Important Aspects of Centrifugal Compressor Testing – Part 2

This is the final part of a two part Tip of the Month (TOTM) series on important aspects related to centrifugal compressor performance testing.  The first part dealt with the review of the testing procedure presented in ASME PTC-10 (also referred to as the Code), selection criteria for test gases and factors to consider in a performance testing.  This TOTM will review the basic assumptions and performance relationships required for an accurate test.  Also discussed are three important principles: volume ratio, Machine Mach Number and Machine Reynolds Number, which also influence the accuracy of the test results.

Introduction
The Code recognizes that the actual testing conditions and the specified design conditions may not be identical.  Basic assumptions are made so that test results can be compared to the original design or some other baseline datum.  For example, a compressor can have a different efficiency depending on where it is operating on a head-flow curve.  However, if the gas composition and operating condition are not the same as the original design, then how accurate are the results?  This question will be discussed below.

There are other important parameters utilized by the Code to analyze compressor performance.  The first two are called flow coefficient and work coefficient.  These are dimensionless parameters that are useful in the interpretation of test results, especially when comparing the test results to the original design or some other datum.  Three more important parameters are called volume ratio, Machine Mach Number, and Machine Reynolds Number. These parameters assure that the aerodynamic properties of a compressor are maintained whenever test gases or alternate operating conditions are used.  In addition, they establish limits on the operating range and help correct head and efficiency for friction losses.   Each parameter will be briefly discussed.

Dimensionless Parameters
Most likely the actual testing conditions and specified design conditions are not identical.  To compensate for the differences, the Code utilizes dimensionless parameters called flow coefficient, work coefficient and total work coefficient.   The Code also makes assumptions regarding each coefficient and their equivalency at test and specified conditions.  Table 1 lists the Code’s principle parameters and the assumptions used to convert test data into values at specified design conditions.

Changes in compressor performance can be determined whenever the speed fluctuates by simply utilizing the affinity laws.  If the compressor flow, head and efficiency characteristics are known at a given speed, then merely applying the affinity laws at an alternate speed will produce a new curve representing the compressor performance at that speed.   This is the same concept behind head and flow coefficients.  In essence, the flow coefficient represents the “normalized flow rate” of the compressor at any speed.  Similarly, the work coefficient and total work coefficient represents the “normalized head” of the compressor at any speed.  The affinity laws also imply that the efficiency represented at the two equivalent conditions will remain the same.  These properties play a major role in shop and field testing of centrifugal compressors.

Table 1
Dimensionless Parameter Assumptions

Dimensionless Parameter1	Description	Mathematical Description1
Flow coefficient	Flow coefficient of the test gas and specified gas are equal using ideal and real gas methods.
Work input coefficient – enthalpy method	Work input coefficients of the test gas and specified gas are equal.  Ideal or real gas laws apply.
Work input coefficient – isentropic or polytropic methods	Work input coefficient of the test gas is corrected for the Machine Reynolds Number to obtain the specified work input coefficient.  Ideal or real gas laws apply.
Efficiency –isentropic or polytropic methods	The efficiency at the test operating condition is corrected by the Machine Reynolds Number to obtain the specified operating condition.
Total work input coefficient – heat balance or shaft balance methods	The total work input coefficient is equal for test and specified gases.

NOTE:
1.     See ASME PTC-10 for complete mathematical description of the coefficients.

Basic Performance Relationships

The Code recognizes three methods of determining compressor work (also called head).  The first is the enthalpy method and is defined by Equation 2.  It represents the difference in the inlet and discharge enthalpy, and results in theactual work supplied to the gas.  The next method of determining work is by the isentropic method.  This method only determines the ideal compressor work and may be calculated utilizing Equation 3 and 4.  The last relationship for determining compressor work is the polytropic method.  Only the ideal work is found by this method and may be calculated using Equations 5 and 6.  All three methods are commonly used by compressor users and manufacturers.

