MULTIDISCIPLINARY ANALYSIS OF HIGH AND LOW PRESSURE TURBINES ON TRANSITIVE MODES IN THE FLIGHT CYCLE

Transcription

1 MULTIDISCIPLINARY ANALYSIS OF HIGH AND LOW PRESSURE TURBINES ON TRANSITIVE MODES IN THE FLIGHT CYCLE S.V.Khakovsky*, R.Z.Nigmatullin*, V.S. Kinzbusky*, V.V. Staodubtsev* *Сental Institute of Aviation Motos 6, Moscow, Russia Abstact In the design pocess of moden high and low pessue tubines it is necessay to povide optimal combination of defining chaacteistics, such as high gasdynamic efficiency, minimal adial gaps, effective cooling, long lifetime, cyclic duability, axial foces, minimal weight. Design and the analysis ae conducted on the basis of the incopoated multidisciplinay appoach to the solution of gas dynamics, a heat tansfe and heat conductivity, duability and vibating condition poblems. Along with stationay modes the developed models allow to calculate tansitional woking modes of the engines and to define thei chaacteistics efficiency, themal states, seconday ai system state, stain stess state. Intoduction The united mathematical model of woking pocess fo whole tubine flow path is consideed. Fom a position of intenal aeodynamics the diect poblem is solved fo the given 3D geomety of whole tubine flow path. The initial system of the govening equations (Reynolds aveaged Navie-Stokes equations) is witten in the divegent fom in the cylindical coodinate system []. The initial equation system is closed with the oto motion equations equations state fo multicomponent mix. Following methodic equiements to simulation of unsteady heat-hydaulic condition of cooled tubines ae developed.. The solution in unifom fomulation of poblems of hydaulics, bounday conditions of heat tansfe, heat conductivity. Calculation of ai heating at each time step 3. Heat tansfe calculation on disk sufaces taking into account vaiation of swiled flow paametes. 4. Calculation of non-stationay heat tansfe coefficients taking into account natual convection on sufaces. Fo modeling of GTE details mode of defomation at design and opeational development the models of vaious levels ae used, which togethe with gas dynamic and themal state calculations allow to obtain optimal design. Aeodynamic models Design of moden tubines is a complex multidisciplinay poblem. Common scheme of aeodynamic tubine design is shown in the Fig. (fo cooled tubines). Aeodynamic design of cooled tubine D optimization methods Numbe of stages, distibutions of heat dops, blade lengths etc. S (meidional plane) optimization appoaches Peliminay adial paamete distibutions, peliminay stength and themal state analysis Design of cascades on S Restictions fom stength consideations,cooling equiements Themal state analysis Cooling scheme Seconday ai system design 3D unsteady calculations 3D URANS Fast 3D steady calculations 3D RANS with mixing plane Stength analysis Static and dynamic calculations Fig.. Common scheme of aeodynamic design of tubine.

2 S.V.KHARKOVS KY, R.Z.NIGMATULLIN, V.S. KINZBURS KY, V.V. S TARODUBTS EV At the initial stage of the design a detemination of tubine flow path shape is pefomed, the flow path geomety detemination can be combined the optimal distibutions of paametes along stages and ows. The flow path geomety detemination is pefomed at the given geometical estictions. Fo example, inlet section can be given (fixed), o tip suface adius can be esticted etc. Similaly, main gas flow paamete distibutions can be selected unde given estictions. Some of these paametes ae fixed, fo example, inlet * flow paametes: total pessue p 0 and tempeatue T * 0, flow angles, mass flow ate G 0. Roto speeds n j ae also usually given. At the exit section total o static pessue can be specified, o output powe is given etc. Heat dops along stages and ows can usually be selected abitay within some limits. To get optimal paamete distibutions, an aveaged poblem (D) of gas flows in the multistage tubine is solved. Losses ae estimated based on semi-empiical dependencies fo tubine (o compesso fo outlet guide vanes) cascades and ows. Based on this infomation, an optimization of tubine gas flow (and geometical) paametes is fulfilled based on some descent methods. At the optimization pocess it is impotant to choose citeion function. In many cases optimal equiement is (fo given pessue atio): N = max, whee N output powe of the tubine. In this case swil at the tubine exit is usually automatically small. Sometimes it is ational to equie maximum of efficiency: η * = max, but in this case often swil appeas behind tubine and OGV can be used. This optimization pocedue is accompanied by cooling and stength estimations, additional geometical estictions appea, so this pocedue is solved seveal times. Obtained at this stage aveaged (at mean adius) tubine paametes can then be used at the geneation of adial paamete distibutions in the flow passage. Initially, these adial distibutions ae detemined using meidional calculation methods, when the flow field is consideed on so called S suface. Both Eule and RANS calculations methods can be used. In these appoaches govening equations ae witten in consevative fom using cuvilinea coodinates z,,, z,,, z,,. The coodinates (,,) ae chosen so that the sufaces =const ae steam sufaces. Then the elation takes place: u z v w 0 () whee (u,v,w) is velocity vecto components in cylindical coodinates. Othe coodinates, can be chosen so that the conditions ae fulfilled: z z 0, z z 0 () As a esult, the main govening equations can be witten in the next consevative fom: U t J J J F z G H Fz G H h (3) J h whee ight hand side does not contain deivatives of gasdynamical paametes. One of the main advantages of this appoach is its obustness fo the cases when stong discontinuities ae in the flow passage, so it is efficient also fo tans- and supesonic tubine stages (fo moe details see []). The descibed diect poblem is used in the optimization pocess. As fo the aveaged methods, it is convenient to use the equiement N = max, whee N is tubine output powe. In this case flow diection at the tubine exit

