Compressor map prediction tool

Transcription

1 IOP Conference Seres: Materals Scence and Engneerng PAPER OPEN ACCESS Compressor map predcton tool To cte ths artcle: Arjun Rav et al 015 IOP Conf. Ser.: Mater. Sc. Eng Vew the artcle onlne for updates and enhancements. Related content - Scroll Compressor Ol Pump Analyss S Branch - Development of a J-T Mcro Compressor P Champagne, J R Olson, T Nast et al. - Computaton of Flow n Screw Compressors Georg Kaltzn, Xaodan Ca, Ramons Reba et al. Ths content was downloaded from IP address on 14/06/018 at 18:07

2 9th Internatonal Conference on Compressors and ther Systems IOP Conf. Seres: Materals Scence and Engneerng 90 (015) 0104 IOP Publshng do: / x/90/1/0104 Compressor map predcton tool Arjun Rav, Lukasz Sznajder and Ian Bennett. Shell Projects and Technology Lange Kleweg 40 88GC Rjswjk, The Netherlands Abstract. Shell Global Solutons uses an n-house developed system for remote condton montorng of centrfugal compressors. It requres feld process data collected durng operaton to calculate and assess the machne s performance. Performance s assessed by comparng lve results of polytropc head and effcency versus desgn compressor curves provded by the Manufacturer. Typcally, these desgn curves are gven for specfc sucton condtons. The further these condtons on ste devate from those prescrbed at desgn, the less accurate the health assessment of the compressor becomes. To address ths specfed problem, a compressor map predcton tool s proposed. The orgnal performance curves of polytropc head aganst volumetrc flow for varyng rotatonal speeds are used as an nput to defne a range of Mach numbers wthn whch the non-dmensonal nvarant performance curve of head and volume flow coeffcent s generated. The new performance curves of polytropc head vs. flow for desred set of nlet condtons are then back calculated usng the nvarant non-dmensonal curve. Wthn the range of Mach numbers calculated from desgn data, the proposed methodology can predct polytropc head curves at a new set of nlet condtons wthn an estmated 3% accuracy. The presented methodology does not requre knowledge of detaled mpeller geometry such as throat areas, blade number, blade angles, thcknesses nor other aspects of the aerodynamc desgn - dffuson levels, flow angles, etc. The only requred mechancal desgn feature s the frst mpeller tp dameter. Descrbed method makes centrfugal compressor survellance actvtes more accurate, enablng precse problem solaton affectng machne s performance. 1. Introducton In the ol and gas ndustry, the remote performance montorng of crtcal machnery s essental to reduce downtme, mantenance costs and mprove producton rates of entre nstallatons. A common machne that s central to most producton and processng assets s the centrfugal compressor. Contnuous performance assessment plays a vtal part n evaluatng the health of these machnes. The performance of a centrfugal compressor s usually descrbed by how the polytropc head vares wth sucton volume flow over a wde range of rotatonal speeds. Orgnal equpment manufacturers (OEM) typcally provde the desgn curves of polytropc head and effcency, whch serve as a benchmark n assessng the machne s performance - but for only a specfc set of nlet condtons. Ideally, a compressor would operate close to the OEM desgn condtons. In realty, the process condtons such as temperature, pressure, molecular weght and rotatonal speed devate, sometmes substantally. Ths devaton mpacts the accuracy of the performance assessment. There comes a pont when the performance map provded by the manufacturer s no longer vald as a reference at new sucton condtons. Accurate performance assessment of compressors requres a map that s vald for varyng sets of sucton condtons and rotatonal speeds. Unfortunately, obtanng new performance Content from ths work may be used under the terms of the Creatve Commons Attrbuton 3.0 lcence. Any further dstrbuton of ths work must mantan attrbuton to the author(s) and the ttle of the work, journal ctaton and DOI. Publshed under lcence by IOP Publshng Ltd 1

