Q&A forum: Centrifugal and Axial Fan Calculator

To answer your questions;

Have you read the technical help pages for the calculator: https://www.calqlata.com/productpages/00060-help.html & https://www.calqlata.com/productpages/00060-QandA.html

You must understand that this calculator is based upon the theory of Charles Innes - the original theorist for impeller design. All designs and theories today are based upon his work. But they apply only to the impeller, not the fan – as explained in the above technical help page. The bottom of that page provides a calculation result from this calculator, which compares favourably with a proprietary design, as it should.

This is the least understood by our customers of all theories, and usually takes a while to get used to the input-output data relationships. But you will get to understand it as you play.

Due to the difficulties our customers have understanding Innes’ theories, this has become our most verified and modified (input vs output) calculator, but it is exactly as Innes designed it. It works.

There are a number of reasons why any efficiency can be greater than 100%:
1) The input data is outside the bounds of the theory – so the answer is incorrect
2) The expected efficiency as defined by Charles Innes has been exceeded – the answer is correct
3) One of the input values is incorrect with respect to another input value – you need to play
4) Etc.

Please note: We only provide the calculator, which applies only to the impeller and is correct according the most recognised associated theory. It is up to its users to get the design configuration needed. That is the purpose of all of our calculators, you play with the input values until you get the output value you are happy with. I would, however, advise you to read the above links carefully, they are very helpful.

First I must point out that vi is the overall (theoretical) velocity generated in the air as it passes the inlet tip of the blade.
And vo is the overall (theoretical) velocity generated the in the air as it passes the outlet tip of the blade.
These can be seen in the calculator's diagram.
They are the [theoretical] air velocities across the impeller (only), according to Charles Innes' theory, which remains valid today. The drive power, which is not included in Charles' Innes theory is based upon that necessary to push a blade through air according to Bernoulli. Both of which are just theories, but they are well known and respected.
However, Charles Innes' theory has problems with 90° straight blades. The calculation results are not always reliable. This is reflected in the fact that 90° straight-bladed impellers induce pressure from only centrifugal flow. Not a particularly efficient design.

When efficiencies and casing design are included in the calculation, actual [fan assembly] output data is usually very different.

Fans' calculations are correct and accurate (according to the theory) for the impeller. The casing figures (pc, vc, ρc, Hc, Pc) are only as expected based upon relative [inlet and outlet - impeller and casing] areas.
Your Client is quite correct, however, to use the flow-rate and outlet cross-section to establish overall outlet velocity; vc (87.27) is a theoretical maximum.

Due to his use of 90° straight blades, your Client's design shows a low efficiency (head loss efficiency (%) {air or mechanical efficiency}: εᴴ = -236.095011), which will significantly affect performance.
If you divide vc by the two primary efficiencies achieved (-236.1 & -219.33) the outlet velocity will be about 16.8 m/s. If you then apply casing design efficiencies the actual velocity will no doubt drop by another 1/3rd (11 m/s). As I do not know your Client's casing design efficiency, this is just a guess.

The purpose of Fans was originally to provide the fan designer with a calculator for the impeller only. It is the only part of the fan design that can be accurately predicted with good reliability.
Normally a fan designer will play with the impeller calculations to achieve maximum; efficiency, head, pressure, flow, power, etc. as required, and then design his/her casing to minimise losses. The performance of the assembly (impeller and casing) will be that documented for their clients.
It is impossible for me to include the true effects of the casing as I have no way of knowing its peculiarities. The design ramifications are infinite. I included the casing input ‘Ac’ simply because so many of your clients have a problem separating impeller design from fan design. I'm not sure it was a good idea in hindsight, though.

Yes
If you blocked off the exit you would achieve maximum pressure, but it would not be that defined by the Fans Calculator.
The Fans calculator uses Charles Innes’ theory which relies on the flow of air across the inlet tip of the blades.
If you have no flow, the theory doesn’t apply.

