{"id":400,"date":"2010-09-01T21:51:18","date_gmt":"2010-09-01T21:51:18","guid":{"rendered":"http:\/\/www.jmcampbell.com\/tip-of-the-month\/?p=400"},"modified":"2011-06-02T14:23:29","modified_gmt":"2011-06-02T19:23:29","slug":"important-aspects-of-centrifugal-compressor-testing-part-2","status":"publish","type":"post","link":"http:\/\/www.jmcampbell.com\/tip-of-the-month\/2010\/09\/important-aspects-of-centrifugal-compressor-testing-part-2\/","title":{"rendered":"Important Aspects of Centrifugal Compressor Testing – Part 2"},"content":{"rendered":"

This is the final part of a two part Tip of the Month (TOTM) series on important aspects related to centrifugal compressor performance testing.\u00a0 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.\u00a0 This TOTM will review the basic assumptions and performance relationships required for an accurate test.\u00a0 Also discussed are three important principles: volume ratio, Machine Mach Number and Machine Reynolds Number, which also influence the accuracy of the test results.<\/p>\n

Introduction<\/strong>
\nThe Code recognizes that the actual testing conditions and the specified design conditions may not be identical.\u00a0 Basic assumptions are made so that test results can be compared to the original design or some other baseline datum.\u00a0 For example, a compressor can have a different efficiency depending on where it is operating on a head-flow curve.\u00a0 However, if the gas composition and operating condition are not the same as the original design, then how accurate are the results?\u00a0 This question will be discussed below.<\/p>\n

There are other important parameters utilized by the Code to analyze compressor performance.\u00a0 The first two are called flow coefficient and work coefficient.\u00a0 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.\u00a0 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.\u00a0 In addition, they establish limits on the operating range and help correct head and efficiency for friction losses. \u00a0\u00a0Each parameter will be briefly discussed.<\/p>\n

Dimensionless Parameters<\/strong>
\nMost likely the actual testing conditions and specified design conditions are not identical.\u00a0 To compensate for the differences, the Code utilizes dimensionless parameters called flow coefficient, work coefficient and total work coefficient.\u00a0 \u00a0The Code also makes assumptions regarding each coefficient and their equivalency at test and specified conditions.\u00a0 Table 1 lists the Code\u2019s principle parameters and the assumptions used to convert test data into values at specified design conditions.<\/p>\n

Changes in compressor performance can be determined whenever the speed fluctuates by simply utilizing the affinity laws.\u00a0 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.\u00a0\u00a0 This is the same concept behind head and flow coefficients.\u00a0 In essence, the flow coefficient represents the \u201cnormalized flow rate\u201d of the compressor at any speed.\u00a0 Similarly, the work coefficient and total work coefficient represents the \u201cnormalized head\u201d of the compressor at any speed.\u00a0 The affinity laws also imply that the efficiency represented at the two equivalent conditions will remain the same.\u00a0 These properties play a major role in shop and field testing of centrifugal compressors.<\/p>\n

Table 1 <\/strong>
\nDimensionless Parameter Assumptions<\/strong><\/p>\n\n\n\n\n\n\n\n\n
Dimensionless<\/strong>
\nParameter1<\/strong><\/td>\n		Description<\/strong><\/td>\nMathematical Description1<\/strong><\/td>\n<\/tr>\n
Flow coefficient<\/td>\nFlow coefficient of the test gas and specified gas are equal using ideal and real gas methods.<\/td>\n\"Equation\"<\/a><\/td>\n<\/tr>\n
Work input coefficient \u2013 enthalpy method<\/td>\nWork input coefficients of the test gas and specified gas are equal.\u00a0 Ideal or real gas laws apply.<\/td>\n\"Equation\"<\/a><\/td>\n<\/tr>\n
Work input coefficient \u2013 isentropic or polytropic methods<\/td>\nWork input coefficient of the test gas is corrected for the Machine Reynolds Number to obtain the specified work input coefficient.\u00a0 Ideal or real gas laws apply.<\/td>\n\"Equation\"<\/a><\/td>\n<\/tr>\n
Efficiency \u2013isentropic or polytropic methods<\/td>\nThe efficiency at the test operating condition is corrected by the Machine Reynolds Number to obtain the specified operating condition.<\/td>\n\"Equation\"<\/a><\/td>\n<\/tr>\n
Total work input coefficient \u2013 heat balance or shaft balance methods<\/td>\nThe total work input coefficient is equal for test and specified gases.<\/td>\n\"Equation\"<\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

