An axial fan is a type of fan that causes gas to flow through it in an axial direction, parallel to the shaft about which the blades rotate. The flow is axial at entry and exit. The fan is designed to produce a pressure difference, and hence force, to cause a flow through the fan. Factors which determine the performance of the fan include the number and shape of the blades. Fans have many applications including in wind tunnels and cooling towers. Design parameters include power, flow rate, pressure rise and efficiency.
Axial fans generally comprise fewer blades (two to six) than centrifugal fans. Axial fans commonly have larger radius and lower speed (ω) than ducted fans (esp. at similar power. Stress proportional to r^2).
Calculation of parameters
Since the calculation cannot be done using the inlet and outlet velocity triangles, which is not the case in other turbomachines, calculation is done by considering a mean velocity triangle for flow only through an infinitesimal blade element. The blade is divided into many small elements and various parameters are determined separately for each element. There are two theories that solve the parameters for axial fans: Slipstream Theory Blade Element Theory
Slipstream theory
In the figure, the thickness of the propeller disc is assumed to be negligible. The boundary between the fluid in motion and fluid at rest is shown. Therefore, the flow is assumed to be taking place in an imaginary converging duct where: D = Diameter of the Propeller Disc. Ds = Diameter at the Exit.
In the figure, across the propeller disc, velocities (C1 and C2) cannot change abruptly across the propeller disc as that will create a shockwave but the fan creates the pressure difference across the propeller disc. and
The area of the propeller disc of diameter D is:
The mass flow rate across the propeller is:
Since thrust is change in mass multiplied by the velocity of the mass flow i.e., change in momentum, the axial thrust on the propeller disc due to change in momentum of air, which is:
Applying Bernoulli's principle upstream and downstream:
On subtracting the above equations:
Thrust difference due to pressure difference is projected area multiplied by the pressure difference. Axial thrust due to pressure difference comes out to be:
Comparing this thrust with the axial thrust due to change in momentum of air flow, it is found that:
A parameter 'a' is defined such that -
where
Using the previous equation and "a", an expression for Cs comes out to be:
Calculating the change in specific stagnation enthalpy across disc:
Now, Ideal Value of Power supplied to the Propeller = Mass flow rate * Change in Stagnation enthalpy; where
If propeller was employed to propel an aircraft at speed = Cu; then Useful Power = Axial Thrust * Speed of Aircraft;
Hence the expression for efficiency comes out to be:
Let Ds be the diameter of the imaginary outlet cylinder. By Continuity Equation;
From the above equations it is known that -
Therefore;
Hence the flow can be modeled where the air flows through an imaginary diverging duct, where diameter of propeller disc and diameter of the outlet are related.
Blade element theory
In this theory, a small element (dr) is taken at a distance r from the root of the blade and all the forces acting on the element are analysed to get a solution. It is assumed that the flow through each section of small radial thickness dr is assumed to be independent of the flow through other elements.
Resolving Forces in the figure -
Lift Coefficient (CL) and Drag Coefficient (CD) are given as -
Also from the figure -
Now,
No. of Blades (z) and Spacing (s) are related as, and the total thrust for the elemental section of the propeller is zΔFx.
Therefore,
Similarly, solving for ΔFy, ΔFy is found out to be -
and
Finally, thrust and torque can be found out for an elemental section as they are proportional to Fx and Fy respectively.