Your client appears to be using lb, ft & R Imperial units in his calculation, together with an input value for Ra of 0.07666666

Metric:
Ri = 8.24992342 J/K/mol
RAM = 0.029324 kg/mol {air}
Ra = Ri/RAM = 281.336905617022 J/kg

Convert:
J > ft.lb = 0.73756215
K > R = 1.8
kg > lb = 2.20462262

Imperial:
Ri = 3.3804618085 ft.lb/R/mole {Ri x 0.73756215 ÷ 1.8}
RAM = 0.064648354 lb/mole {RAM x 2.20462262}
Ra = Ri/RAM = 52.28999061 ft.lb/lb

I would normally expect therefore, that his input value for Ra should be 52.28999061 for air

The problem is the requirement for a high outlet pressure relative to the desired flow rate.

A high (reversed) inlet angle (θᵢ) will artificially increase pressure for best results.

You can play with the input and output diameters and the impeller width to achieve the desired flow rate.

You should remember, however, that the Fans calculator only provides the performance characteristics of the impeller.
Alternatively, You could design an impeller that gives a lower pressure and higher flow-rate and then increase pressure and decrease flow rate by playing with the casing outlet dimensions (PV=RT).

We should point out that a casing outlet with cross-sectional area no smaller than the impeller outlet area will result in the lowest noise-level.

Our Fans calculator calculates the airflow and power consumption for an impeller.
You would have to design the casing/cowling yourself and calculate the effects that would have on the impeller performance.
The casing/cowling options are infinite and do not lend themselves to general calculations.

Fan technology is well established and proven to work for all blade angles that comply with Charles Innes' theory, which has been the industry standard since 1916
Impeller design is difficult to understand if you don't take the time to try and understand the basic principles.
Performance is as much dependent upon casing design as it is on the impeller. The Fan calculator only calculates the performance of the impeller.
It is difficult to accommodate casing design as the options are infinite. However, the principle design requirement for a casing is the relative areas between impeller outside perimeter and casing outlet. A larger casing outlet will assist flow, a smaller outlet will assist pressure.

The customer concerned set his blade outlet angle such that it is driving air back into the impeller with greater energy than his inlet angles are able to overcome. He has completely misunderstood the basic principles of driving air through an impeller and refuses to accept the fact.

Inlet blade angles greater than 90° will not drive air out through an impeller, they will drive it back into the inlet cavity.

Moreover, if you do not set your inlet blade angles shallow enough to provide sufficient positive outward drive to overcome inward drive from outlet blade angles greater than 90° the theory will become unstable, as would be such an impeller.

It is important you try to understand the behaviour of air as it passes through the fan. Whilst it is largely based on common-sense, if you ignore basic flow characetristics you will never get your impeller to work, theoretically or practically.

Please take look at the tips we provide in our technical help page

As a result of this question, CalQlata successfully carried out an internal verification based upon the energy required to shift such a mass.

Whilst it was considered prudent to re-issue the 'Fans' calculator now calculating the impeller speed (RPM) required to generate an entered value for volumetric flow rate based upon the required energy;
the aforementioned rule of thumb still applies.

The standard theory on centrifugal fans was generated by Charles H Innes in 1916 ("The Fan"), and it appears to have stood the test of time.
His theory is based upon the aerodynamics of the blade transferring air from the toe of the blade to the outer lip in a single revolution of the impeller.
He also states that the greater the number of blades the more uniform the flow; i.e. more of the airflow will be laminar (less turbulent). An infinite number of blades will generate the most uniform flow. However, he also states that this comes with increased skin friction.
At some point the losses from skin friction will exceed the inlet and outlet losses and a compromise is needed.
Innes suggests that six blades is the best for a low aspect ratio (<0.67) increasing to twelve blades for aspect ratios approaching one.
This recommendation is based upon his own (extensive) experience.