3 9th Internatonal Conference on Compressors and ther Systems IOP Conf. Seres: Materals Scence and Engneerng 90 (015) 0104 IOP Publshng do: / x/90/1/0104 curves for an exstng compressor from the vendor can be tme consumng and resource ntensve. Therefore, the methodology of predctng the compressor map at changng process condtons s proposed. There are many approaches that can be adopted to obtan a compressor map. One of these s to create a numercal model of the centrfugal compressor stage and conduct CFD smulatons. An alternatve approach s to use emprcal correlatons for predctng performance maps. A detaled nformaton of the stage geometry s needed; at least on a one dmensonal (1D) bass. The detaled geometry s often unknown as ths s proprety nformaton of the vendor. Examples of 1D methods are gven by [1], [], [5].Ths paper presents a methodology that requres nether aerodynamc nformaton (.e. dffuson ratos, flow angles) nor the mpeller geometry such as the throat areas, blade thckness and blade angles. It only requres the desgn performance curve from the OEM and the mpeller tp dameter whch s typcally provded n the datasheet of the machne. The followng paper s structured as follows. Secton descrbes the methodology regardng how to correct the orgnal performance map for a dfferent set of sucton condtons, lmtatons, valdaton and results. Conclusons are presented n the last secton Nomenclature D mp - Impeller tp dameter (m) k - Specfc heat rato (-) Mu - Tp speed Mach number (-) MW - Molecular weght (kg/kmol) Q - Volume flow rate (m3/s) t - Temperature ( C) U - Impeller blade tp speed (m/s) R - Unversal gas constant [J/ (mol K)] Z - Compressblty (-) H p - Polytropc Head (kj/ kg) N - Rotatonal speed (rpm) S - Cubc splne polynomal a, b, c, d - Coeffcents of splne polynomal (-) σ - Second dervatve of cubc splne polynomal h - Equdstant spacng m - Number of ntervals n the pecewse cubc splne polynomal - Varable for teraton Greek Symbols Φ - Volume flow coeffcent (-) Ψ - Head coeffcent (-) Subscrpts OEM desgn new suc p - Orgnal Equpment Manufacturer - desgn nlet condtons - new nlet condtons - sucton condtons - polytropc. General methodology and verfcaton. The process nlet condtons such as temperature, compressblty, specfc heat rato, molecular weght and crcumferental speed all determne the compressor map. One non-dmensonal parameter that takes all these factors nto account s the tp speed Mach number. The key prncple s that f the Mach numbers are the same for two dfferent sets of sucton condtons, then ther correspondng nondmensonal curve of head coeffcent vs. volume flow coeffcent are equvalent. Ths approach

4 9th Internatonal Conference on Compressors and ther Systems IOP Conf. Seres: Materals Scence and Engneerng 90 (015) 0104 IOP Publshng do: / x/90/1/0104 follows smltude wth equvalent Mach numbers, flow and head coeffcent for the desgn and the new set of nlet condtons. An equvalent non-dmensonal curve also ensures aerodynamc smlarty whch s mportant to smulate the equvalent flow of gas through the mpellers. An equvalent flow coeffcent for the desgn and the new set of sucton condtons ensures the velocty trangles at the nlet of the stage to be the same. To vsualze ths concept a sample calculaton has been done for two dfferent set of sucton condtons, for whch the proxmty of Mach numbers.e to 0.5 was obtaned. All the values are depcted n Table 1. Orgnal polytropc head curves for these two set of nlet condtons provded by the OEM are shown n Fgure 1. Correspondng non-dmensonal curves obtaned after converson are dsplayed n Fgure. Good agreement between these two curves valdates the mentoned hypothess. In both the graphs the red curve represents the desgn sucton condtons and the black curve represents the new sucton condtons. Table 1 Set of nlet condtons and Mach numbers for correspondng performance curves depcted n Fgure 1 and Fgure. Desgn nlet condtons New nlet condtons Temperature [ C] Pressure [bara] Molecular weght [kg/kmol] Rotatonal speed [rpm] Mach number[-] Polytropc head [kj/kg] Volume flow [m3/h] Head coeffcent (Ψ ) [-] Volume flow coeffcent (Ф) [-] Fgure 1 Polytropc head curves for dfferent sets of nlet condtons. Fgure Equvalent non-dmensonal curves for dfferent sets of nlet condtons wth the smlar Mach number. To present an example of the complete curve predcton methodology, data from a randomly chosen centrfugal compressor was used. The nputs are the desgn performance map of a varable speed compressor and ts correspondng sucton condtons.e. pressure, temperature and gas 3

