Efficiency of the Compressor and Degree of Reaction

 The compressor in the aerospace sector generally is over 5MW of power. Here, axial flow compressors are used. An axial-flow compressor is a compressor consisting of sets of rotors and stators. It works by initially converting the kinetic energy gained by air particles in the rotor to pressure energy in the stator. 

The rotors and stators are cambered airfoils with or without the variable angle of attack. Rotors rotate around the axis while stators are fixed in their positions. 

 Earlier reciprocating engines were mostly used in the aviation industry which was not able to provide enough thrust for advanced aircraft. And which led to the introduction of axial flow turbine engines. Now, from the 90s to today the air efficiency of the compressor of a turbine engine has increased a lot due to development in technology such that it can achieve a compression ratio of 40:1. 

         These air compressors are having various uses in industrial sectors, aerospace sectors, and research use. Every sector compressor has its efficiency and power generation as per their use. In Industrial applications, a subsonic engine is used having a per stage pressure ratio of 1.05-1.2 and has an efficiency of 88-92% per stage. In the aerospace industry such as in engines and ships, engines are in the subsonic or transonic region. They have a pressure ratio of 1.15-1.6 with an efficiency of the air compressor 80-85%. In research, supersonic engines are used. Which have a very high-pressure ratio of 1.8-2.2, with an efficiency of the air compressor a little low as 75-85%.

 Compressor Efficiency formula

  The efficiency of compressors lies in the range of 80-95% depending on their usage and condition. A compressor efficiency formula is given as: 

This efficiency is always changing from the first usage to the last usage. It depends on the usage hours, any wear and tear happening in the compressor, quality of air being sucked, etc. 

Volumetric Efficiency of Compressor

         The volumetric efficiency of the compressor is the measure of how much a compressor can hold and act on that air. Mathematically it is the ratio of the volume of air sucked into the swept volume of cylinder/duct inside which blades are aligned.

        Polytropic Efficiency of Compressor

  Polytropic efficiency is the measure of the stage efficiency of the whole system. So, for compressors, it is the stage efficiency of a multistage compressor containing similar efficiency. Polytropic efficiency is defined as:

 Where, 

= polytropic efficiency

n = polytropic exponent / number of moles

k = isentropic component. 

Compressors have a polytropic efficiency of 80-85%. The polytropic efficiency of a compressor is also said to be aerodynamic efficiency as it does not include thermal effects. 

Degree of Reaction 

In determining the blades for a compressor degree of reaction is signified as a very important factor. It is also used to determine the proper machine for a particular use. It is defined as the ratio of isentropic heat drop in the rotor to isentropic heat drop in the stator.

Formulated as: 

For turbines and for pumps these definitions and formulas are quite different. For turbines, it is defined as isentropic enthalpy change in the rotor to isentropic enthalpy change in the stator. And for pumps, it is defined as static pressure rise in the rotor to static pressure rise in the stage. 

4 reaction values determine the efficiency of a compressor and its usage in large aspects. Those 4 reaction values are:

• 50% reaction: Stages with this degree of reaction are used in compressors having equal heat drops in the rotor and stator. Due to this the boundary layer separation does not occur in the blade surface avoiding stagnation pressure losses. 
• Less than 50% reaction: It determines that heat or pressure drop in the rotor is less than the same in the stator.
• Greater than 50% reaction: It is just the opposite of less than 50% reaction rate. It signifies that the heat or pressure drop in the rotor is more than the same in the stator. 
• Degree or Reaction is Zero: It is a special case that rarely occurs. It means that the complete pressure drop is in the stator. This implies that the stator is acting as a nozzle to convert pressure energy into kinetic energy. It occurs in impulse turbines. 

Conclusion

  The compressor used in the aerospace sector is generally an axial compressor that continuously pressurizes the air in its axial direction with the help of rotor and stator blades. Similar to turbines and pumps a compressor’s design is also evaluated based on its efficiency. Generally, axial flow compressors have an overall efficiency of 80-95% depending on their situation.

Volumetric efficiency, polytropic efficiency, isentropic efficiency, and degree of reaction, all affect the overall efficiency of a compressor. An axial-flow compressor uses about 50-60% of the power generated by turbines of the engine. 

The degree of reaction is another measure of the design quality of engines and pumps.