Efficiency compares the inputs used by a system to the outputs produced. It is a commonly used concept, but one which is prone to a great deal of misuse in many industries. This article provides insight into the parameter known as “efficiency,” how it’s calculated, and importantly, it’s uses and limitations in predicting blower energy consumption and comparing alternate system designs.

**What is Efficiency?**

In engineering, efficiency usually refers to the ratio of the work done or the energy developed by a machine, engine, etc., to the energy supplied to it. It is usually expressed as a percentage, although in most calculations it is used as a decimal. Efficiency is always less than 100%.

For any system, efficiency can be calculated simply:

This simplicity is deceptive. The discussion of blowers encompasses many different types of efficiency:

- Isentropic efficiency
- Polytropic efficiency
- Design point efficiency
- Average efficiency
- Wire-to-Air efficiency
- Bare blower efficiency

The frame of reference, the calculation method, and the operating point have a bearing on the value of efficiency. It’s easy to see that it’s important to define terms and parameters clearly in discussions or comparisons of blower efficiency.

The most common method for evaluating aeration blowers is isentropic efficiency. Isentropic compression is an ideal, reversible process. It is an adiabatic process; i.e., no heat transfer occurs. Real compression never meets these conditions, of course. However, if all calculations and comparisons for a given blower system are made based on the assumption of an isentropic process then comparisons will be accurate. Power calculations will also be correct if parameters are the same for calculating efficiency and calculating power.

The isentropic efficiency of a bare blower is the isentropic power of the discharge air divided by the input power.

Where:

%η_{s} = isentropic efficiency, percent

P_{s} = isentropic power of air stream, hp

P_{in} = actual power input to the blower or blower system, hp

q_{m} = mass air flow rate, lbm/min

k = ratio of heat capacities, c_{p}/c_{v}, = 1.4 for air at standard conditions

R_{air} = specific gas constant for air/water vapor mixture, = 53.51 ft∙lbf/lbm∙°R for air at

standard conditions

T_{i} = inlet temperature, °R = °F + 460

p_{d,i} = discharge and inlet pressure, psia = psig + barometric pressure

Where:

ρ = density, lbm/ft^{3}

q_{v} = volumetric flow rate, ft^{3 }/min

In the wastewater industry standard conditions are defined as 68 °F, 14.7 psia, and 36% relative humidity. The thermodynamic properties of air will differ at any other conditions. This will change the value of k as shown in Figure 1 and the specific gas constant as shown in Figure 2. The calculation of isentropic power normally uses the values of thermodynamic parameters at the blower inlet.

##### Figure 1. Variation of k with temperature and humidity.

##### Figure 2: Variation of R_{mix} with temperature and humidity.

The method and location of the power measurement must be identified to make the efficiency value useful. For example, power may be measured at the blower shaft to determine bare blower efficiency. Wire-to-Air efficiency, on the other hand, requires measurement of the electrical power preceding any drives, motors, or controls.

The isentropic efficiency of a bare bower may be calculated using basic measurements of temperature and pressure at the blower inlet and discharge:

Where:

T_{d} = discharge air temperature, °R

Polytropic efficiency compensates for the non-ideal behavior of real-world blowers. Instead of k, the polytropic exponent “n” is used in calculations.

Where:

n_{polytropic} = polytropic coefficient, percent

Although polytropic efficiency is theoretically more accurate than isentropic efficiency, isentropic efficiency is used more often. In most cases the difference in projected power and performance is insignificant compared to measurement errors, assumptions, and other inaccuracies.

**Uses of Efficiency**

It is often necessary to estimate the power consumption of a blower system under varying operating conditions. For example, determining the cost effectiveness of increased aeration diffuser submergence requires estimating the increase in power consumption at higher discharge pressure. Aeration systems typically operate over a wide range of airflows due to seasonal and diurnal load changes. Variations in flow normally generate variations in blower discharge pressure too.

If the blower system efficiency at an evaluation point is known, it is a simple matter to calculate the power.

The calculation of total system power consumption should use Wire-to-Air efficiency.

Where:

%η_{wa} = wire to air efficiency of system, percent

%η_{s} = isentropic efficiency of bare blower, percent

%η_{s} = efficiency of motor, percent

%η_{s} = efficiency of variable frequency drive (VFD), percent

Electric power is measured in kW and electric energy is billed in kilowatt hours (kWh). Power draw must be converted from horsepower (hp) to kW and multiplied by the number of hours in the period to determine cost.

kW = hp . 0.746

In many evaluations it is sufficient to use average flow rate, average pressure and composite (average) power cost to determine the annual energy expense. For more exact cost determinations the values of on-peak, off-peak, and demand charges for electric power should be used. Exact evaluation also requires using flow rates expected for these various billing periods. Additional information about duty cycle variations can be obtained in a previous article, Control Efficiency Article.