Twelve blades, however, may not be suitable for very large diameter impellers of high aspect ratios.
In my own (less extensive) experience, I have settled for five blades for aspect ratios of 0.5 increasing to an inlet pitch of similar dimension to the radial depth of the blade.
I would multiply the skin friction in the calculation by the number of blades and would also use a higher value than that suggested by Innes for frictional resistance (0.125) on the basis that 'used' fan blades (that have been in service for some time) will have slightly eroded surfaces (i.e. 0.15 to 0.2).
With regard the expected accuracy of the calculator, if Innes is correct, then the calculations in CalQlata's Fans calculator should be ±0%. But I would only consider this to be the case for properly designed impellers in dry air. Moisture in the air (>1%) can cause a reduction in efficiency. In normal everyday conditions, with a used fan that has been properly designed and maintained, I would expect an accuracy better than ±10% (i.e. ±4% to ±8%), but this does not include the effects of the inlet and outlet diffusers, which can improve or reduce the impeller's effective efficiency.

I (personally) have never seen a fan deliver more than its impeller volume per revolution unless the atmospheric outlet pressure is less than the inlet pressure (an effective vacuum). Therefore, I am unable to refute Innes' theory. I am happy, however, to leave this debate open to anybody that can show Innes' theory to be incorrect. Please let us know if you can do this mathematically and supported with practical evidence.

The theories in the calculator are correct for all sizes, i.e. for fans with impellers smaller than a millimetre to greater than 10m.
The problem with ever decreasing size is friction.

As your fan gets smaller the ratio of surface area with volume increases, and the smaller it gets the greater this ratio becomes.
If we use a pipe as an analogy:
Dia   Area               Volume           A:V        δε
24   150.7964474   1809.557368   0.083
23   144.5132621   1661.902514   0.087   4.167%
22   138.2300768   1520.530844   0.091   4.348%
21   131.9468915   1385.442360   0.095   4.545%
20   125.6637061   1256.637061   0.100   4.762%
19   119.3805208   1134.114948   0.105   5.000%
18   113.0973355   1017.876020   0.110   5.263%
17   106.8141502   907.9202769   0.120   5.556%
16   100.5309649   804.2477193   0.125   5.882%
15   94.24777961   706.8583471   0.13 0  6.250%
14   87.9645943   615.75216010   0.143   6.667%
13   81.68140899   530.9291585   0.154   7.143%
12   75.39822369   452.3893421   0.167   7.692%
11   69.11503838   380.1327111   0.180   8.333%
10   62.83185307   314.1592654   0.200   9.091%
 9   56.54866776   254.4690049   0.220   10.000%
 8   50.26548246   201.0619298   0.250   11.111%
 7   43.98229715   153.9380400   0.286   12.500%
 6   37.69911184   113.0973355   0.330   14.286%
 5   31.41592654   78.53981634   0.400   16.667%
 4   25.13274123   50.26548246   0.500   20.000%
 3   18.84955592   28.27433388   0.670   25.000%
 2   12.56637061   12.56637061   1.000   33.333%
 1   6.283185307   3.141592654   2.000   50.000%

In this case ‘δε' represents the increase in inefficiency over the previous size
As A:V increases the ratio of surface area to volume increases, and this increase is exponential. As you can see from the table when the pipe size falls to 3" the increase becomes rapid. Look at the difference between a 24" to 23" (4%) and that for 4" to 3" (25%)

Surface friction has a far greater effect on efficiency in a fan than it does in a pipe because the ratio of surface area (contact surface) is greater than in a pipe. Therefore, a similar table to that above for fans would show an even more marked increase at smaller diameters.

Centrifugal fans are less suited to smaller diameter for a number of reasons.
1) The surface area in contact with the flowing air is greater than for axial fans
2) The air is forced to change direction
3) The shape of the inlet and outlet ducts is not best suited for reducing frictional losses (circular is better than rectangular)

This is why centrifugal fans tend to be targeted for larger fans and axial configurations for smaller diameters
I am not saying you shouldn't try to design a small centrifugal fan if that best suits your purposes, simply that you take extreme care in its design. For example, the following should be considered:
1) Use a material with a very low surface friction (or coat the material, but bear in mind that the loss of the coating during the design life will result in a loss of efficiency).
2) Reduce the number of blades
3) Minimise the surface area of material in contact with the flowing air
4) Eliminate sudden changes in shape

For what it’s worth, if I were designing a very small high-performance fan, I would start with a multistage axial configuration (along with suitable venturies if I was looking for pressure as opposed to flow).

