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Designing
Air Flow Systems |
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A theoretical
and practical guide to the basics of designing air flow systems. |
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1.
Air Flow 1.1.
Types of Flow 1.2.
Types of Pressure
Losses or Resistance to Flow 1.3.
Total
Pressure, Velocity Pressure, and Static Pressure 2.
Air Systems 2.1.
Fan Laws 2.2.
Air Density 2.3.
System Constant 3.
Pressure Losses of
an Air System 3.1.
Sections in Series 3.2.
Sections in Parallel 3.3.
System Effect 4.
Fan Performance
Specification 4.1.
Fan Total Pressure 4.2.
Fan Static Pressure 5.1.
Methodology 5.2.
Assumptions and
Corrections 6.
Problem # 1 – An Exhaust System 7.
Problem # 2 – A Change to the
System’s Air Flow Rate 8.
Problem # 3 – A Supply System |
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Flow of air or any other fluid is
caused by a pressure differential between two points. Flow will originate from an area of high
energy, or pressure, and proceed to area(s) of lower energy or pressure.
Duct air
moves according to three fundamental laws of physics: conservation of mass,
conservation of energy, and conservation of momentum.
Conservation of mass simply states that an air mass is neither created
nor destroyed. From this principle it follows that the amount of air mass
coming into a junction in a ductwork system is equal to the amount of air mass
leaving the junction, or the sum of air masses at each junction is equal to
zero. In most cases the air in a duct is assumed to be incompressible, an
assumption that overlooks the change of air density that occurs as a result of
pressure loss and flow in the ductwork. In ductwork, the law of conservation of
mass means a duct size can be recalculated for a new air velocity using the
simple equation:
V2 = (V1 * A1)/A2
Where V is velocity and A is Area
The law of energy conservation states that energy cannot
disappear; it is only converted from one form to another. This is the basis of
one of the main expression of aerodynamics, the Bernoulli equation.
Bernoulli's equation in its simple form shows that, for an elemental flow
stream, the difference in total pressures between any two points in a duct is
equal to the pressure loss between these points, or:
(Pressure loss)1-2 = (Total pressure)1 - (Total pressure)2
Conservation of momentum is based on
Laminar Flow
Flow
parallel to a boundary layer. In HVAC
system the plenum is a duct.
Turbulent Flow
Flow which is perpendicular and near
the center of the duct and parallel near the outer edges of the duct.
Most HVAC applications fall in
the transition range between laminar and turbulent flow.
1.2. Types of Pressure Losses or
Resistance to Flow
Pressure loss is the loss of total pressure in a duct or fitting.
There are three important observations that describe the benefits of using
total pressure for duct calculation and testing rather than using only static
pressure.
·
Only total pressure in ductwork always drops in the direction of flow.
Static or dynamic pressures alone do not follow this rule.
·
The measurement of the energy level in an air stream is uniquely
represented by total pressure only. The pressure losses in a duct are
represented by the combined potential and kinetic energy transformation, i.e.,
the loss of total pressure.
·
The fan energy increases both static and dynamic pressure. Fan ratings
based only on static pressure are partial, but commonly used.
Pressure loss in ductwork has three components, frictional
losses along duct walls and dynamic losses in fittings and component losses in
duct-mounted equipment.
Component Pressure
Due to physical items with known pressure drops, such as
hoods, filters, louvers or dampers.
Dynamic Pressure
Dynamic losses are the result of changes in direction and velocity of air
flow. Dynamic losses occur whenever an air stream makes turns, diverges,
converges, narrows, widens, enters, exits, or passes dampers, gates, orifices,
coils, filters, or sound attenuators. Velocity profiles are reorganized at these
places by the development of vortexes that cause the transformation of
mechanical energy into heat. The disturbance of the velocity profile starts at
some distance before the air reaches a fitting. The straightening of a flow
stream ends some distance after the air passes the fitting. This distance is
usually assumed to be no shorter then six duct diameters for a straight duct.
Dynamic losses are proportional to dynamic pressure and can be calculated using
the equation:
Dynamic loss = (Local loss coefficient) * (Dynamic
pressure)
where the Local loss coefficient, known as a C-coefficient,
represents flow disturbances for particular fittings or for duct-mounted
equipment as a function of their type and ratio of dimensions. Coefficients can be found in the ASHRAE Fittings
diagrams.
A local loss coefficient can be related to different
velocities; it is important to know which part of the velocity profile is
relevant. The relevant part of the velocity profile is usually the highest
velocity in a narrow part of a fitting cross section or a straight/branch
section in a junction.
Frictional Pressure
Frictional losses in duct sections are result from air viscosity and
momentum exchange among particles moving with different velocities. These losses also contribute negligible losses or gains in air systems unless there
are extremely long duct runs or there are significant sections using flex duct.
The easiest way of defining frictional loss per unit length
is by using the Friction Chart (ASHRAE, 1997); however, this chart (shown below) should be used for
elevations no higher of 500 m (1,600 ft), air temperature between 5°C and 40°C
(40°F and 100°F), and ducts with smooth surfaces. The Darcy-Weisbach Equation should be used for “non-standard” duct type such as flex
duct.
Friction Chart (ASHRAE HANDBOOK, 1997)
1.3. Total Pressure, Velocity Pressure, and Static
Pressure
It is convenient to calculate pressures in ducts using as a
base an atmospheric pressure of zero. Mostly positive pressures occur in supply
ducts and negative pressures occur in exhaust/return ducts; however, there are
cases when negative pressures occur in a supply duct as a result of fitting
effects.
