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1 Purdue Unversty Purdue e-pubs Internatonal Compressor Engneerng Conference School of Mechancal Engneerng 01 Approach To The Numerc Geometry Analyss of Postve Dsplacement Compressors, Its Applcaton To A Sngle Screw Compressor Smulaton And Verfcaton By Experment Krll Mchalovch Ignatev Krll.Ignatev@Emerson.com Follow ths and addtonal works at: Ignatev, Krll Mchalovch, "Approach To The Numerc Geometry Analyss of Postve Dsplacement Compressors, Its Applcaton To A Sngle Screw Compressor Smulaton And Verfcaton By Experment" (01). Internatonal Compressor Engneerng Conference. Paper Ths document has been made avalable through Purdue e-pubs, a servce of the Purdue Unversty Lbrares. Please contact epubs@purdue.edu for addtonal nformaton. Complete proceedngs may be acqured n prnt and on CD-ROM drectly from the Ray W. Herrck Laboratores at Herrck/Events/orderlt.html

2 1171, Page 1 Approach To The Numerc Geometry Analyss of Postve Dsplacement Compressors, Its Applcaton To A Sngle Screw Compressor Smulaton And Verfcaton By Experment Krll IGNATIEV Emerson Clmate Technologes, Inc. Sdney, OH, USA E-mal: Krll.Ignatev@Emerson.com; Phone: ABSTRACT Thermodynamc models to smulate postve dsplacement compressors are well known for a few decades already and can descrbe the compressor performance qute well. One of the most complex part of the smulaton process however s the postve dsplacement compressor geometry smulaton. In the current context, under geometry smulaton, values of workng compressor volumes, as well as cross-sectons of port openngs, at dfferent shaft (rotor) angles are consdered. In the current paper, as an example, the Greene formula approach was appled to a geometry smulaton of a sngle screw compressor. Workng chamber geometry was defned by cuttng t wth the gate rotor blade; flute volume was computed usng Greene formula; sucton and dscharge ports were ntersected wth ths volume so that port openng contours were defned and ther respectve cross sectonal areas were calculated. The results of ths geometry smulaton were appled for a thermodynamc model of a sngle screw compressor. Expermental nvestgaton of a sngle screw workng process usng pressure transducers has been conducted. Geometry smulaton data was appled to calculate compresson work from expermental pressure traces. Pressure-volume dagrams obtaned expermentally were compared to the smulated ones. Also, ndcator work obtaned from smulaton and experment, was compared to the power nput to the shaft, and demonstrated good correlaton. 1. INTRODUCTION Tradtonally, volume and area computatons are done ether by utlzng close form analytcal formulaton, or by numercal area ntegraton. A very good llustraton n respect to Sngle Screw compressor was demonstrated by Ben, Hamlton (198), Hera et all (1986) and Sun et all (010) A very good llustraton of the same approach fn case of scroll compressor geometry s provded by Bell et all (010). In all of these approaches the areas are dvded nto zones wth of smpler geometry, areas of these zones are computed by numercal ntegraton and added together. Interestngly, n the vast majorty of postve dsplacement compressors, workng volume and portng s acheved by a relatve moton of sold parts. From ths perspectve, t s benefcal to calculate volumes and cross- sectonal areas of ports from the mathematcal descrpton of these sold body surfaces. The most flexble way s to represent the analyzed surfaces numercally as a polygon as an array of node coordnates. Ths approach allows for smulaton analyss structure to be splt nto 3 steps: 1. From the generc compressor parameters, descrbng a specfc compressor type (n the current example, a sngle screw compressor), generate numerc descrpton of surfaces as polygons;. Based on ths descrpton, calculate volumes and portng cross- sectonal areas numercally usng the Green formula (numerc geometry analyss). 3. Apply the numerc geometry analyss results for thermodynamc workng process smulaton. Step 1 of ths process s compressor-dependent. Step, though t s also somewhat compressor dependent, contans the vast majorty of procedures whch are ndependent of the compressor type. Step 3 can be common for all compressor types. The data nteracton between geometry smulaton and compresson process smulaton s acheved through a data exchange n a tabular form, where chamber volumes, volume changes, and portng crosssectonal areas are tabulated as a functon of compressor shaft rotaton. The same tabular form, as t would be shown Internatonal Compressor Engneerng Conference at Purdue, July 16-19, 01

3 1171, Page below, can be used for expermental pressure trace evaluaton. Therefore, the purpose of the geometry analyss s to generate ths table, based on specfc parameters of the compressor. Expermental Pressure trace analyss for a Sngle Screw compressor has been prevously conducted by Hera et all (1986).. GEOMETRY ANALYSIS 1.1.Geometry Analyss: Greene Formula The man dea of the geometry smulaton s the followng: Snce the compresson volumes, as well as portng crosssectonal areas are formed by ntermeshng sold surfaces, t makes sense to derve those volumes and areas from the descrpton of those sold surfaces. The mathematcal formulaton, whch can be appled n ths case, s the very well-known Green formula: In a fnte dfference form: S Q P dxdy x y P 0, Q x: S S N 1 j1 X j1 S X L Pdx Qdy dxdy j ( Y j1 L xdy Y oj ) (1) () Fgure.1. Volume element llustraton n a cylndrcal coordnate system For a volume computaton n case of cylndrcal coordnate system (Fg.1): V Xdxdy ; Q For non-axsymmetrcal Volume computaton: S x ; P 0 ; V l x dy (3) V 1 x d dy l (4) Internatonal Compressor Engneerng Conference at Purdue, July 16-19, 01

4 1171, Page 3 In Fnal Dfference form: V The equatons above demonstrate, that f we have a mathematcal descrpton of an ntersecton contour (coordnates of nodes), then the approprate area or volume can be calculated. It s nterestng to note, that f the contour represents a polygon, then the formulatons () and (5) gve the precse answer. That allows for sgnfcant reducton of number of nodes... Mult-step geometry smulaton process X M N 1 1 Y Y 1 J If has been demonstrated, that f we can defne a contour, then ts area or volume can be calculated usng equatons (3) or (5). The followng contour defnton algorthm s suggested: 1. Defne a geometry of one of the ntersecton parts. By applyng the relatve moton, numercally cut the other part 3. The workng volume as a contour of ntersecton of those two parts, s defned In order to do t numercally, two fundamental numercal procedures were developed: X 1. A procedure to defne f two segments ntersect or not, and f they are, defne the node of ntersecton; Snce there can be a rare occason that a node of ntersecton can concde wth one of the begnnng and end-nodes of the segment, each segment ncludes one begnnng node but excludes the endng node. X. A procedure to defne, f a node s located nsde a polygon, or outsde the polygon. X J (5) An llustraton example of ntersecton of a gate rotor blade wth a rotor, and the product ntersecton contour, s presented on Fg.. Fgure. Intersecton of gate rotor blade, rotor and ther product There s a possblty, that the ntersecton of two polygons can yeld multple polygons. From the numerc consstency perspectve, ths opton was ncluded, but the descrpton of these multple polygons was done by a sngle polygon connectng all those polygons together. After the ntersectng contour was defned, equaton (5) was appled to calculate the volume of the workng chamber of the sngle screw compressor (flute) Internatonal Compressor Engneerng Conference at Purdue, July 16-19, 01

5 1171, Page 4.3. Port Openng Computatons. The same procedures were used to defne port openngs at dfferent shaft angles. The outsde openng of the flute was unwrapped and also presented as a contour. Dfferent port openngs were also projected on the same unwrapped surface, so the same contour ntersecton procedure can be appled. A specfcs of the sngle screw compressor s that the poston of both the Volume slde and Capacty slde can be ndependently adjusted durng the compressor operaton. Changng the poston of the Capacty slde results n delayed communcaton of the flute and the sucton sde of the compressor, therefore the compresson process s delayed and compressor capacty can be reduced. Changng the poston of the Volume slde allows for adjustment of the dscharge port openng and therefore ndependent adjustment of the bult-n volume rato of the compressor. The numerc procedure descrbed above calculates these adjusted port openngs, based on the specfc value of the poston of each of the sldes. Fgure 3. Flute projecton wth port openngs at start poston and dscharge poston Fg. 3 llustrates flute and port nteracton at dfferent phases of the compresson process: start poston (begnnng of gate rotor blade engagement wth rotor groove), and durng the dscharge process. Internatonal Compressor Engneerng Conference at Purdue, July 16-19, 01

6 1171, Page 5 Fgure 4. Graphc Interpretaton of the Geometry Analyss Results Fg.4 Illustrates graphc nterpretaton of the results flute volume and port openngs Vs. shaft angle. Ths nformaton can then be used for compresson process smulaton, as well as expermental PV analyss 3. THERMODYNAMIC MODEL As t was stated earler, geometry analyss results were used for compresson process smulaton. Compresson model s based on a numercal ntegraton of a well-known and wdely used set of thermodynamc equatons, representng Energy, Mass and flow through an orfce equatons respectvely: du PdV dt Nn j1 S Nn j1 j h j NOUT 1 P, T P P out Volume and cross-sectonal areas values are used from the table of the results of the geometry analyss. The values are tabulated every degree. Lnear approxmaton s utlzed for the values n between. Refrgerant propertes were accessed through DLL routnes of REFPROP software package. As the ntal condtons, Sucton pressure and temperature was assumed n the flute; Intal poston was selected at the moment of gate rotor startng to engage the flute ( frst touch ). j n h NOUT 1 out n (6) 4. EXPERIMENTAL COMRPESSION PROCESS INVESTIGATION Expermental compressor nvestgaton setup ncluded: -Placement and nstallaton of pressure transducers; -Selecton and Placement of synchronzaton devces -Setup of pre-amplfers and data acquston system -Operatonal condtons nstrumentaton; -Post processng of the acqured data Internatonal Compressor Engneerng Conference at Purdue, July 16-19, 01

7 1171, Page 6 Three dfferent optons for pressure transducer placement were consdered: In the end of the rotor groove; n the tp of the gate rotor; a set of statonary transducers just above the gate rotor. Due to challengng ssue of transferrng a sgnal from movng part, the set of statonary transducers was selected, followng the approach descrbed by Hera et all (1986). In a sngle screw compressor, compresson process s qute fast one. It means that a great care should be taken n synchronzng the pressure transducer sgnal wth the rotaton of the compressor shaft. In order to do that, Bently Nevada proxmty probes were used. One probe was readng a sgnal from a pn located on the crankshaft, ths gvng a sgnal once a revoluton. The other one was placed n compressor housng and was readng the rotor grooves, (provdng 6 sgnals per revoluton); angular poston of these sgnals has been qute accurate due to known geometry of the rotor and locaton of the Bently probe on the compressor housng. To acqure pressure transducer sgnals, data acquston system HT600 was used. Sgnals were acqured at a samplng rate of 0 mcro seconds(correspondng to 0.6 DEG of shaft revoluton) for the duraton of approxmately 6 revolutons. Durng compressor test, when compressor operaton s set at the desred condton, pressure transducer data s acqured, together wth the Bently probe traces, and a tme stamp, and stored as a data fle. Durng the post processng of the data, compressor overall performance and operatng condtons, lke sucton and dscharge pressures and temperatures, Sucton mass flow, operatng speed, power consumpton, volume and capacty slde postons, s retreved and synchronzed wth the transducer trace usng the tme stamp. Capacty and volume slde postons are used to re-run the geometrcal analyss for the partcular postons of the sldes. Compressor smulaton s performed usng ths geometry analyss and actual operatng condtons. Pressure traces are generated usng synchronzng sgnals from the Bently probes. Due to the nature of the pressure transducer placement, flute pressure trace s formed from the segments generated by ndvdual pressure transducers, and the procedure for dynamc transducer calbraton s appled. Flute Pressure traces are generated for consecutve 6 flutes compressng on one sde of the compressor (we have transducers nstalled only on one sde of the sngle screw compressor). Expermental pressure trace s compared to smulaton trace. Fg.5 llustrates a comparson between expermental and smulaton flute pressures at a followng condton: Tevap=-6.8C (0F), Tcond=34.5C (90F), deltat superheat=6c, capacty slde at 100% poston, volume [rato] slde at16% poston, workng flud: Ammona. Pressure traces llustrate a very good match between smulated compresson lne and measured compresson. Also, compresson lnes for consecutve flutes 1 through 6, are very close. Fgure 5. Expermental Vs. Smulated Pressure Trace Internatonal Compressor Engneerng Conference at Purdue, July 16-19, 01

8 1171, Page 7 5. CONCLUSIONS Generalzed numercal approach to Geometry analyss of postve dsplacement compressors based on Greene formula has been ntroduced. As an example, ths approach has been appled to a sngle compressor screw geometry analyss Based on the geometry analyss, compresson process smulaton program has been developed Expermental analyss of the compresson process n a sngle screw compressor has been conducted Geometry analyss has been also used for post processng of expermental sngle screw compressor pressure traces Pressure traces of the consecutve flutes are matchng each other very well- therefore there s a very good repeatablty of compresson process n the consecutve flutes of a sngle screw compressor. Pressure traces obtaned expermentally showed very good correlaton wth the pressure traces obtaned by smulaton NOMENCLATURE subscrpts V Volume (m3) S Area (m) l contour (m) x, X coordnate (m) y, Y coordnate (m) Δφ angle ncrement (rad), j ndexes (-) U Internal Energy (kj) P Pressure (Pa) n, out M Mass of gas (kg) h Enthalpy (kj/kg) d Dfferental sgn (-) η Flow coeffcent (-) ρ Gas Densty (kg/cub.m) T Gas Temperature (K) n N Summaton Number n, out REFERENCES 1. T.Ben, J. Hamlton, 198, Modelng Of An Ol Flooded Sngle Screw Ar Compressor, Proc. Internatonal Compressor Engneerng Conference At Purdue, pp T. Hera, T. Sagara, K. Tsuz, 1986, Performance analyss of OIF Sngle screw compressor, Proc. Internatonal Compressor Engneerng Conference At Purdue, pp I. Bell, E.A. Groll, J.E. Braun, G. Kng, 010, Update on Scroll Compressor Chamber Geometry, Proc. Internatonal Compressor Engneerng Conference At Purdue, #1489, pp Shuo Sun, Wefeng Wu, Xalng Yu, Quake Feng, 010, Analyss of Ol Flm Force In Sngle Screw Compressor, Proc. Internatonal Compressor Engneerng Conference At Purdue, #1413, pp 1-8 Internatonal Compressor Engneerng Conference at Purdue, July 16-19, 01

9 1171, Page 8 ACKNOWLEDGEMENT The author greatly acknowledges the great support of the project by the engneerng organzaton of the Vlter dvson of Emerson Clmate Technologes, Inc, especally Jean- Lous Pcouet and Wayne Wehber to name a few. The author greatly apprecates ther help and advce, as well as help of other people from Vlter, whch was nstrumental especally durng the expermental phase of the project. Internatonal Compressor Engneerng Conference at Purdue, July 16-19, 01