# Fan aerodynamics

It is not the intention of this book to give detailed data for the aerodynamic design of fans. As has been said elsewhere, it rather seeks to inform both manufacturers and users of the in­formation necessary at their common interface, so that correct choices are made to their mutual advantage.

Nevertheless, it is of value to cover the basics of the theory, to show what is and is not possible, It will also show the back­

Figure 3.1 Theoretical flow pattern in a centrifugal fan impeller with backward inclined bladed impeller

Energy in air at impeller exit = torque x angular displacement

= rate of change of (tangential momentum x radius x angular

Displacement)

= tangential momentum x radius x angular displacement

— m vw2 r2 to

In like manner the energy in air at impeller inlet

= m vw1 r, co

Now r, co = u., and r2 co = u2

Energy given to the air by the impeller

= m (vw2 U2 — vw1u.,)

 U2 and Q = nd2 b2
 Cot Я2 2U2 J
 Now, as: P=PVW2 P=PVw2
 7td, b
 Q
 MgH =m (v H^(«.
 U, — V»
 U0
 U, — V„
 U0
 Or
 The theoretical or Euler head H developed by the impeller is de­fined as the height to which the same weight of gas could be raised by an equal amount of work. Thus:
 P = pu2
 U, + ■
 -cot (180°-Я2)
 7td, b.
 Q

 In fan work it is usual to know the pressure developed (p = pgH) and therefore p = p(vw2 u2 — vw1 u.,). Under normal circumstances at the design duty, the air will en­ter the easiest way, i. e. radially and then vw1 =0. Thus:

 Figure 3.3 Theoretical flow pattern at impeller outlet for forward curved blades

 Equ 3.15

 P = PVW2 u2

 Considering the impeller in cross-section with a width at its tip of b2, it may be said that the volume of air or gas delivered per unit timeQ= n d2 b2 v{2. Now the impeller blades at the outlet may be either: A) Backward inclined (straight, curved, or aerofoil) as in Figure 3. 1. When U2 = Vw2 + Vf2 cot P2 Or Vw2 =U2-Vf2 COtP2

 Flow rate—Q Figure 3.4 Theoretical p-Q characteristics for different values of impeller dis­charge angle

 Equ 3.16

 This theoretical characteristic is a straight line with a downward slope. B) Radial (straight shrouded, open or backplate paddle, or radial tipped) as in Figure 3.2 when vw2 = u2 and vf2 = v2 P=pu22 Equ3.17 This theoretical characteristic is a horizontal straight line. C) Forward curved as in Figure 3.3 when vw2 — u2 = vf2 cot (180°-[32)

 Tangential whirl velocity at entry to the impeller blade. Both of these factors reduce the pressure that the fan is capable of pro­ducing, but they do not affect the efficiency. Friction losses These are caused by gas friction and also include volute losses. (The volute is that part of the fan which converts velocity energy into pressure energy. This is normally achieved by ar­ranging the discharge channel so that the cross-sectional area gradually increases, thus reducing the flow velocity.) Shock losses Losses arise at entry to, and exit from, the impeller blade be­cause the blade angles are only correct for the design duty. On both sides of this shockless flow condition losses will occur. Other losses • Leakage: occurs from discharge to suction and through the shaft entry hole. • Disc friction: due to the rotation of the impeller shroud and backplate within the gas. • Mechanical losses: caused by the bearing friction and fric­tion at any shaft seal. These losses differ from those of the previous three groups in that whilst they affect the overall ef­ficiency they do not alter the basic fan characteristic. The actual characteristic, with its losses are shown for a back­ward inclined impeller in Figure 3.5. Actual against theoretical

 Equ3.18

 This theoretical characteristic is a straight line with an upward slope. It will be seen that for a given speed of rotation and a given pres­sure, the volume flow rate is dependent on the width of the im­peller and the blade angle. Reputable centrifugal fan manufac­turers will have many different width ranges with varying blade numbers and outlet blade angles to meet all duties economi­cally. All these theoretical characteristics are shown in Figure 3.4. The theoretical pressure will be reduced by the following fac­tors, the aim of the fan engineer being to keep them to a minimum: Relative rotation losses In addition to the normal flow of fluid within the impeller, the iner­tia effect of the fluid causes a rotation of the fluid relative to the impeller. Also, when the impeller is mounted between bearings due to the effect of the rotating shaft, the fluid will have a definite

 Figure 3.8 Axial flow blade velocity triangles

 Figure 3.5 Deviation of actual fan characteristics for impeller having backward inclined vanes

 Figure 3.7 Characteristics for forward curved fan

Characteristics for radial and forward curved fans are shown in Figure 3.6 and Figure 3.7 respectively.

Important Note

It must be emphasised that all the above assumes straight flow into the impeller eye and consideration of the equations will show that if this is not the case then the pressure developed will be reduced.

Variable inlet vanes purposely use this fact to impart swirl in the direction of rotation. This can be progres­sively increased by closure of the vanes with a corre­sponding reduction in the pressure developed. There will of course be some additional friction losses. Further information is given in Chapter 6, Section 6.5.

More importantly, from the system designer’s view­point, it will be seen that if straight flow into the fan inlet is not achieved due to poor inlet connections, then the fan will not develop its test pressure. Insufficient straight ducting on the fan inlet side, sagging flexible connections, absence of straighteners in bends, and too tight bends can all be responsible. Where fans are mounted in plenum chambers there must be a suffi­cient distance from the fan inlet(s) to the chamber walls for the same reason.

Often the system designer is himself short of space. He may then have to provide less than ideal connections. A section on system effect factors (Chapter 5, Section 5.4) has therefore been included and this will enable the designer to make such allowances as are neces­sary in specifying the fan duty so that the required flow may be achieved.

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