5 9th Internatonal Conference on Compressors and ther Systems IOP Conf. Seres: Materals Scence and Engneerng 90 (015) 0104 IOP Publshng do: / x/90/1/0104 composton for whch the head curves were obtaned. Wth the use of the presented methodology the new compressor map.e. polytropc head (H p ) vs. volume flow rate (Q) relatonshps for a new set of sucton condtons wll be derved. The coordnates of H p and Q of orgnal compressor map provded by the OEM at desgn sucton condtons and vared N are shown n Table. Table Polytropc head (H p ) and volumetrc flow (Q) for desgn sucton condtons and varyng rotatonal speeds (N) provded by the OEM. The rotatonal speeds are n % of the rated speed. N 1 100% N 90% N 3 80% N 4 70% N 5 55% Q 1 H p1 Q H p Q 3 H p 3 Q 4 H p 4 Q 5 H p Man calculaton procedure The desgn compressor map converson to new sucton condtons s done wth the use of followng non-dmensonal parameters. Head coeffcent (Ψ), volume flow coeffcent (Ф) and Mach number (Mu) are calculated usng outlned set of equatons (),(3) and (4) accordng to [3]. Mentoned equatons requre the converson of N nto mpeller blade tp speed (U), whch s done as follows: N ( 1) 60 U= D mp H p ψ () U 4Q (3) πd U mp U Mu (4) k (-1 ) t suc suc Zsuc R MW The polytropc head and volume flow curves presented n Table are converted to nondmensonal curves n the form of Ψ and Ф for vared Mach numbers usng the abovementoned equatons. Mach number s varyng as the rotatonal speed s changng. Obtaned coordnates of converted curves, now n the form of non-dmensonal curves are presented n Table 3 and vsualzed n Fgure 3. Tp speed Mach number Mu 1 corresponds to the non-dmensonal curve for the reference rotatonal speed.e. N 1 as shown n Table. The same logc holds for Mu, Mu 3, Mu 4 and Mu 5.Ths non-dmensonal map for varyng Mach number s used as a baselne for the calculaton of the compressor map for the new set of nlet condtons. 4

6 9th Internatonal Conference on Compressors and ther Systems IOP Conf. Seres: Materals Scence and Engneerng 90 (015) 0104 IOP Publshng do: / x/90/1/0104 Table 3 The non-dmensonal performance map values of head coeffcent (Ψ) and volume flow coeffcent (Ф) for varyng Mach number (Mu) at desgn sucton condtons. Mu 1 Mu Mu 3 Mu 4 Mu Ф [-] Ψ [-] Ф [-] Ψ [-] Ф [-] Ψ [-] Ф [-] Ψ [-] Ф [-] Ψ [-] Head Ceoffcent (Ψ ) [-] Mach Number (Mu) Volume flow coeffcent (Φ) [-] Fgure 3 Invarant non-dmensonal curves of head coeffcent (Ψ) and volume flow coeffcent (Ф) for dfferent Mach numbers at desgn nlet condtons. The legend descrbes the mpeller tp speed Mach number (Mu) for each curve. At ths pont the Mach numbers for new set of nlet condton and shaft speeds are calculated (Mu new ). To draw the full non-dmensonal curves for new condtons.e. new head coeffcent (Ψ new ) aganst new volume flow coeffcent (Ф new ) the curve approxmaton method s used. The mathematcal method employed by the Authors was cubc splne nterpolaton technque, whch s brefly presented n subchapter..1. It allowed obtanng coordnates of non-dmensonal Ψ new vs. Ф new curves for desred Mu new based on exstng Ψ vs. Ф curves for dfferent Mu. In Table 4 the new coordnates of head coeffcent (Ψ new )and volume flow coeffcent (Ф new ) obtaned n gven example are presented The same s vsualsed n Fgure 4 5

7 9th Internatonal Conference on Compressors and ther Systems IOP Conf. Seres: Materals Scence and Engneerng 90 (015) 0104 IOP Publshng do: / x/90/1/0104 Table 4 Volume flow coeffcent (Ф new ) and Head coeffcent (Ψ new ) for new sucton condtons. Mu new = 0.65 Mu new = 0.6 Mu new = 0.56 Mu new = 0.50 Mu new = 0.44 Ф new Ψ new Ф new Ψ new Ф new Ψ new Ф new Ψ new Ф new Ψ new Head coeffcent (Ψ) [-] Non-dmensonal curves for new set of nlet condtons The red curves are the nondmensonal curves obtaned Volume flow coeffcent (Ф) [-] Mach number new condtons Fgure 4 The nterpolated non-dmensonal curves of new head coeffcent (Ψ new ) and volume flow coeffcent (Ф new ) for varyng Mach number at new sucton condtons. In Fgure 4, the black curves wth dfferent markers represent the non-dmensonal curves for varyng Mach numbers for the new set of nlet condtons. The red curves are the non-dmensonal curves for desgn sucton condtons from Fgure 3.In the last calculaton step the coordnates of nondmensonal curves consstng of Ψ new and Ф new from Table 4 are recalculated back to obtan the actual polytropc head curves.e. new polytropc head (H p_new ) vs. volumetrc flow rate (Q new ) for desred set of process condtons and shaft speeds. It s done wth the use of equatons ( 5) and ( 6) U new H p new ( 5) new ( 6) Qnew newu newdmp 4 To valdate the methodology, the newly obtaned compressor map was compared to the avalable map that was generated by the OEM at the same sucton condtons durng the machne s performance test. These curves are shown n Fgure 5. The accuracy acheved n polytropc head predcton wth the use of descrbed methodology reaches c.a. -3% of error when predcted curve s compared to the orgnal OEM s characterstc. The specfc results regardng the accuracy of the method are depcted 6