3 MULTIDIS CIPLINARY ANALYS IS OF HIGH AND LOW PRESS URE TURBINES ON TRANSITIVE MODES IN THE FLIGHT CYCLE usually is faily unifom and close to axial diection. The descibed optimization pocedue is epeated seveal times with additional estictions fo cooling and stength. Obtained distibutions of paametes can then be used fo the pofiles geneation at diffeent sections of the vanes and blades (in this pocess optimization methods ae applied on the sufaces of evolution S ). Simultaneously, cooling system is designed, and stength calculations ae pefomed. Then the tubine geomety optimization is fulfilled using 3D RANS calculation methods. It is iteation pocess (Fig. ). Finally, unsteady URANS calculations ae pefomed to get moe accuate tempeatue fields, etc. Some examples of ealized tubine design ae pesented. The fist example is a designed tubine fo small aviation engine (Fig. ). Single stage high pessue tubine is cooled, total pessue atio is π*~4.0. In these conditions eithe vane o blade ow (o both) wok at supesonic velocities. The compaisons of calculated and expeimental data fo the tubine efficiency ae shown in the Fig. 3. Fig.. High and low pessue tubines fo small aviation engine. Isentopic Mach numbe field. * * / design n.0 n 0.8 * p Fig. 3. Some esults fo High Pessue Tubine: solid lines expeimental data fo n =80%, 00%; design intent; + - 3D RANS calculation at n =00%; - 3D RANS calculation at n =80%. Models of cooling system and themal state Reliability and woking capacity of gas tubine engine duing all life cycle depend fist of all on a themal condition of elements of a design of tubines - blades, disks, cases and othes, both on stationay, and on tansitive modes. Expeimental definition of fields of tempeatue of the tubine on opeating conditions (fo example, on a mode of the maximum loading) engine woks is pactically impossible. Theefoe, a basis fo calculation of static duability and cyclic duability of elements of the tubine in all spectum of opeating conditions ae settlement fields of tempeatues. This field is also a basis fo calculation of a condition of gaps, both in labyinth seals, and between the case and woking blades. The field of tempeatue of each detail is defined by heat tansfe conditions on its sufaces (bodes) and mateial themal popeties of a detail. Bounday conditions of heat tansfe ae defined by both of gas steams and cooling ai paametes. Paametes of ai steam depend though heat tansfe on tempeatue of a suface of a detail, that is fom a counted tempeatue field. The poblem, in which bounday conditions depend on the solution, is called as conjugated. Thus, thee is a necessity of the decision of the intefaced * 0 / p * 3

4 S.V.KHARKOVS KY, R.Z.NIGMATULLIN, V.S. KINZBURS KY, V.V. S TARODUBTS EV poblem of heat tansfe o, in othe wods, definition of a themal condition of a detail. The themal condition of a detail is inteconnected set of a tempeatue field of a detail and bounday conditions of heat tansfe on its bodes. It is necessay to notice, that ecently a wide ciculation in the wold including leades Design Buo of Russia, eceive 3D methods of modeling of a stationay themal condition of tubine details, fist of all - cooled blades. Modeling is conducted in joint statement of the decision of a poblem of heat tansfe between gas and a solid body. Vaious models of tubulence ae used. Poblems 3D extenal heat tansfe, 3D a viscous flow and heat tansfe in cavities of cooling system and 3D the heat conductivity equation ae geneally solved. It is possible to undeline that methods 3D 3 modeling of a stationay themal condition, as a matte of fact, ae developed. As well as any othe settlement method, 3D 3 equies veification with use of the vaious expeimental data eceived both in modeling, and in natual conditions. Now veification pocesses 3D methods of calculation of heat tansfe poceed, thee is a gadual genealization of settlement-expeimental esults. Howeve application 3D 3 methods emains vey much and vey much labou-intensive pocess, that pactically does not allow to count a non-stationay themal condition of cooled blades and othe basic details and units of GTE. Theefoe objectively thee is a necessity of modeling of non-stationay pocesses of heat tansfe and heat conductivity by means of fast, exact and, cetainly, veified methods. In CIAM the wide spectum of techniques and complexes of applied pogams on numeical modeling of a themal condition of details GTE which includes flat, axisymmetical, quasi 3D and theedimensional models is developed. The given spectum of models allows to count cooled vanes and blades of the tubine, disks of oto wheels and coveed deflectos, shaft, egiments nozzle guide devices, the case, stato design details (fo moe details see []). Each of complexes of pogams essentially consists of following blocks: The module of constuction of geometical model and its automatic splitting into final elements; The module of constuction of hydaulic model; The module of an establishment of confomity between geometical and hydaulic models; The module of calculation of hydaulic netwoks; The module of calculation of bounday conditions of heat tansfe on design sufaces; The module of the decision of the stationay and non-stationay equation of heat conductivity (two-dimensional o theedimensional). Modules of visualization of the initial infomation and esults of calculation of a themal condition (the flat and theedimensional dawing). The heat conductivity equation daes in the pesence of themal souces (dains), unde bounday conditions of the second and thid sot, including adiant heat tansfe, conditions of contact heat tansfe. Integation of the equation of heat conductivity is caied out with use of a method of final elements. Result is the system of the linea algebaic equations, concening unknown values of tempeatue in gid knots. The technology of constuction of model of a heat-hydaulic state of cooled tubines is developed and applied. The technology consists of following stages:. On the basis of the compute dawing of the engine constuction of geometical model, a potayal of hydaulic model, a confomity establishment between geometical and hydaulic models, initialization of geometical sub-aeas is caied out.. Constuction of finite elements mesh 3. Initialization of hydaulic sites, constuction of a hydaulic netwok 4. Infomation geneation on factos of hydaulic esistance, the tansvese aeas, heat tansfe laws on hydaulic sites. Fomation of a contact heat tansfe zones 5. Fomation of zones of heat tansfe on othe sufaces and the specification fo them heat tansfe laws. Fomation of angula coefficients fo calculation of adiant heat tansfe 4