Follow-Up Email:

I believe that your input/output data is based upon the following units:
Input Data:
θᵢ,   45 {°}
θₒ,   120 {°}
Øᵢ,   0.02 {m}
Øₒ,   0.075 {m}
w,   0.01 {m}
ρᵢ,   1.165 {kg/m³}
pᵢ,   101322.5 {N/m²}
Ṯ,   291 {K}
g,   9.80663139 {m/s²}
Rₐ,   8.3143 {J/K/kg}
F,   0.125
N,   7000 {RPM}
Output Data:
Q,   0.004788 {m³/s} [287.28 l/min]
H,   38.207032 {m}
δp,   436.50484 {N/m²}
pₒ,   101,759.00 {N/m²}
ρₒ,   42.058538 {kg/m³}
ε,   47.55515 {%}
T,   0.002851 {N.m}
P,   4.394551 {N.m/s}
A,   0.001486 {m²}
v,   3.221569 {m/s}
Lˢ,   0.00427 {m}
Lᶠ,   0.035085 {m}
Lᵉ,   42.096188 {m}
vᵢ,   7.625286 {m/s}
vₒ,   28.734015 {m/s}
v₁ᵢ,   7.619792 {m/s}
v₁ₒ,   2.031945 {m/s}
v₂ᵢ,   7.330382 {m/s}
v₂ₒ,   27.488935 {m/s}
v₃ᵢ,   10.776012 {m/s}
v₃ₒ,   2.346287 {m/s}
v₄ᵢ,   -0.289409 {m/s}
v₄ₒ,   28.662079 {m/s}

With regard to your concerns about flow rate:
Q = 0.004788m/s = 287.28 l/min
A very good rule of thumb for any fan is that its impeller will pass its (contained) volume of air in one revolution.
If I apply this argument to the volume of your impeller, I get: 287.2593783 l/min
So the calculator and the rule of thumb both appear to be working correctly.
However, the above would only be achievable if chamber, impeller, inlet and outlet designs added nothing to the losses#. As mentioned before, their influence becomes significantly greater as the size of the fan reduces. Like you, I would expect closer to 100 l/min for a centrifugal pump of the size you are designing unless all aspects of the fan design were perfect in every way. In fact, even with the best possible materials and designs, I would not expect see better than 200 l/min for such a small (centrifugal) fan
With larger fans (i.e. 6" and greater), it should be much easier to achieve the calculated values.

May I venture a couple of comments on the input data?
The value of Rₐ is for the specific gas constant;
Rₐ (Rᵢ/RAM) = 283.5312934 J/K/kg
as opposed to ideal gas constant;
Rᵢ = 8.3143 J/K/mole
You can see how we use these symbols in our definitions page {https://www.calqlata.com/help-definitions.html > Gas Constant}
The differences you will notice are in outlet density {ρₒ}, the minimum area diffuser requirement {A} and all the velocities {v}

The recommended angle for the blade inlet should be used where possible as you will see improvements in efficiency, outlet pressure, outlet velocity and power consumption. Whilst I agree that such improvements are very small between 45° to 46.109°, every little helps when attempting to minimise defects (for such small fans).

I notice that the outlet angle (120°) has turned the blades from backward facing to forward facing (see https://www.calqlata.com/productpages/00060-help.html Fig 3). I am not sure if this was intentional (special requirements) but the smaller the outlet angle for a backward facing blade, the better its efficiency.
Using your customer’s input data with θᵢ = 46.109° and θₒ = 8° the efficiency increases from 47.5% to 72% and the power required to run the fan drops from 4.4W to 2W. Whilst you lose head and pressure the efficiency gain is greater than the loss.
By setting the outlet angle (θₒ) to 25° you achieve virtually the same head and pressure but with an efficiency of over 57% and a drop in power consumption of 25%

# Note: the efficiency quoted (ε {%}) is for blade design only