8 9th Internatonal Conference on Compressors and ther Systems IOP Conf. Seres: Materals Scence and Engneerng 90 (015) 0104 IOP Publshng do: / x/90/1/0104 n Table 5. Such level of accuracy s regarded as satsfactory Comparson of OEM Vs Mappng tool. Polytropc head curves for dfferent rotatonal speeds The black curves- Mappng tool. Red markers- OEM Polytropc Head [kj/kg] Volume flow [m3/h] Fgure 5 Comparson of compressor map generated by compressor mappng tool and map provded by the OEM. The red markers are the polytropc head curves from the OEM. The black curves are obtaned from the compressor mappng tool. Table 5 Valdaton of Compressor Mappng predcton tool wth the values obtaned from the OEM for the Rotatonal speed (N) = 9683 rpm. Flow Polytropc head OEM Polytropc head Devaton n Polytropc [m3/h] [kj/kg] Mappng tool[kj/kg] head[%] % % % % % Ths method s only applcable when each stage of a centrfugal compressor s treated separately. Each stage refers to the number of mpellers stacked together between the sucton and dscharge of a compressor

9 9th Internatonal Conference on Compressors and ther Systems IOP Conf. Seres: Materals Scence and Engneerng 90 (015) 0104 IOP Publshng do: / x/90/1/ Method lmtatons One should remember that the accuracy of the method depends on the range of the operatng envelope of the nvarant non-dmensonal curve varyng wth Mach number. Hgher naccuraces n curve approxmaton are seen when curve extrapolaton s used. The followng conventon s employed to defne the upper and lower boundary of Mach numbers at desgn nlet condtons for whch the presented methodology renders accurate results. Mu low - Mach number at desgn nlet condtons for lowest N; Mu hgh - Mach number at desgn nlet condtons for hghest N; Extrapolaton lmts the accuracy of presented method. Therefore the followng constrants are mposed at newly calculated Mu new. It s checked whether the Mu new s wthn the range of Mach numbers calculated for the desgn condtons as shown below. There are three possble cases: 1. Mu low <Mu new <Mu hgh the newly obtaned Mach number s between boundary values of lowest and hghest Mach numbers, therefore the nterpolaton method wll be used to calculate coordnates of new head and volume flow coeffcent curve. Experence has shown that nterpolaton allows to obtan non-dmensonal curve approxmaton wth hgh accuracy;. Mu new <Mu low the newly obtaned Mach number s smaller than the lowest Mach number obtaned for desgn nlet condtons, therefore the extrapolaton method wll be used to calculate coordnates of new head and volume flow coeffcent curve; 3. Mu new >Mu hgh the newly obtaned Mach number s greater than the hghest Mach number obtaned for desgn nlet condtons, therefore the extrapolaton method wll be used to calculate coordnates of new head and volume flow coeffcent curve; In nd and 3 rd case the followng condton must be met to ensure an acceptable accuracy of the curve approxmaton: Mulow Mu new Check f 5% (case ) Mu new Mu new Mu hgh Check f 5% Mu new (case 3) The three condtons are vsualsed n Fgure 6. The red curves are the nvarant non-dmensonal curves for desgn nlet condtons. The dotted curves are the extrapolated curves correspondng to case and 3. The dashed curve s the nterpolated curve correspondng to case 1. Extrapolaton or nterpolaton of the new non-dmensonal curve of Ψ new vs. Ф new for the new Mu new s done dependng on whch of the three aforementoned condtons s met. The accuracy of the extrapolaton largely deterorates and the method s rejected for devatons n new Mach number greater than 5% from the hghest or lowest desgn Mach number, as t was mentoned earler. It must be also mentoned that ths method s only applcable when each stage of a centrfugal compressor s treated separately. Each stage refers to the number of mpellers stacked together between the sucton and dscharge of a compressor. 8