NOTE:
\n1. \u00a0\u00a0\u00a0 See ASME PTC-10 for complete mathematical description of the coefficients.<\/p>\n

Basic Performance Relationships<\/strong><\/p>\n

\"Equations\"<\/a>
\n\"Equations\"<\/a><\/p>\n

The Code recognizes three methods of determining compressor work (also called head).\u00a0 The first is the enthalpy method and is defined by Equation 2.\u00a0 It represents the difference in the inlet and discharge enthalpy, and results in theactual<\/em> work supplied to the gas. \u00a0The next method of determining work is by the isentropic method.\u00a0 This method only determines the\u00a0ideal<\/em> compressor work and may be calculated utilizing Equation 3 and 4.\u00a0 The last relationship for determining compressor work is the polytropic method. \u00a0Only the\u00a0idea<\/em>l work is found by this method and may be calculated using Equations 5 and 6.\u00a0 All three methods are commonly used by compressor users and manufacturers.<\/p>\n

Volume Ratio<\/strong>
\nThe volume ratio is an important aerodynamic parameter.\u00a0 It maintains similar flow conditions as gas properties and operating conditions change.\u00a0 The best way to describe volume ratio is to consider a multi-stage compressor.\u00a0 The mass of gas entering the first impeller must equal the mass entering other impellers.\u00a0 However, the actual gas volume entering the first stage is not the same for other impellers.\u00a0 The gas is compressed and heated, which results in a reduction of volume.\u00a0 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.\u00a0 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.<\/p>\n

A centrifugal compressor performance test is frequently performed with a gas other than the specified gas.\u00a0 In addition, the compressor may operate at conditions other than the original design. \u00a0To 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.\u00a0 Equations 1-6 can be used to determine the conditions that match the test and specified volume ratio.\u00a0 The Code sets limits on deviations of the test gas properties and operating conditions, which is found in Table 2 of Part 1.<\/p>\n

Seven variables define the volume ratio relationship between a test gas and the specified gas.\u00a0 The variables and the influence each has to increase or decrease the volume ratio is shown in Table 2.\u00a0 For example, if the k-value of the test gas is greater than the specified gas, the volume ratio will decrease.\u00a0 Similarly, if the test gas suction temperature is less then the volume ratio will increase.\u00a0 Also note another important fact, and that is changes in the suction pressure of the test gas have no effect on volume ratio.<\/p>\n

Table 2 – Variable Influence on Volume Ratio<\/strong><\/p>\n

\n\n\n\n\n\n\n\n\n\n\n
Variable<\/strong><\/td>\nChange<\/strong><\/td>\nVolume Ratio<\/strong><\/td>\nChange<\/strong><\/td>\nVolume Ratio<\/strong><\/td>\n<\/tr>\n
Head<\/td>\nIncrease<\/td>\nIncrease<\/td>\nDecrease<\/td>\nDecrease<\/td>\n<\/tr>\n
Molecular Weight<\/td>\nIncrease<\/td>\nIncrease<\/td>\nDecrease<\/td>\nDecrease<\/td>\n<\/tr>\n
Suction Temperature<\/td>\nIncrease<\/td>\nDecrease<\/td>\nDecrease<\/td>\nIncrease<\/td>\n<\/tr>\n
Compressibility<\/td>\nIncrease<\/td>\nDecrease<\/td>\nDecrease<\/td>\nIncrease<\/td>\n<\/tr>\n
k-value<\/td>\nIncrease<\/td>\nDecrease<\/td>\nDecrease<\/td>\nIncrease<\/td>\n<\/tr>\n
Speed<\/td>\nIncrease<\/td>\nIncrease<\/td>\nDecrease<\/td>\nDecrease<\/td>\n<\/tr>\n
Suction pressure<\/td>\nIncrease<\/td>\nNo change<\/td>\nDecrease<\/td>\nNo change<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

As previously mentioned, the volume ratio of the specified gas must match the volume ratio of the test gas.\u00a0 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?\u00a0 A common practice is to change the test speed to compensate for the mismatch of volume ratios.\u00a0 This practice is illustrated in Figure 1.\u00a0 Note how the compressor speed is decreased so that the volume ratio changes imposed by other variables add up to zero.<\/p>\n

