the finite volume based code, FLUENT. The SIMPLE (Semi Implicit Method on Pressure Linked Equations) method is used for pressurevelocity coupling”
Analyzing the results
Contours of velocity and path lines in the vertical midplane of the pulverizer are given in Figure 1 on page 132. It can be seen that a profile for fully developed flow in the air inlet duct is obtained. The primary air exits from the nozzle ring as a highly swirling air stream that moves upward through the pulverizer. The highspeed air jet flow that comes from an air nozzle ring is then reduced in the main pulverizer housing.
Figure 1. Contours of velocity magnitude in the vertical midplane of the pulverizer. 
Figure 3 shows the contours of velocity vectors above air nozzle ring at the lower part of the coal pulverizer. Primary air is nonsymmetrically fed at the bottom of the pulverizer. The air stream goes down through the inclined air inlet duct and then enters the bottom part of the pulverizer. Then it splits into two streams in front of the cylindrical obstacle, which is at the bottom part of the grinding table. The velocity in these two streams increases due to lower flow area while turning over the cylindrical solid object. The split flow streams then come together at the back of the cylinder. Inclined blades accelerate and orient the flow through the air nozzle ring.
Figure 3. Velocity vectors (m/s) above air nozzle ring at the lower part of the coal pulverizer. 
The required air jet velocity in a pulverizer has a lower limit, because a minimum air velocity is needed to entrain the coal upwardly from the rotary table and prevent it from falling back down through the air port openings into the air plenum. This minimum air jet velocity is a function of the coal particle size and weight.
For a coal particle size of about 40 mm the minimum required jet velocity, which prevents the coal particles from falling back down through the air ports, is approximately 40 m/s. The minimum jet velocity is the terminal velocity which can be calculated as = 33 m/s for coal particles with a density of 1100 kg/m3.
Figure 4. Contours of velocity magnitude (m/s) on the horizontal plane at the air nozzle ring. 
As can be seen from Figure 3 maximum air jet velocity calculated from CFD model is 50 m/s, which is larger than the minimum required jet velocity. Multiphase swirling turbulent flow in the pulverizer is simulated using Reynold Stress Turbulence Model and EulerianEulerian multiphase approach with six phases, one phase for air flow and five more for coal particles having size distribution.
The mixture model, which is the computationally less expensive multiphase model, fails due to the presence of heavier particles.
Figure 5. Velocity vectors (m/s) in the air classfier having stationary and moving blades. 
The mixture model works for small particle sizes à‚— such as 10 àŽ¼m. Therefore, Eulerian model of the EulerianEulerian approach, which is the most complex of the multiphase models available in FLUENT, was selected in this study.
Figures 6 and 7 show contours of volume fraction of 45 àŽ¼m and 250 àŽ¼m of coal respectively. All particles follow in a circumferential motion near the walls due to swirling air flow. Particles of small and intermediate sizes are carried up from the grinding to the classifier zone. Larger particles of coal, 250 àŽ¼m, stay closer to the grinding zone and have difficulty reaching the classifier zone. Twoway coupling of the mutliphase flow regime, which takes into account fluidparticle interaction, captures the coal/air mixture flow pattern successfully.
Figure 6. Contours of volume fraction of 45 àŽ¼m coal particles at the vertical midplane of the pulverizer. 
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Figure 7. Contours of volume fraction of 250 àŽ¼m coal particles at the vertical midplane of the pulverizer. 
This study contributes to a better understanding of the operation of the stationary and rotating classifiers often used in many process industry applications.
References
1 Versteeg, H.K. and Malalasekera, W., “An Introduction To Computational Fluid Dynamics”, The Finite Volume Method, Second Edition, England, 2007.
2 FLUENT 6.3 Users Guide, Lebanon, USA, 2008.
3 Vijiapurapu, S., Cui, J. and Munukutla, S., “CFD Application for Coal/Air Balancing in Power Plants” Applied Mathematical Modeling, vol.30, pp. 854866, 2006.
4 Patankar, S.V., Numerical Heat Transfer and Fluid Flow, Hemisphere Publishing, New York, 1980.
Footnote
Bernd Epple of Darmstadt University, Jan Ericson of Vattenfall (Sweden) and Mogens Berg of Vattenfall (Denmark) also contributed to this article.