# Decoding "efficiency" for mechanical draft fans

## Indoor air quality: In the industrial sector, efficiency is a hot topic, and one increasingly relevant to the design of mechanical draft fans

“Efficiency” is a buzzword in today’s economy. We are on a constant quest to improve efficiency in all aspects of our lives. We are obsessed with green energy, energy-efficient cars, the optimization of our power grid systems, and with improving the efficiency of our household appliances. Our daily interactions with everything around us demand that we become energy conscious. In the industrial sector, efficiency is also a hot topic, and one increasingly relevant to the design of mechanical draft fans.

Mechanical draft fans are used in heavy industrial process operations to move fluid medium from one point to another (See Figure 1). They create draft in a process system so that flow medium can be induced, forced, and boosted. These machines consume a large amount of power, so understanding their “efficiency” dynamics is important.

**Efficiency matters**

While there is a lot of talk about efficiency improvements, we often lose sight of how this parameter is derived and defined. Oftentimes, project specifications call for “efficiency” and competing fans are evaluated without proper qualifications and constraints. Equipment manufacturers are faced with the dilemma of deciding which efficiency rating to use when quoting to their clients. Often, projects are awarded based on superior efficiency ratings without giving much consideration to the way in which those ratings are derived.

Currently, there are many different types of fan efficiency ratings prevalent in discussions of draft fan engineering. For instance, a centrifugal fan is selected and sized for certain flow characteristics requiring a finite brake-horsepower. For a given point of operation, while the brake-horsepower remains the same, the efficiency may take different forms.

More specification is required, then, and ratings need to be explained and evaluated to see if they are relevant to the projects in question. This article explains each of these ratings and provides some working guidelines for assessing fan efficiency.

**Defining efficiency**

Efficiency is a calculated value. A fan’s total efficiency is defined as the ratio of theoretical air horsepower (AHP) to the actual brake-horsepower (BHP) input to the fan shaft. The equation that describes fan total efficiency can be expressed as:

Ƞ_{t }= (AHP/BHP) x 100

Losses between AHP and BHP can be attributed to skin friction, turbulence, leakage, and mechanical friction. So, total efficiency can also be expressed as a culmination of hydraulic, volumetric, and mechanical efficiency.

Ƞ_{t} = Ƞ_{h} x Ƞ_{v} x Ƞ_{m}

Ƞ_{h} = Hydraulic efficiency

Ƞ_{v} = Volume efficiency

Ƞ_{m} = Mechanical efficiency

Hydraulic efficiency accounts for the imperfection of the flow path. Volumetric efficiency takes into account leakage through shaft seals and recirculation around the inlet cones and fan casing. Mechanical efficiency accounts for mechanical losses in the bearing, coupling, and seals in a fan system.

Total efficiency can be used to calculate another important variable, a fan’s static efficiency, which is defined as the ratio of fan static pressure (FSP) to fan total pressure (FTP), multiplied by the fan total efficiency.

Ƞ_{s} = Ƞ_{t} (FSP/FTP)

FSP = Fan static pressure

FTP = Fan total pressure

It is important to note the difference between these two efficiencies. Fan total efficiency gives higher number while static efficiency calculates a lower number. Paradoxically, a calculated higher efficiency does not demand a lower horsepower motor. Motor horsepower requirement for a given fan stays the same. The efficiency numbers are really a fluid dynamics phenomenon. The higher total efficiency is a function of total pressure, which combines static and velocity pressure components, whereas static efficiency only accounts for static component.

**Deriving efficiency**

The power required to drive mechanical draft fans is viewed as parasitic load. Therefore, minimizing input power to the fan will offer direct economic benefit to the plants. The intellectual knowledge base about the power and efficiency is bound to help engineers to properly specify a fan and manufacturers to optimize and design a better fan.

The origin of production or consumption of power for fluid machinery has its roots in the fundamental thermodynamic relation:

w = -ʃ v dP

w = work

v = Specific volume

dP = Change in pressure

The AHP for a steady one-dimensional streamline flow can be derived from a classical energy equation, the simplified version of which can be mathematically expressed in the following form:

AHP = ṁw_{s} = ρQgh_{S}

Q = Volumetric flow rate, ft^{3}/s

ρ = Density, slugs/ft^{3}

h_{s} = Head, ft

However, the actual input power (BHP) to drive a fan is described by the following mathematical relation:

BHP = (Q x SP x K_{p})/ (CONST x Ƞ)

Ƞ = Efficiency, %

Q = Volumetric flow rate, ft^{3}/min

SP = Static pressure, “w.c.

K_{p} = Compressibility constant

CONST = conversion constant = 6362

BHP = Input power

Draft fan engineers are most familiar with this formula and use it frequently to rate a fan. This equation can also be used for calculating hydrodynamic horsepower in a ducted flow. Rearranging the equation to calculate for efficiency, efficiency then becomes:

Ƞ = (Q x SP x K_{p})/ (CONST x BHP)

As a practical expression, this equation shows that fan efficiency is a function of volume, system pressure, and input power to the fan shaft. The other factor that affects this relation is the compressibility (K_{p}) of the fluid. Compressibility accounts for relative volume change due to a change in pressure inside the fan casing. This number generally varies from 0.90 to 0.99 for mechanical draft fans.