Airflow through a duct system creates three types of
pressures: static, dynamic (velocity), and total. Each of these pressures can be
measured. Air conveyed by a duct system imposes both static and dynamic
(velocity) pressures on the duct's structure. The static pressure is responsible
for much of the force on the duct walls. However, dynamic (velocity) pressure
introduces a rapidly pulsating load.
Static pressure
Static pressure is the measure of the potential energy of a
unit of air in the particular cross section of a duct. Air pressure on the duct
wall is considered static. Imagine a fan blowing into a completely closed duct;
it will create only static pressure because there is no air flow through the
duct. A
balloon blown up with air is a similar case in which there is only static
pressure.
Dynamic (velocity) pressure
Dynamic pressure is the kinetic
energy of a unit of air flow in an air stream. Dynamic pressure is a function of
both air velocity and density:
Dynamic pressure = (Density) * (Velocity)2 / 2
The static and dynamic pressures are mutually convertible;
the magnitude of each is dependent on the local duct cross section, which
determines the flow velocity.
Total Pressure
Consists of the pressure the air exerts in the direction of
flow (Velocity Pressure) plus the pressure air exerts perpendicular to the
plenum or container through which the air moves. In other words:
PT = PV + PS
PT = Total Pressure
PV = Velocity Pressure
PS = Static Pressure
This general rule is used to derive what is called the Fan
Total Pressure.
See the section entitled Fan Performance Specifications for a definition
of Fan Total Pressure and Fan Static Pressure.
For kitchen ventilation applications an air system consists
of hood(s), duct work, and fan(s). The relationship between the air flow rate
(CFM) and the pressure of an air system is expressed as an increasing
exponential function.
The graph below shows an example of a system curve. This curve shows
the relationship between the air flow rate and the pressure of an air
system.
Complex systems with branches and junctions, duct size
changes, and other variations can be broken into sections or sub-systems. Each section or
sub-system has its own system curve. See the diagram below for an illustration of
this concept.
Use the Fan Laws along a system
curve. If
you know one (CFM, S.P.) point of a system you could use Fan Law 2 to determine
the static pressure for other flow rates. They apply to a fixed air system. Once any element of
the system changes, duct size, hood length, riser size, etc.. the system curve
changes.
CFM x RPM
x
Fan Law 1
------- =
-------
CFM known RPM known
SP x CFM2 x RPM2x
Fan Law 2
------ = ------- = -------
SP known CFM2known RPM2known
BHPx CFM3x RPM3x
Fan Law 3
------ = ------- =
-------
BHPknown CFM3known
RPM3known
Other calculations can be utilized to maneuver around a fan
performance curve.
For example, to calculate BHP from motor amp draw, use the following
formula:
1 phase motors
3 phase
motors
BHP = V * I * E * PF
BHP = V * I * E * PF * 1.73
746
746
where:
BHP = Brake Horsepower
V = Line Voltage
I = Line Current
E = Motor Efficiency (Usually about .85 to .9)
PF = Motor Power Factor (Usually about .9)
Once the BHP is known, the RPM of the fan can be
measured. The
motor BHP and fan RPM can then be matched on the fan performance curve to
approximate airflow.
The most common influences on air density are the effects
of temperature other than 70 °F and barometric pressures other than 29.92” caused by
elevations above sea level.
Ratings found in fan performance tables and curves are
based on standard air. Standard air is defined as clean, dry air
with a density of 0.075 pounds per cubic foot, with the barometric pressure at
sea level of 29.92 inches of mercury and a temperature of 70 °F. Selecting a fan to operate at conditions
other then standard air requires adjustment to both static pressure and brake
horsepower. The volume of air will not be affected in a
given system because a fan will move the same amount of air regardless of the
air density. In other words, if a fan will move 3,000 cfm at 70 °F it will also move 3,000 CFM at 250 °F. Since 250 °F air weighs only 34% of 70°F air, the fan will require less BHP but it will also
create less pressure than specified.
When a fan is specified for a given CFM and static pressure
at conditions other than standard, the correction factors (shown in table below)
must be applied in order to select the proper size fan, fan speed and BHP to
meet the new condition.
The best way to understand how the correction factors are
used is to work out several examples. Let’s look at an example using a
specification for a fan to operate at 600°F at sea level. This example will clearly show that the fan
must be selected to handle a much greater static pressure than specified.
Example #1:
A 20” centrifugal fan is required to deliver 5,000 cfm at 3.0 inches
static pressure. Elevation is 0 (sea level). Temperature is 600°F. At standard conditions, the fan will require
6.76 bhp
1.
Using the chart below, the correction factor is 2.00.
2.
Multiply the specified operating static pressure by the correction factor
to determine the standard air density equivalent static pressure. (Corrected static
pressure = 3.0 x 2.00 = 6”. The fan must be selected for 6 inches of
static pressure.)
3.
Based upon the performance table for a 20 fan at 5,000 cfm at 6 inches
wg, 2,018 rpm is needed to produce the required performance.
4.
What is the operating bhp at 600 °F?
Since the horsepower shown in the performance chart refers
to standard air density, this should be corrected to reflect actual bhp at the
lighter operating air.
Operating bhp = standard bhp ¸ 2.00 or 6.76 ¸ 2.00 = 3.38 bhp.
Every air system or sub-system has a system constant. This constant can
be calculated as long as you know one (CFM, Static Pressure) point. You use a
variation of the fan laws to calculate the system constant. To calculate the
system constant:
K system = S.P./(CFM)2