Efficiency is often used to compare blowers from different suppliers, or to compare different technologies for blowers or the controls. The blower system with the highest efficiency will have the lowest power cost, all other things being equal.

It is all too common for an efficiency comparison to be skewed by invalid procedures. For example, Wire-to-Air efficiency should not be compared to bare blower efficiency. If a blower has high efficiency but insufficient turndown the actual power consumption over the process operating range may be higher than a more flexible system with lower efficiency. In that case the most efficient blower may not provide the lowest power consumption. Ultimately the owner’s energy cost is based on energy consumption, not efficiency. Comparing average efficiency to design point efficiency can also result in false conclusions.

Using efficiency correctly for both power projections and blower comparisons requires engineering judgement. Calculation results should be taken as approximations if the factors that affect efficiency aren’t identical or well defined for all evaluations.

**Factors that Affect Efficiency**

There are many factors that affect efficiency. Mechanical design and quality, of course, are significant influences. However, even for a given blower, efficiency is not a constant.

One of the most common, yet often overlooked influences on efficiency is the variation in inlet air conditions. Inlet air temperature changes air density, affecting efficiency. Relative humidity, which affects the air’s molecular weight, also has an effect. Both factors change the relationship between volumetric airflow, which is the key parameter for determining blower efficiency, and oxygen delivered to the aeration system, which is the key parameter for determining aeration process performance.

##### Figure 3: Blower efficiency varies with flow, temperature and humidity.

The efficiency of a blower system will change as the airflow rate changes. Dynamic blowers often have the best efficiency point (BEP) near the design flow rate, and the efficiency drops as airflow decreases. The maximum efficiency a of lobe type PD blower occurs at maximum airflow rate. Screw type PD blowers, on the other hand, often have their BEP near the middle of the airflow range.

Pressure also influences efficiency. For constant-speed centrifugal blowers the efficiency at a given volumetric flow rate is nearly constant, regardless of changes in discharge pressure. PD blowers decrease in efficiency when discharge pressure rises because internal leakage (slip) increases at higher pressure ratios.

**Importance of Control**

Perhaps the most neglected influence on blower system efficiency is the control method used to modulate flow rate.

PD blower airflow can only be changed by varying speed. The influence of control method on PD blower efficiency is not a consideration. The efficiency of centrifugal blower systems, however, changes with control method. This is particularly evident at the low-flow segment of the operating range.

There are three methods in common use for controlling dynamic blower airflow. The oldest method is inlet throttling. Butterfly valves are used to create a pressure drop upstream of the blower inlet, shifting the performance curve. This is the least efficient control method as shown in Figure 4.

##### Figure 4: Efficiency variation with control method.

The most efficient method for modulating a centrifugal blower is variable speed, which is almost exclusively accomplished by using a Variable Frequency Drive (VFD). Much of the high efficiency attributed to turbo blowers (gearless single stage centrifugals) is due to the use of variable speed for control.

Guide vane controls, inlet and/or discharge, are the most common control method for geared single stage blowers. The efficiency of guide vanes is between that of throttling and VFD control. The use of VFDs on large blowers has historically been limited because of the economics associated with medium voltage (600 < V < 6000) VFDs. As technology and cost structures change, however, variable speed control of large geared centrifugal blowers will probably become more common.

VFD control can be used with any type of dynamic blower, including geared single stage and multistage designs. Any limitations on VFD application are due to economics, not thermodynamics.

**Summary**

Blower system efficiency can be defined as the ratio of output power to input power. This is deceptively simple. The underlying thermodynamics and blower performance characteristics are actually complex.

The term “efficiency” is widely used and widely misused in blower evaluations. When properly defined and properly implemented efficiency can be a valuable parameter in predicting blower energy consumption and comparing alternate system designs.

When performing blower evaluations it is imperative to remember that no blower system has one “efficiency” value applicable across the entire operating range. Inlet conditions, relative air flow rate, and pressure variations all change the efficiency and the evaluation. Control method selection is particularly critical to optimizing system performance.

For more information contact Tom Jenkins, President, JenTech Inc., email: info@jentechinc.com or visit www.jentechinc.com. Mr. Jenkins has texts now available in hardcopy and electronic versions titled “Aeration Control” and “Facility Design” (visit www.wiley.com).

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