Dynamic Similitude Theory: Key to Understanding the ASME Compressors Performance Test
Authors: Key Bill 
Published: December 2007

Summary
Centrifugal compressors for gas-lift or injection stations in remote or inaccessible locations should be performance tested by the manufacturer before installation. Because the gas available to the manufacturer is quite different from that at the site, equations correlating test conditions to actual conditions are required.
Developed in the 1960's, the American Soc. of Mechanical Engineers' (ASME) Power Test Code-10 (PTC- 10) is the acknowledged industry standard defining these correlations. The physics and mathematics of these correlations are not contained in the code, which is typical of all industry standards.
All fluid flow is governed by the conservation equations of mass, energy, and momentum. The original authors of the code took this basic fact and developed the correlations that are essential for proper testing.

Introduction
The task of verifying a centrifugal compressor's performance at a manufacturer's facility is quite tedious and complicated. Engineers not normally involved in the process can be overwhelmed and confused by the ASME PTC-10, the document that establishes the test rules. Because the objective of the test code is to set forth the test rules, it does not provide the user with any theoretical explanation of why the test conditions are identical to operating conditions. Without this background, it is difficult to understand the test procedure and even more difficult to interpret the test results.
This paper explains the theory behind the PTC-10 and presents a practical application.

PTC-10 Test Objective
The objective of a PTC-10 test is to allow the compressor operator to verify that the machine will perform as specified: it will deliver the specified flow, at the specified inlet conditions, to the specified pressure rise, with the specified efficiency and speed (RPM). Hence, the four parameters that must be verified during testing are flow rate, pressure rise, efficiency, and speed.
Three different testing techniques (classes) are defined by the code. In Class 1, the test gas and specified gas, as well as inlet and outlet conditions, are identical. In Class 2, the test gas is not the same as the operating gas. The compressor test speed, pressure, temperature, and flow rates are all adjusted so that the test condition is dynamically equivalent to the specified condition. The test in Class 3 is identical to a Class 2 test, except that certain thermodynamic properties of either gas exceed the limits of Table 4 of the Code.
Since a Class 1 test is straightforward, a detailed explanation is not required. For Classes 2 and 3, PTC-10 stipulates that the following values, calculated from the test and specified conditions, be identical to within a few percentage points:volumetric flow ratio (dimensionless),capacity/speed ratio,Mach number (dimensionless), andReynolds number (dimensionless).
When these numbers are equal, dynamic similitude between the test and specified conditions is obtained.
A Class 3 test is performed when the ratio of specific heats, for either gas varies excessively from compressor inlet to outlet. Additionally, when either of two thermodynamic functions, X and Y (defined in later sections), exceeds certain values, a Class 3 test is required. The only actual differences that occur between these two classes are the equations used for calculating the compressor performance. In all other aspects, these classes are identical.
The process used to verify that the test and specified parameters are identical is as follows.Test conditions are selected so that dynamic similitude is achieved.The specified and test parameters of flow, pressure rise, efficiency, and speed are transformed to dimensionless numbers with the equations in PTC-10.The machine is then run with the test gas at the test flow rate, and the corresponding pressure rise is then measured. Compressor efficiency is calculated from the measured temperature rise.Comparisons between the test parameters and specified parameters are then made.
If the test values do not equal or exceed the specified values within limits agreed to by the purchaser, the manufacturer must take corrective action.