\"Figure<\/a><\/p>\n

In summary, the operating conditions and physical properties of a performance test should be carefully examined.\u00a0 It is critical that the test gas volume ratio closely match the volume ratio of the specified gas.\u00a0 The closer the test gas volume ratio is to the specified gas, the more accurate are the performance test results.<\/p>\n

Mach Number<\/strong>
\nThe Mach number influences the maximum amount of gas that can be compressed for a given impeller speed.\u00a0 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.\u00a0 As the gas flow rate increases so does the velocity within the compressor\u2019s internal flow path until it approaches the fluid acoustic velocity, thus limiting the flow.\u00a0 Therefore, gas velocities that approach a Mach number of one indicate choke flow inside the compressor.<\/p>\n

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.\u00a0 The Code also sets allowable limits on the deviation between the specified and test gas Machine Mach Numbers.\u00a0 This helps assure the accuracy of the performance test.\u00a0 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.\u00a0 See Figure 2 for allowable deviation limits.\u00a0 If the value exceeds the permitted deviation the test gas operating conditions may need adjusting to comply with to these limits.<\/p>\n

\"Figure<\/a><\/p>\n

Figure 2 – Allowable Deviations for Machine Mach Number<\/strong><\/p>\n

Reynolds Number<\/strong>
\nThe effect that the Reynolds Number has on a compressor is similar to the effect it has on pipes.\u00a0 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.\u00a0 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.
\n\"Equation\"<\/a>
\nThe allowable Machine Reynolds Number departure limits between the test gas and specified gas are given in Figure 3.<\/p>\n

By Joe Honeywell<\/em><\/p>\n

\"Figure<\/a><\/p>\n

Figure 3 \u2013 Allowable Machine Reynolds Number Departures <\/strong>
\nReferences<\/strong><\/p>\n

    \n
  1. ASME PTC-10, \u201cPerformance test Code on Compressors and Exhausters<\/em>\u201d, 1997<\/li>\n
  2. Short Course \u201cCentrifugal Compressors 201<\/em>\u201d, Colby, G.M., et al. 38th Turbomachinery Symposium, 2009.<\/li>\n<\/ol>\n

     <\/p>\n

    Nomenclature<\/strong>
    \n    \"Nomenclature\"<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

    This is the final part of a two part Tip of the Month (TOTM) series on important aspects related to centrifugal compressor performance testing.\u00a0 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 […]<\/p>\n","protected":false},"author":28,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"nf_dc_page":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2},"jetpack_post_was_ever_published":false},"categories":[5],"tags":[],"coauthors":[],"class_list":["post-400","post","type-post","status-publish","format-standard","hentry","category-mechanical"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p1pQc4-6s","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"http:\/\/www.jmcampbell.com\/tip-of-the-month\/wp-json\/wp\/v2\/posts\/400","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/www.jmcampbell.com\/tip-of-the-month\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/www.jmcampbell.com\/tip-of-the-month\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/www.jmcampbell.com\/tip-of-the-month\/wp-json\/wp\/v2\/users\/28"}],"replies":[{"embeddable":true,"href":"http:\/\/www.jmcampbell.com\/tip-of-the-month\/wp-json\/wp\/v2\/comments?post=400"}],"version-history":[{"count":5,"href":"http:\/\/www.jmcampbell.com\/tip-of-the-month\/wp-json\/wp\/v2\/posts\/400\/revisions"}],"predecessor-version":[{"id":1065,"href":"http:\/\/www.jmcampbell.com\/tip-of-the-month\/wp-json\/wp\/v2\/posts\/400\/revisions\/1065"}],"wp:attachment":[{"href":"http:\/\/www.jmcampbell.com\/tip-of-the-month\/wp-json\/wp\/v2\/media?parent=400"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/www.jmcampbell.com\/tip-of-the-month\/wp-json\/wp\/v2\/categories?post=400"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/www.jmcampbell.com\/tip-of-the-month\/wp-json\/wp\/v2\/tags?post=400"},{"taxonomy":"author","embeddable":true,"href":"http:\/\/www.jmcampbell.com\/tip-of-the-month\/wp-json\/wp\/v2\/coauthors?post=400"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}