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Axial flow fan design

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Today

1. Background2. Dimensionless numbers3. Hub-to-tip ratio4. Velocity diagrams5. Free vortex velocity distribution6. Blade element theory7. Testing of axial flow fans

• The majority of this presentation comes from:• Dixon & Hall (2010)• Wilkinson (2017)• Bruneau (1994)

Turbomachinery

Axial flow fans (incompressible)

Axial flow cooling fans

• Axial flow fans are used to convey air for HVAC, ventilation or cooling.

Howden.com

Axial flow fans

Matimba power plant air-cooled condenser (ACC).

– 288, 9.1 m diameter, axial flow fans

– installed 45 m above ground level– Eskom currently building two new

4800 MW direct dry-cooled plants, Medupi and Kusile.

Axial flow fans

• Can have IGVs and or outlet stator• High flow, low pressure• 4 to 8 blades• Hub-tip ratio of 0.1 to 0.6• Flow axial in meridional plane• Inlet area = outlet area

Axial flow fans• Significant dimensionless numbers, derived using

Buckingham PI – theorem.

• For incompressible flow:

Axial flow fans• Significant dimensionless numbers, derived using

Buckingham PI – theorem.

• Power coefficient

• Flow coefficient

• Pressure coefficient

• Reynolds number

53

_

DρNPP =

3NDQφ =

22DNgHψ =

μρNDRe

2

=

Use fluid density to calculate

Incompressible flow machines

• The dimensionless numbers are applicable to:• A specific machine (scale the effect of speed and density).• And for a geometric similar one.

• The requirements for scale models tests are:• Geometric similarity (lengths).• Kinematic similarity (velocity).• Dynamic similarity (forces).

Dimensional Analysis• Efficiency:

• Since Φ, ψ and are dimensionless, efficiency is also dimensionless.

• The same for similar machines

Pφψ

DNgH

NDQ

PDρN

PρgHQη

=

××=

=

223

53

P

Dimensional Analysis• Specific speed:

• Start with:

• Eliminate D. We then get specific speed:

• Specific speed enables us to arrange similar machines in terms of speed - , flow – and pressure capacity. If we therefore have the pressure, flow rate and speed, we can get an indication of machine type and efficiency.

3NDQφ=

22DNgHψ =

radians

Dimensional Analysis• Specific speed (Csanady, 1964)

Dimensional Analysis• Specific diameter:

• Eliminate N. We get specific diameter:

Dimensional Analysis• The Cordier diagram (1953) is widely used:

Dimensional Analysis• The Lewis diagram (1996) is more explanatory:

Axial flow cooling fan• Typical design specification

Determined by cooling requirements of heat exchanger installation

Determined by efficiency, structural and noise limitations on fan installation

Determined by location of heat exchanger installation

Axial flow cooling fan• Typical fan curves

• Fan static pressure

Axial flow cooling fan• Typical fan curves

• Fan shaft power

Axial flow cooling fan• Typical fan curves

• Fan static efficiency

Axial flow cooling fan• Consider the use of the term fan “static pressure”

There are two terms used for fans, namely fan total pressure and fan static pressure:

Fan static pressure is actually fan total-to-static pressure. It is typically used in installations where the outlet kinetic energy of the fan is dissipated. Typical for ACCs where outlet air is dissipated.

Fan total pressure is actually fan total-to-total pressure and is used where the outlet kinetic energy of the fan plays a significant role in the system design. Typical for ducted fans where outlet energy can be recovered.

Note that efficiency is defined in the same manner

Axial flow fan

Note the condition of the inlet and outlet flow

• Velocity triangles• IGVs can lead to excessive inlet losses but does give

a well conditioned outlet flow.

Axial flow fan

• Velocity triangles for rotor-only fan

Axial flow fan

• Design process:• The most important part is to

start right to finish right.• The first step is to specify the

hub-to-tip ratio correctly.• Hub-to-tip ratio selected

based on the method of Van Niekerk (1958).

Axial flow fan

• Hub-to-tip ratio• Based on the work of Van Niekerk (1958) with modifications by

Bruneau (1994)• Calculates total-to-total and total-to-static efficiencies for different

hub-to-tip ratios at design point• The derivation of this equation is shown in the work of Bruneau

(1994).• Isolated foil theory is assumed, which requires the blade solidity to

be less than 0.7. If this is not the case, cascade theory has to be considered.

Axial flow fan

Hub-to-tip ratio

Hub swirl factor

Tip flow coefficient

Axial flow fan

• The following information is required in order to perform the calculation:

• Range of hub-to-tip ratios to be used, in this case 0.1 to 0.9• Design flow rate• Design fan total-to-static pressure• Tip radius• Fan rotational speed• Estimate of fan annulus efficiency• Estimate of aerofoil section drag to lift ratio

Axial flow fan

• The calculation assumes a free vortex velocity profile downstream of the fan. This means that:

Assuming zero inlet swirl

A first approximation for k is obtained by assuming ts efficiency of 60% and assuming that the static pressure rise at the average radius is equal to the fan static pressure.

