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Wednesday, 30 October 2019

VELOCITY TRIANGLE FOR CENTRIFUGAL FAN AND BLOWER

We were discussing various important topics based on the basics of centrifugal compressor, axial flow compressor construction and working principle and difference between fans and blowers in our previous posts. 

Today we will be interested here to understand a very important topic i.e. velocity triangle for centrifugal fan and blower with the help of this post. 

Velocity triangle for centrifugal fan and blower 

Before going ahead, we must have information about the basics of a fan and blower. So, let us recall here first the fundamentals of a fan and blower and further we will see a very important type of fan and blower i.e. Centrifugal fan and blower. Further, we will classify the various types of blades of an impeller and finally we will find out the velocity triangle for a centrifugal fan and blower. 

Basics of fan and blower 

As we have already discussed in our recent post that if a hydraulic machine delivers the working fluid i.e. air with a high static pressure and relatively lower velocity then that hydraulic machine will be termed as compressor and that compressor might be centrifugal compressor or axial flow compressor. 

At the outlet of compressor, the working fluid will have high energy in the form of high static pressure and relatively lower velocity or kinetic energy. 

Suppose, if our requirement is to secure the air from a hydraulic machine with high velocity of flow or with high kinetic energy and lower static pressure, then we will use fans and blowers. 

Therefore, fans and blowers are those turbomachines which will deliver the air at high flow velocity and with relatively much lower static pressure. 

Centrifugal fan and blower

For relatively high-pressure applications, centrifugal fans and blowers are used.  Following figure displayed here indicates the various important components of a centrifugal blower. 

Centrifugal fan and blower 

A centrifugal blower will have an impeller, volute casing, inlet and outlet as displayed in the given figure of centrifugal blower. 

Centrifugal blower impeller will have blades fixed between the inner and outer diameters. Impeller might be fixed over the extended portion of motor shaft at its given sheet or impeller could also be fixed over a separate shaft which will be supported by two additional bearings and this shaft will be coupled with the shaft of electric motor for transmitting the mechanical energy to the impeller shaft and hence impeller. 

Working fluid i.e. air or gas will enter in to the impeller axially through the inlet nozzle where working fluid will be accelerated slightly before it will enter to the impeller. 

Energy will be imparted to the working fluid by the rotating impeller in the terms of static pressure and kinetic energy. Further, working fluid coming out from the impeller will flow through the volute casing or spiral casing and some kinetic energy of the working fluid will be converted in to the static pressure depending upon the requirement at the outlet of the blower. 

Velocity triangle for a centrifugal fan and blower 

As we have studied earlier in our previous post that fans and blowers are same machines only the static pressure rise is different for fans and blowers. 

Now we will see here the velocity triangle, as displayed here in following figure, at inlet and outlet of different types of blades of an impeller of a centrifugal blower. 


Velocity triangle at inlet and outlet of different types of blades of an impeller of a centrifugal blower 

Let us first understand here the various nomenclatures that we are using here.  

u= Mean blade velocity at inlet = πD1N/60
u= Mean blade velocity at outlet = πD2N/60
V1 = Absolute velocity of air at inlet to rotor or impeller
V2 = Absolute velocity of air at outlet to rotor or impeller
Vr1 = Relative velocity of air at inlet
Vr2 = Relative velocity of air at outlet
Vω1 = Velocity of whirl at inlet or tangential component of absolute velocity of air at inlet
Vω2 = Velocity of whirl at outlet or tangential component of absolute velocity of air at outlet
Vf1 = Velocity of flow at inlet
Vf2 = Velocity of flow at outlet
α1=Absolute angle at inlet or outlet angle
α2=Inlet angle to the diffuser
β1=Inlet angle to the rotor or impeller blade
β2= Outlet angle to the rotor or impeller blade
m = Mass flow rate of air in Kg/sec  

Before understanding the velocity triangle at the inlet and outlet of different type of blades of an impeller of a centrifugal blower, we must have to see here the different types of impeller blades. 

Different types of impeller blades 

On the basis of outlet angle to the impeller blade i.e. β2, impeller blades are classified in to three types and these types of impeller blades are as mentioned here. 

Forward swept blade

Forward swept blades are displayed in above figure at the left-hand side. Curvature of such blades will be in the direction of rotation of impeller. Outlet angle to the impeller blade i.e. β2 will be more than 900 or we can say that for a forward swept blade, β2> 900

Forward swept blades will be used where relatively large flow rates and high-pressure rise are required.  

Radial blade 

Radial blades are also displayed in above figure. Such blades will be radial at its outlet, but at the inlet of such blades there will be curvature and this curvature will be in the direction of rotation of impeller. 

Therefore, we can say that radial blades will be radial outward but at the inlet, blades will be curved in the direction of rotation of the impeller i.e. forward swept. 

Outlet angle to the impeller blade i.e. β2 will be equal to the 900 or we can say that for a radial blade, β2 = 900

Radial blades are less prone to blockage, dust erosion and failure. Therefore, radial blades are used to handle the dust laden air or gas. In simple words, we can say that radial blades will be quite able to handle the working fluid i.e. air or gas contained with more impurities and dust. 

Backward swept blade 

Backward swept blades are displayed in above figure at the right-hand side. Curvature of such blades will be in the opposite to the direction of rotation of impeller. Outlet angle to the impeller blade i.e. β2 will be less than 900 or we can say that for a backward swept blade, β2 <900

Backward swept blades will be used where relatively lower flow rates and low-pressure rise are required. 

Velocity triangle 

Velocity triangle at the inlet for each type of blade, that we have discussed above, will be similar. 

Absolute velocity of air at inlet to impeller blade will be axial and it means that there will not be any tangential component of absolute velocity of air at inlet i.e. velocity of whirl at inlet (Vω1) will be zero. 

Entry of working fluid i.e. air or gas to the impeller blade will be same for each type of blade. 

Velocity triangle at the inlet of impeller blade has been displayed here in the given figure. 

Velocity triangle at the outlet of the impeller blade has been also displayed here in the given figure for each type of impeller blade. 

We can note down here the very important points from the velocity triangles as mentioned below. 

Vω2 > u2, if β2 >900, forward swept blades
Vω2 = u2, if β2 =900, Radial blades
Vω2 < u2, if β2 <900, Backward swept blades 

Value of Vω2 for a forward swept blade will be higher as compared with the value of Vω2 for a backward swept blade. 

(Vω2) Forward swept blade > (Vω2) Backward swept blade 

Now we will determine the work done by the impeller on air or energy transferred to the fluid and it could be written as mentioned here. 


E = m [Vω2u2- Vω1u1]  

As we have studied above that, Vω1= 0 

Therefore, Work done by the impeller on air or energy transferred to the working fluid will be given by following equation as mentioned below. 


E = m Vω2u

We can conclude here a very important point that work done by the impeller on air or energy transferred to the air will be more in case of forward swept blade as compared to that for backward swept blade. 

Therefore, we can say that forward swept blades will be used where we need more work and more flow will be required and more static pressure rise will be there. 

Therefore, we have seen here the basic concepts of fans and blowers, centrifugal fan and blowers, different types of impeller blades and finally we have also seen the velocity triangles at the inlet and outlet of different type of impeller blades. 

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Further we will find out, in our next post,.  


Reference:  

Fluid Machines, By Prof S.K. Som 
Image courtesy: Google   


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