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      Separators in the cement industry              
      2   Cyclones                  
      2.1   Introduction:                  
          - In cement manufacturing industries, large-sized cyclone separators are used as main process equipments in  
            significant numbers for handling high volumetric flow rates of dust-laden gases.      
          - The cyclone is a simple mechanical device commonly used in the grinding circuits to remove relatively large particles
            from gas streams.                
          - Cyclones are often used as precleaners to remove more than 80% of the particles greater than 20µm in diameter.  
          - Smaller particles that escape the cyclones can then be collected by more efficient control equipment like bag filters  
            and electroprecipitators.                
          - Cyclones are relatively inexpensive since they have no moving parts and they are easy to operate.    
          - The most common type of cyclone is known as reverse flow cyclone separator.      
      2.2   Advantages of cyclones:                
          - Low capital cost.                
          - Ability to operate at high temperatures and pressures.          
          - Low maintenance requirements because no moving parts.          
          - Constant pressure drop.                
          - Can separate both solid and liquid particles, sometimes both simultaneously.      
      2.3   Disadvantages of cyclones:                
          - Low efficiency especially for very small particles.            
          - High operating costs in case of high pressure drop.            
          - Subject to erosion or clogging if abrasive solids are processed.          
      2.4   Principle of operation:      
          - The spiral pattern of gas flow is developed by the manner in  
            which the gas is introduced.      
          - It enters along the side of the cyclone body wall and turns a  
            number of times to spiral down (external vortex) to the  
          - Particles in the gas are subjected to centrifugal forces which  
            move them radially outwards, against the inward flow of gas  
            and towards the inside surface of the cyclone.    
          - When the gas reaches the bottom of the cyclone, it reverses  
            direction and flows up the center of the tube, also in a spiral  
          - This spiral fashion is also called inner vortex and fine  
            particles are carried with the air and leave the cyclone  
            through the immersion tube.      
          - Solids at the wall are pushed downwards by the outer vortex   
            and are going out by the solids exit.      
          - Gravity has been shown to have little effect on the     
            cyclone's operation.        
          - See the figures on the right side and below.    
        Click on the picture to enlarge  
      2.5   Forces affecting the particles              
          - We consider a reverse flow cyclone with a cylindrical section of radius R.        
          - Particles entering the cyclone with the gas stream are forced into a circular motion.      
          - The forces acting on a particle following a circular path are drag, buoyancy and centrifugal force (Fd, Fb and Fc).  
          - The balance between these forces determines the equilibrium orbit adopted by the particle.    
          - The drag force is caused by the inward flow of gas and acts radially inwards.        
          - Considering a particle of diameter x and density ρp following an orbit of radius r in a gas of density ρf and viscosity µ,
            we have the tangential velocity of the particle be Uϴ and the radial inward velocity of the gas be Ur.    
          - If we assume that the Stokes’ law applies under these conditions then the drag force is given by:    
          - The centrifugal and buoyancy forces acting on the particle moving with a tangential velocity component Uϴ at radius r are:
          - We can neglect the buoyancy force.              
          - And at a steady state, we have:              
                      Click on the picture to enlarge    
      2.6   Flow Characteristics                
          - The rotational flow in the forced vortex within the cyclone body gives rise to a radial pressure gradient.    
          - This pressure gradient, combined with the frictional pressure losses at the gas inlet and outlet and losses due to changes in flow 
            direction, make up the total pressure drop.            
          - The pressure drop, measured between the inlet and gas outlet, is usually proportional to the square of gas flow rate through
            the cyclone.                  
          - A resistance coefficient, the Euler number Eu, relates the cyclone pressure drop Δp to a characteristic velocity:  
            Where ρf is the gas density              
          - The velocity v is based on the cross-section of the cylindrical body of the cyclone:      
             Where Q is the gas flow rate and D is the cyclone inside diameter        
          - The Euler number represents the ratio of pressure forces to the inertial forces acting on a fluid element.  
          - Value is practically constant for a given cyclone geometry, independent of the cyclone body diameter.