10 9th Internatonal Conference on Compressors and ther Systems IOP Conf. Seres: Materals Scence and Engneerng 90 (015) 0104 IOP Publshng do: / x/90/1/0104 Head coeffcent (Ψ) [-] Extrapolated Invarant non-dmensonal curve Interpolated Mu hgh Mu low Volume flow coeffcent (Φ) [-] Fgure 6 Interpolated (dashed) and extrapolated (dotted) non-dmensonal curves for new set of nlet condtons from nvarant non-dmensonal curves..1. Curve approxmaton method Mathematcal method used to nterpolate or extrapolate curves whch was employed n the presented curve predcton tool s the Cubc Splne method. Ths technque provdes smooth contnuous approxmated curves compared to pecewse lnear nterpolaton. Cubc splne nterpolaton formula s contnuous n the frst and second dervatves and both wthn the ntervals and nterpolatng nodes. It also provdes an nterpolatng polynomal whch has a smaller error compared to other nterpolatng polynomals such as Lagrange or Newton s A bref descrpton of the orgnal cubc splne nterpolaton method employed n the presented performance map predcton tool s provded hereunder. f=cubcsplne(x nput, x, y)=s (x) (7) x nput s the new Mach number for new set of nlet condtons; x s the dataset comprsng known values of Ф obtaned at desgn nlet condtons; y s the dataset comprsng known values of Ψ obtaned at desgn nlet condtons; Splne nterpolaton s dvded nto small sub-nterval and each of these sub-ntervals s nterpolated by usng a thrd degree polynomal. Accordng to [4], for a set of m+1 data ponts (x, y ) and where no two x are the same on a gven nterval, a cubc splne (S ) can be defned on each sub-nterval (x,x +1 ) by S x a (x nput 3 x ) +b (x x ) +c (x x )+d (8) For m pecewse polynomal, four tmes m boundary condtons are needed to determne the coeffcents a, b, c, and d. The boundary condtons are descrbed n the equatons outlned below: nput x y for = 0 : m 1 S (9) Sm 1 ym (10) S x 1 S 1 x 1 for 0: m (11) nput 9

11 9th Internatonal Conference on Compressors and ther Systems IOP Conf. Seres: Materals Scence and Engneerng 90 (015) 0104 IOP Publshng do: / x/90/1/0104 ' ' x S x for 0: S m (1) " " x S x for 0: S m (13) S " x S x 0 " 0 0 m 1 m (14) A new varable σ for the second dervatve of the polynomal s ntroduced. Another varable h s defned for equdstant spacng. " S x (15) h x 1 By usng the equatons (8), (9), (10), (11), (1), (13), (14) and (15)the coeffcents a, b, c, d are obtaned. d y ; b x 1 y 1 y 1 (16) ; a ; c h 6h h 6 3. Concluson and Lmtatons In ths paper, a generc methodology s proposed, whch enables correcton of the orgnal polytropc head curves for actual operatng condtons based on the equvalence of non-dmensonal parameters. The general procedure and valdaton of the method has been descrbed. Wth mnmal nputs of process condtons, frst tp mpeller dameter and a desgn performance map from the manufacturer, a compressor performance map for a new set of nlet condtons can be predcted wthn an accuracy of -3%. The effectve mplementaton of ths method n remote condton montorng system enables actual compressor performance assessment wth the use of corrected polytropc head curves, whch more accurately reflect the theoretcal behavour of a healthy machne at gven condtons. Addtonally, t can ad the performance revew of the machne for new operatng condtons and advse the engneers on ste f the compressor can operate at the new condtons. Another key feature of ths method s the accurate locatons of the operatng ponts on the compressor maps, whch s essental for surge and choke protecton. The presented feature can eventually facltate solaton of undesrable compressor behavour at an early stage and, therefore, help dentfy potental falure modes, thus reducng downtme and mantenance costs of the compressor and surroundng equpment. The method has been valdated for 0 dfferent centrfugal compressors, thus provng ts readness. References [1] Aunger R H 000 Centrfugal Compressor- A Strategy for Aerodynamc Desgn and Analyss (New York, USA: ASME Press). [] Cumpsty N A 1989 Compressor Aerodynamcs (Harlow, Essex, UK: Longman Scentfc &Techncal). [3] Lu dtke K H 004 Process Centrfugal Compressors (Berln: Sprnger) [4] Plato R. 003 Concse Numercal Mathematcs vol 57 (Provdence R.I: Amercan Mathematcal Socety). [5] Swan E 005 Improvng a one-dmensonal centrfugal compressor performance predcton method Proc of the Insttuton of Mechancal Engneers Part A: Journal of Power and Energy 19(8) pp