### 1.6.2. Polytropic Efficiency

The isentropic efficiency has one significant drawback in that there is no way to separate the fluid dynamic losses from the total (fluid dynamic + thermodynamic) losses. This means that devices having different pressure ratios will have different isentropic efficiencies even though they may both be of similar fluid dynamic quality. An example would be two compressors of different pressure ratios. The higher pressure ratio compressor will have a lower isentropic efficiency because of thermodynamic losses. This property can make it difficult to comparatively evaluate different compressor designs. A similar argument applies to turbine design.

To work around this drawback, the assumed "ideal" path followed by the process does not have to be isentropic. Instead, one can evaluate the polytropic efficiency by following a path along a line of constant efficiency. Aungier [65] discusses how a constant efficiency path on a T-s diagram can be approximated by the following equation:

| (1–41)

This equation can be rearranged to give the following two relationships:

| (1–42)

The entropy change along this path is evaluated by integrating the last expression:

| (1–43)

Rearranging this expression gives the value of the constant along the given path:

| (1–44)

In order to evaluate the polytropic efficiency, evaluate the polytropic enthalpy change along the alternative path defined by the path equation. First, start with the second law:

| (1–45)

The term is the polytropic work, or enthalpy change, and is what must be solved. First, the term is substituted using Equation 1–42 to give:

| (1–46)

Integrating this equation along the polytropic path gives:

| (1–47)

Note: The term has been renamed to to signify that the work is the polytropic enthalpy change.

The final form of the polytropic work is obtained by simply substituting for :

| (1–48)

Now that you have an expression for this enthalpy change, you can compute the polytropic efficiency:

| (1–49)

| (1–50)

The polytropic efficiencies are also evaluated relative to a selected inlet boundary condition and output by the flow solver as both local (at every node in the flow) and global (overall device) quantities.

Similar to the isentropic efficiency, total to total and total to static versions of the polytropic efficiency are similarly evaluated by replacing stagnation quantities at point 2 with static quantities.

Release 18.2 - © ANSYS, Inc. All rights reserved.