Volume Ratio
The volume ratio is an important aerodynamic parameter.  It maintains similar flow conditions as gas properties and operating conditions change.  The best way to describe volume ratio is to consider a multi-stage compressor.  The mass of gas entering the first impeller must equal the mass entering other impellers.  However, the actual gas volume entering the first stage is not the same for other impellers.  The gas is compressed and heated, which results in a reduction of volume.  If the gas properties and operating conditions of the test gas are different from the specified gas, then the volume entering and leaving each stage will also be different.  Therefore, to duplicate the aerodynamic performance of a compressor at the specified design condition it is important to simulate the equivalent flow of gas through the impellers by carefully matching the volume ratio.

A centrifugal compressor performance test is frequently performed with a gas other than the specified gas.  In addition, the compressor may operate at conditions other than the original design.  To assure an accurate performance test that simulates the original design, the volume ratio of the specified gas must match the volume ratio of the test gas at the respective operating conditions.  Equations 1-6 can be used to determine the conditions that match the test and specified volume ratio.  The Code sets limits on deviations of the test gas properties and operating conditions, which is found in Table 2 of Part 1.

Seven variables define the volume ratio relationship between a test gas and the specified gas.  The variables and the influence each has to increase or decrease the volume ratio is shown in Table 2.  For example, if the k-value of the test gas is greater than the specified gas, the volume ratio will decrease.  Similarly, if the test gas suction temperature is less then the volume ratio will increase.  Also note another important fact, and that is changes in the suction pressure of the test gas have no effect on volume ratio.

Table 2 – Variable Influence on Volume Ratio

As previously mentioned, the volume ratio of the specified gas must match the volume ratio of the test gas.  So if each of the physical properties of the test gas can change the volume ratio, what can be done so that the two volume ratios match?  A common practice is to change the test speed to compensate for the mismatch of volume ratios.  This practice is illustrated in Figure 1.  Note how the compressor speed is decreased so that the volume ratio changes imposed by other variables add up to zero.

In summary, the operating conditions and physical properties of a performance test should be carefully examined.  It is critical that the test gas volume ratio closely match the volume ratio of the specified gas.  The closer the test gas volume ratio is to the specified gas, the more accurate are the performance test results.

Mach Number
The Mach number influences the maximum amount of gas that can be compressed for a given impeller speed.  The limiting flow is known as stonewall (also called choke flow) and is typically found on the compressor characteristic head-flow curve at maximum flow condition for a given speed.  As the gas flow rate increases so does the velocity within the compressor’s internal flow path until it approaches the fluid acoustic velocity, thus limiting the flow.  Therefore, gas velocities that approach a Mach number of one indicate choke flow inside the compressor.

The Code defines a term called the Machine Mach Number which is the ratio of the outlet blade tip velocity of the first stage impeller to the acoustic velocity at inlet conditions.  The Code also sets allowable limits on the deviation between the specified and test gas Machine Mach Numbers.  This helps assure the accuracy of the performance test.  When shop testing a compressor, the Machine Mach Number at the operating condition is calculated and compared to the difference of the specified gas and test gas.  See Figure 2 for allowable deviation limits.  If the value exceeds the permitted deviation the test gas operating conditions may need adjusting to comply with to these limits.

Figure 2 – Allowable Deviations for Machine Mach Number

Reynolds Number
The effect that the Reynolds Number has on a compressor is similar to the effect it has on pipes.  The gas flowing through the internal passages of a compressor produce friction and energy loss which influences the machine efficiency. For centrifugal compressors, the Code defines a term called the Machine Reynolds Number and places limits on the allowable values during a performance test and is defined by Equation 8.  If the Machine Reynolds Number for the test condition and specified condition differs then a correction factor is applied to the test efficiency and head values. See Equation 9 for the correction factor.

The allowable Machine Reynolds Number departure limits between the test gas and specified gas are given in Figure 3.

By Joe Honeywell

Figure 3 – Allowable Machine Reynolds Number Departures
References

1. ASME PTC-10, “Performance test Code on Compressors and Exhausters”, 1997
2. Short Course “Centrifugal Compressors 201”, Colby, G.M., et al. 38th Turbomachinery Symposium, 2009.

Nomenclature