Axial flow fan

• Fan annulus efficiency:

• Spanwise average airfoil lift-to-drag profile

• Simultaneously the hub swirl factor is limited to prevent backflow at the hub:

Axial flow fan

• Vortex design• The vortex design is by designing on an outlet swirl velocity distribution and

then applying simple radial equilibrium in order to determine the axial velocity distribution. The SREE is basically a balance of the radial forces due to curvature of the streamlines, with zero radial flow.

Axial flow fan

• Vortex design (repeated from Dixon & Hall)• Stagnation enthalpy can be written as:

• From thermodynamics

Axial flow fan

• Vortex design (repeated from Dixon & Hall)• The SREE now becomes:

• Assuming that the stagnation enthalpy and entropy stays constant w. radius

• Assuming incompressible flow

Axial flow fan

• Vortex design (repeated from Dixon & Hall)• Combining the previous equation and the SREE:

• Assuming constant total pressure distribution, we again get the previous equation:

• This last equation gives us the ability to derive an axial velocity distribution of a swirl distribution is given.

Axial flow fan

• Vortex design• It should be apparent that the vortex design is multi-

dimensional. The decision for swirl distribution is affected by many factors.

• The free- vortex distribution gives close to the optimum efficiency.

• The free vortex distribution might however result in excessive blade twist.

• At this stage it is required to sub-divide the blade span into a set number of radial sections.

Axial flow fan

• Example

Axial flow fan

• Blading design• Once the vortex distribution is fixed, the blading design can be completed.• The vortex design gives the required velocity triangles downstream of the

blade, at the different radial locations.• It is advisable to select a base profile for the design at this stage. This can

however be omitted and made part of the design question.• Isolated airfoil theory is used.• Blade profile properties (at the different radii) assume the average flow

conditions to prevail over the blade.

Axial flow fan

• Blading design• The blade loading factor is derived from Dixon by assuming the drag

contribution to be negligible:

• The loading factor therefore gives a balance between the chord length and blade section lift coefficient required to satisfy the velocity requirements.

• Five factors have to be considered:» Efficiency – higher speeds and chords lead to higher Re number, giving

higher resistance against stall. Centrifugal load should however be considered.

» Noise – higher solidity means possible lower running speed, less blades lead to less noise sources.

» Manufacture - shorter chords lead to easier manufacture.» Stability – extreme blade setting angles, close to stall should be avoided.» Cost – less blades

Axial flow fan

• Blading design• The design solution is therefore to have the minimum number of blades

(cost) at the highest possible speed (efficiency) with the largest manufacturable chord (manufacturing) far from stall (stability) at the minimum possible noise. The last requirements is often ignored.

• The chord distribution is therefore selected to be in the order ~1 m. The number of blades is then manipulated to give Lift coefficient values between 0.5 and 1.0.

• The fan efficiency is then estimated from:

Axial flow fan

• Blading design• Blade sectional properties can be obtained from published data or XFOIL:

Axial flow fan

• Blading design• For the efficiency estimation, the losses are given as:

• The drag coefficients are estimated from airfoil profiles that correlate to the calculated lift coefficient. The blade stagger angle is finaly defined from the sectional lift curve, as:

Axial flow fan

• Typical results

Axial flow fan testing

• Testing are performed using standardised airways. According to ISO 5801 part a, there are four standard test configurations.

• Type A: free inlet-outlet• Type B: Free inlet, ducted outlet• Type C: Ducted inlet, free outlet• Type D: Ducted inlet, ducted outlet

• The test configuration selected based on the eventual system configuration.

Axial flow fan testing

• For large diameter cooling fans, we use a Type A test facility:

Axial flow fan testing

• Fan is tested to scale at the same tip speed to maintain kinematic similarity.

• The flowrate is calculated as:

• The fan static pressure is calculated as:

• Fan shaft power

• and static efficiency is calculated as:

Axial flow fan testing

• Test results are scaled to standard speeds and density.

• Scaling is generally accurate if in fully turbulent region

Axial flow fan testing

• Scaled fan installed.• Attention is paid to repeatable accurate setting of the

blade angle.

Axial flow fan testing

• Fan test results: pressure curve• When matching a system to an experimental fan, make sure that the

matching is done correctly.

Axial flow fan testing

• Fan test results: efficiency• The correct efficiency can only be obtained if matching is done correctly.

Conclusion

1. Dimensionless numbers2. Hub-to-tip ratio3. Velocity diagrams4. Free vortex velocity distribution5. Blade element theory6. Testing of axial flow fans

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