      2.7   Mechanical parts:                
          - Tangential inlet volute                
          - Cylindrical section                
          - Immersion tube                
          - Conical section                
          - Discharge (rotary valve, pendulum flap)            
      2.8   Cyclones families:                
          - Conventional  
          - High efficiency        
          - High capacity        
            See the figure on the right:      
                    Click on the picture to enlarge      
      2.9   Design of the cyclones:                
          - Dimensions:    
            a = Height of tangential inlet        
            b = Width of tangential inlet        
            De = Diameter of air outlet tube        
            S = Immersion length of outlet tube        
            D = Cyclone diameter          
            h = Length of cylindrical section        
            z = Length of conical section        
            H = Cyclone length          
            B = Diameter of material outlet        
                    Click on the picture to enlarge      
          - On the sheet below, we can have a good idea of the standard cyclone dimensions for each family:    
          - Regardless of the configuration selected, we must follow the following recommendations:    
            * a S to avoid the by-pass of the particules from the input section directly to the tube exit    
            * b ≤ (D-De)/2 to avoid an excessive pressure drop             
            * H ≥ 3D to keep the tip of the vortex formed by the gases inside the conical section of the cyclone    
            * The inclination angle of the cone of the cyclone should be ≈ 7-8° to ensure a quick slide of the powder    
            * De/D ≈ 0,4-0,5, H/De ≈ 8-10 and s/De ≈ 1 to ensure the operation with the maximum efficiency
      2.10   Cyclones scale-up:                
          - The scale-up of cyclones is based on a dimensionless parameter, the Stokes number, which characterizes the separation
            performance of a family of geometrically similar cyclones.           
          - The Stokes number (Stk50) is defined as:            
          - It is interesting to find that, for well-designed and well-known cyclones, there is a direct correlation between Eu and Stk50:
          - For Stairmand high-efficiency cyclones: Stk50 = 1,4/10000 and Eu = 320        
          - For Stairmand high-capacity cyclones: Stk50 = 6/1000 and Eu = 46          
      2.11   Cyclone's efficiency:                
          - A model widely accepted is use for determining the efficiency of a cyclone.        
          - In this model, Ne is the number of revolutions the gas falling in the outer vortex.      
            The equation is:                
          - See the "Design of cyclones" section to know the parameters.          
          - With the model of Lapple (1951) which is an empirical relationship in order to calculate the cut size (50% of efficiency),
            we have:                  
            Vi is gas inlet velocity in m/h (range in m/sec: 15-30 m/sec) and          
            µ is the air viscosity in kg/m.h              
            b is the width of the tangential inlet in m            
            ρp is the solid density in kg/m3              
            ρf is the air density in kg/m3              
          - The efficiency (Ƞi) of any size of particle is given by the following formula:        
            Where Di is the particle of reference of a range            
          - The overall efficiency of the cyclone is a weighted average of the collection efficiencies for the various size ranges and is 
            given by:                  
            Where mi is the mass of particles in a certain range and          
            M is the total mass of particles              
          - This efficiency can be undervalued with the concentration of solid particles in the air flow rate.    
          - Then, when the concentration is higher than 2 gr/m3, a correction is applied:        
            where Ƞ1 is the efficiency found,              
            C1 is 2 (gr/m3),                
            Ƞ2 is the new efficiency and              
            C2 is the concentration in dust         
      2.12   Cyclone's pressure drop:                
          - In the evaluation of a cyclone design, pressure drop is a primary consideration. Because it is directly proportional to the
            energy requirement, under any circumstance, knowledge of pressure drop through a cyclone is essential in designing
            a fan system.                
          - Many models have been developed to determine the cyclone pressure drop but one of the well accepted is the model
            of Shepherd and Lapple (1939).              
          - The formula of Δp is:                
            K is a constant:                
            K = 16 for tangential inlet without neutral inlet vane          
            K = 7,5 if tangential inlet with neutral inlet vane and large cyclones        
          - It is better to keep a pressure drop lower than 2,5 kPa.          
      2.13   Design modifications and consequences:              
      2.14   General methodology for the design of cyclones            
          - 1. Select a configuration (conventional, high efficiency or high capacity)        
          - 2. Select a speed at inlet (15-30 m/sec)            
          - 3. In function of the flow rate importance, it is useful to have a 1st estimation of the cyclones number    
          - 4. Calculate the diameter of the cylindrical section of the cyclone D        
          - 5. Calculate the other dimensions of the cyclone on the basis of the table for the selected configuration  
          - 6. Calculate the pressure drop              
          - 7. To analyze if D and Δp are excessively large. Analyze the possibility of using various cyclones in parallel.  
             For nc cyclones in parallel repeat items 2 and 3 using the value of Q/nc in place      
          - 8. Calculate efficiencies for fractions and the total            
          - 9. Compare the calculated efficiency with desired. If you do not achieve the desired value, use a larger value of speed inlet
          - 10. Estimate the cost of the cyclone              
            An example of cyclone calculation is presented on the following page.        
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