Selecting the correct fan is as important as deciding how
that fan is controlled. Generally the OEM fans are of the best design and
quality, but there are a number of parameters that should be looked at when
choosing a
fan. Use the highest blade diameter possible, all things being equal, an 18"
diameter fan will outflow a 16" fan by nearly 20%, moreover, a larger radiator
surface area is covered. Secondly, a high peak to average motor current
indicates a high efficiency motor, a motor with a 3:1 peak to average current
ratio will consume 1/3 less current than one with a 2:1 ratio for the same
horsepower output. And finally, a 50% blade to open area ratio
provides the highest flow rate per horsepower, and both the high peak to average
current motor and the high blade to open air ratio blade provide higher
backpressure performance. . The table below will allow you to
determine if what you are buying provides the airflow that a given manufacturer
claims. Note that a less than 50% blade to open air ratio, as well as a
non-optimum blade design will flow less than the number given. Simply enter
the data into the red boxes below to indicate the calculated cfm. A mathematical
analysis is presented below the spreadsheet.
Ipeak/Irun: Peak to average current (most oems:3 or 4, most
aftermarket 2, Ramchargers 5)
Fan D: Fan diameter
Motor D : Motor diameter
Compressible Fluid Flow of an Electric Cooling Fan
Brian L. Baskin
Delta Current Control
All Rights Reserved
The Work of Kinetic Energy
The work output of a fan, neglecting turbulence losses is characterized by
the equation:
W = ½mv2
equation 1.0
Where W represents the work accomplished in joules, m represents the total
mass of the liquid or gas accelerated in kilograms, and v represents the change
in velocity of the gas in meters per second. The power consumed is represented
by the first derivative of work with respect to time and is shown below:
P = (½mv2)/t
equation 2.0
P = (½(m/t)v2)
equation 2.1
Where P represents the power needed to do an amount of work in joules per
second (watt) and t represents time in seconds.
The mass can be represented as volume if the density of the material is
known. The density of atmospheric gas, primarily nitrogen, oxygen, and argon is
equal to one cubic meter per kilogram or 35.31 cubic feet per kilogram. One cfm
then equals 1/2119 cubic meters per second or 1/2119 kilograms per second.
The terminal velocity is a product of cfm and outlet area, the output area of
a fan is characterized by the equation:
A = (1/39.37)2(p D2/4) = D2/1974
equation 3.0
Where A represents the output area in square meters and D represents the
total blade diameter in inches.
Terminal velocity can then be represented by volume in cubic meters per
second divided by the area and the equation:
v = (cfm/2119)/(D2/1974) = .932*cfm/D2
equation
4.0
The work over time is then represented in imperial units by the equation:
P = ½(cfm/2119)(.932*cfm/D2)2
equation 5.0
cfm = (4883* P*D4)1/3
Keep in mind that this represents an ideal fan without turbulence and with
uniform velocity.
Motor Efficiency
Unfortunately, not all of the power a motor receives is transformed into
work. Resistive, magnetic, and frictional losses all serve to lower the
efficiency of a motor.
Both magnetic and resistive losses can be represented as a single bulk
resistance in series with the load.
The ratio of bulk resistance to total series resistance can be found by
comparing the running current to the locked-rotor current.
RB/RT = IR/IP
equation 6.0
RB = (IR/IP)RT
equation
6.1
The ratio of load resistance to total series resistance is then the
difference between the total series resistance and the bulk resistance.
RL = RT(1-IR/IP)
equation
7.0
The ratio of bulk resistance to load resistance is then:
RB/RL = (IR/IP)/(1-IR/IP)
equation 8.0
RB = RL(IR/IP)/(1-IR/IP)
equation 8.1
RB = RLIR/(IP -IR)
equation 8.2
The ratio of Voltage across the load to the total voltage is proportional to
the load resistance divided by the total resistance and is represented by the
equation:
VL/VT = (1-IR/IP)
equation
9.0
The power received by the load is represented by the equation below:
PL = (Vin)(1-IR/IP)(IT)
equation 10.0
Frictional losses, proportional to rpm are represented by the equation:
PF = k(rpm/rpmmx)
equation 11.0
Where k is a friction constant. Because bulk to total resistance is dependant
on the same rpm to rpm max ratio, equation 11.0 can be represented by: