DATA REDUCTION METHOD FOR STEAM FLOW FIELDS

Transcription

1 Te XX Symposium on easuring Tecniques in Turbomacinery Transonic and Supersonic Flow in ascades and Turbomacines DT REDUTON ETHOD FOR STE FLOW FELDS.Nový / Doosan Škoda Power Ld., Pilsen, zec Republic D.Jíca / Doosan Škoda Power Ld., Pilsen, zec Republic P.Šafařík / zec Tecnical Universiy in Prague, Faculy of ecanical Engineering, Prague, zec Republic.Hajšman / Doosan Škoda Power Ld., Pilsen, zec Republic BSTRT Te paper deals wi daa reducion meod developed for seam flows. Te meod is based on conservaion laws balances of mass, momenum, and energy fluxes. Termodynamic properies of seam according o e PWS-F97 formulaion are applied. Te daa reducion meod is described and discussed. NTRODUTON Daa reducion sysems belong o a needful sofware equipmen of aerodynamic laboraories. Tey are applied for soluion of reference parameers of flow. Te correc sysem as o be based on e conservaion equaions for mass, momenum, and energy, and is supplemened by equaion of sae. onsequenly bo e flow daa and e omogeneous daa are equivalen wi respec o e conservaive pysical properies. Te daa reducion meod as been developed originally for an ideal gas. Te daa reducion meod was presened in [1] and e meod was developed for more general cases. For example, oal emperaure disribuion was approved in [] and disribuion of concenraion of anoer injeced gas was presened in [3]. nalysis of e reducion meod was performed in [3] and is range of valid argumens was derived. Te exisence of limis of valid argumens is conneced wi occurrence of effecs a compressible fluid flow. Tey are - exisence of maximum mass flux, exisence of maximum velociy of gas flow, exisence of limi load, exisence of sock waves in compressible fluid flow field, ec. Furer analysis in [4] proved condiions for flow parameers deermined from double soluion of e sysem of equaions of e daa reducion meod. However, e sysem of [1] o [4] is based on eory of an ideal gas. n is paper auors inend o presen e daa reducion meod for seam flow fields. Te complex relaions beween ermodynamic parameers of seam are e reason a equaion of sae of ideal gas canno be applied. n [5] daa reducion meod was exended for soluion of wodimensional seady flow fields of seam. Termodynamic properies of seam according o e PWS-F97 formulaion [6] are recommended for is purpose. Te daa reducion meod for seam flow fields is described in is paper and ranges of valid argumens enering ino soluion of reduced daa [7] will be sown. NOENLTURE p pressure, Pa a speed of sound, m.s -1 ρ densiy, kg.m -3 T emperaure, K κ raio of ea capaciies (Poisson consan), dimensionless r specific gas consan, J.kg -1.K -1 v velociy, m.s -1 specific enalpy, kj.kg -1 s specific enropy, kj.kg -1.K -1 α angle, x dryness fracion, dimensionless y disance coordinae, m DT REDUTON ETHOD FOR TWO- DENSONL FLOW FELD OF STE Le us ave a line y in wo-dimensional flow of seam according o Fig.1. On e line, abscissa T is an infiniesimal conrol volume aving is leng. Upsream of is volume are disribuions of pressure p(y), densiy ρ(y) and velociy vecor (i.e. disribuion of flow angle α(y) of velociy vecor oriened o normal of abscissa T and of absolue value of velociy vecor v(y)) of flowing seam along abscissa T. Le ere are given disribuions of pressure p(y), densiy ρ(y) and angle α(y). is possible o obain disribuion of specific enalpy (y) by means of e PWS- F97 from p(y) and ρ(y). Disribuion of absolue value of velociy vecor v(y) is solved wen e assumpion of consan oal specific enalpy (y) = = given consan. 1 Lyon, FRNE 4-5 Sepember 14

2 Te XX Symposium on easuring Tecniques in Turbomacinery Transonic and Supersonic Flow in ascades and Turbomacines Te aim of e daa reducion meod is o solve omogeneous values of parameers pressure p, densiy ρ, specific enalpy, absolue value of velociy vecor v and angle α downsream of e conrol volume. Of course, equaion of sae Eq.(8) olds bo locally and globally. Te sysem of equaions, Eqs. (4) o (8), is a maemaical basis of e daa reducion meod and is soluion deermines reduced parameers. For ideal gas e sysem of equaions, Eqs. (4) o (7), supplemened wi equaion of sae 1 p (1) Fig. 1: Parameers for wo-dimensional seam flow. Te principle of e daa reducion meod is o solve conservaion equaions of mass, momenum, and energy. onsequenly inegrals of mass flux, of momenum flux in normal direcion o infiniesimal conrol volume (o abscissa T ), and momenum flux in circumferenial direcion o conrol volume yv y y cos dy (1) yv ycos y py dy () yv ysin ycosy dy (3) negrals,, and will be applied o calculaions of argumens of e daa reducion meod. Te balance equaions ave inegrals,, and on eir rig sides. ass: v cos (4) omenum normal o y: v cos p (5) omenum in direcion of y: Energy: v cos sin (6) y y v y (7) Equaion of sae of seam: PWS F 97 f p, ρ (8) is modified ino non dimensional form and reduced parameers can be solved analyically [3]. is raio of ea capaciies. For seam flows e sysem of equaions, Eqs. (4) o (8), can be solved by means of ieraive numerical procedure. n e firs ieraive sep, e value of specific enalpy is cosen. Ten e pressure p() and densiy ρ() are solved from following equaions derived from conservaion equaions. p (9) (1) By means of e PWS-F97, e specific enalpy PWS-F97 is deermined PWS F f p, ρ 97 (11) and en i is consequenly applied in Eq. (5) for e following ieraive sep unil: PWS F 97 (1) eraive procedure seems o be fas. grapical aid can elp o find soluions of e sysem of conservaive equaions supplemened wi equaion of sae for seam wen diagram wi curves of = f(p) dependency and PWS-F97 = f(p). Poins of inersecion deermine approximaely e soluion being soug. is sown a wo soluions of specific enalpy and e corresponding pressure p exis. is essenial aving an experience o deermine proper soluion. Te final calculaion of values of e ermodynamic and flow parameers is performed by means of PWS daa and sysem of equaions from daa reducion meod: Lyon, FRNE 4-5 Sepember 14

3 Te XX Symposium on easuring Tecniques in Turbomacinery Transonic and Supersonic Flow in ascades and Turbomacines Densiy f ρ (p, ) (13) Velociy p v (14) Flow angle arcsin ( v) (15) Temperaure T f (p, ) (16) T Specific enropy s f (p, ) (17) s Speed of sound a f (p, T) (18) a Toal pressure p p f (s, ) (19) Toal emperaure T ft(p, ) () Dryness of seam x f (p, ) (1) x RNGES OF VLD RGUENTS FOR DT REDUTON ETHOD N STE FLOW Te ranges of valid argumens for ideal gas flows fields were analyically derived in [3] and are expressed in diagram ~ ~. and are modified inegrals from balances of momenum fluxes in periperal and axial direcions, respecively. is modified inegral from balance of mass flux. Te ranges of valid argumens for ideal gas are presened in Fig.1. Furer analysis in [4] proved e ranges of valid argumens and moreover deermined dependencies of reduced flow parameers. Deerminaion of e ranges of valid argumens for daa reducion meod in seam flow fields analyically is very difficul due o complex sae equaion of seam. Te auors proposed [7] a numerical approac of mapping of large number of sae calculaions presened in diagrams ~. rgumens,, and a a are solved from Eqs. (4), (5), and (6). Fig.: Ranges of valid argumens for daa reducion meod in an ideal gas flow [4]. 3 Lyon, FRNE 4-5 Sepember 14

4 Te XX Symposium on easuring Tecniques in Turbomacinery Transonic and Supersonic Flow in ascades and Turbomacines alculaions were performed for oal specific enalpy = 3 kj/kg. Termodynamic parameers specific enalpy and specific enropy s were cosen. Pressure p, densiy, and speed of sound a oal condiions a were solved by means of e PWS-F97 formulaion [5]. Velociies were solved from Eq. (8) by: v () Te angles were cosen. cieved resuls are presened in diagrams in Figs. 3 and 4 were envelopes of e depiced curves deermine e range of valid argumens for daa reducion meod in seam flow fields. Fig. 3: Dependencies of argumens of daa reducion meod in seam flow field, velociies, v [m/s] = cons. Fig. 4: Dependencies of argumens of daa reducion meod in seam flow field, flow angles, [ ] = cons. 4 Lyon, FRNE 4-5 Sepember 14

5 Te XX Symposium on easuring Tecniques in Turbomacinery Transonic and Supersonic Flow in ascades and Turbomacines PPLTON OF DT REDUTON ETHOD FOR TWO-DENSONL FLOW FELDS OF STE Five ses of daa ave been prepared [5] as a ask for verificaion of e daa reducion meod in eam flow field. alculaions were performed for oal specific enalpy = 31 kj/kg. Resuls are sown in Fig. 5 and ey are also sown in Table 1 along wi relaive uncerainies of e calculaions. Very close values of e 1 s and nd soluions for e ask No. 3 are remarkable. Values of uncerainies iger an 1% prove e soluion no o be e proper one or e need o be analyzed in more deail. Proper soluion as e values of uncerainies lower an.1%. Fig.5: Resuls from daa reducion meod for wo-dimensional seam flow. (Number denoes number of ask, blue poins 1 s soluion, red squares nd soluion). [J/kg] npus Resuls given resul relaive uncerainy resul relaive uncerainy resul Task No relaive uncerainy resul relaive uncerainy resul relaive uncerainy p [Pa] [J/kg] [kg/m 3 ] 1 s v [m/s] soluion [rad] s [J/kgK] p [Pa] [J/kg] [kg/m 3 ] nd v [m/s] soluion [rad] s [J/kgK] Tab.1: Resuls from daa reducion meod for wo-dimensional seam flow. 5 Lyon, FRNE 4-5 Sepember 14

6 Te XX Symposium on easuring Tecniques in Turbomacinery Transonic and Supersonic Flow in ascades and Turbomacines RESULTS and DSUSSON Te daa reducion meod is exended for soluion parameers of wo-dimensional flow fields of seam. Te meod is based on mass, momenum and energy balance equaions, and on equaion of sae of seam PWS-F97. Soluion of sysem of equaions was prepared and verified. Furer developmen of e daa reducion meod will coninue. Disribuions of parameers of experimenal daa from secions of seam flow field are used for evaluaion of balance inegrals. Ten e sysem of conservaion equaions supplemened wi equaion of sae for seam (enalpy calculaed PWS_F97 = f (p, ), p is pressure, is densiy) is solved by means of ieraive numerical procedure. Resuls by means of daa reducion meod for seam flows are solved and presened. Proper soluion as e values of uncerainies lower an.1%. Range of valid argumens for daa reducion meod in e seam flow can be deermined and is presened (see Figs.3 and 4). rgumens are solved from quaniies: is balance inegral of mass flux, is balance inegral of momenum flux in axial direcion, is balance inegral of momenum flux in circumferenial direcion, a is speed of sound a sagnaion condiions. n e region of ransonic and supersonic velociies, e sysem of conservaion equaions as wo soluions. denificaion e correc soluion sould be sudied. cieved resuls, and furer developmen and applicaions of e developed meod are e basis for furer discussions and developmen of e daa reducion meod. REFERENES [1] J. mecke : Daa Reducion of Wake Flow easuremens wi Plane ascades, V- Repor 67 49, Göingen, (in German) [].L.G. Oldfield, D.L. Sculz, J.H. Nicolson: Loss easuremens Using a Fas Traverse in an LPT Transien ascade. n: Proceedings of 6 Symposium on easuring Tecniques in Transonic and Supersonic Flows in ascades and Turbomacines, Lyon, [3] J. mecke, P. Šafařík: Daa Reducion of Wake Flow easuremens wi njecion of an Oer Gas, DLR-Forscungsberic No.95-3, Göingen, 1995 [4] P. Šafařík: ulicomponen ixure Flows in Flow Pars of acines, esis, zec Tecnical Universiy in Prague, Prague, (in zec) [5]. Nový, P. Šafařík,. Hajšman, D. Jíca: On Daa Reducion eod for Flow Fields of Seam, pp n: Topical Problems of Fluid ecanics 14, Proceedings, Prague, 14 [6] Revised Release on e PWS ndusrial Formulaion 1997 for e Termodynamic Properies of Waer and Seam, PWS, 7 [7] P. Šafařík,. Nový.. Hajšman, D. Jíca: Range of Valid rgumens for Daa Reducion eod in e Seam Flow Fields, pp n: Te pplicaion of Experimenal and Numerical eods in Fluid ecanics and Energy 14, Universiy of Žilina, Žilina, 14 KNOWLEDGENTS Te suppor from e Tecnology gency of e zec Republic in e frame of e ompeence enre dvanced Tecnology of Hea and Elecriciy Oupu, No.TE136 is graefully acknowledged. Tanks o Doosan Škoda Power Ld. wo conribue is researc possible. 6 Lyon, FRNE 4-5 Sepember 14