5 MULTIDIS CIPLINARY ANALYS IS OF HIGH AND LOW PRESS URE TURBINES ON TRANSITIVE MODES IN THE FLIGHT CYCLE 6. The specification themophysical popeties fo geometical sub-aeas. 7. Fomation of data fo definition of paametes in bounday knots of hydaulics and heat tansfe calculation on design sufaces (fo a non-stationay mode - fo example, in a flight cycle). Calculation of a stationay and nonstationay themal condition of otos is caied out with application intefaced axisymmetical models of a themal condition of design GTE. Distibution of ai mass flow on banches of cooling systems GTE is defined at calculation of an one-dimensional flow on banches of the equivalent hydaulic model with use of typical hydaulic esistance. Distibutions of mass flow G, tangential V and adial V components of velocity, pessue P and tempeatue T along disk cavities ae defined fom the calculation of the one-dimensional diffeential equations system of movement (4)-(5), enegy (6), indissolubility (7) and a state (8): d d V dv d d G d V V dp d d (4) (5) V V dl dq (6) T C P C P CPG d C PG d d (7) F V 0 d P RT (8) whee is otation fequency. Fo fiction facto =k +k on oto and stato sufaces ae used expeimental citeia coelations. and stesses of cicumfeential tangential fiction on disk (9) and stato (0) coespondingly at local adius Re 0.047Re (9).8, 0. Re, V (0) Fo calculation of flow in othe elements of cooling system the genealized data about pessue losses ae used. Calculation of heat tansfe coefficients on a otating disk suface is defined on a basis citeia equations obtained fom the calculations of the bounday laye equations with use of expeimental data about a adial pofile velocity in an bounday laye of a disk, otating in unlimited space. Fo calculation of heat tansfe coefficients on othe sufaces the genealized data on heat tansfe ae used. 3 The stength investigations The tubine wheels ae one of main subassembly of gas tubine engine, which fomed its key paametes. Tubine pats wok at high level of tempeatue on stationay and un-stationay egimes on the assumption of cyclic loading and evolutions of aicafts. Tubine wheels undego of the hostile envionments, high tempeatue gadients, centifugal and gas loads. The calculations of stess stain state (SSS) and stength of these wheels is necessay to made with take into account elastic, plastic and ceep defomations, tempeatue fields and the changing of popeties of blade and disk mateials on continuous duty. The load factos, multiduty opeations on the assumption of flight cycles, stationay and tansient egimes ae necessay to take into consideation fo stength calculation of tubine blades also. GTE designing fo blade's stength calculations diffeent level models ae used [3]. These calculations in the aggegate with calculations of gas dynamic and tempeatue state allow to made optimal stuctue. The stength eliability assuance of tubine wheels in the conditions of the distubing facto such as high cycle fatigue and deteioation come to be by calculation and tests methods. Paticulaly the woks fo exception of fluid-induced vibations and dangeous esonance oscillation ae caied out fo pevention of fatigue failue with help the test deteminations of vibation stess and enduance limit. 5

6 S.V.KHARKOVS KY, R.Z.NIGMATULLIN, V.S. KINZBURS KY, V.V. S TARODUBTS EV The most accuacy data of the duability and dynamic behavio of tubine wheels can calculate with help: 3D modeling of the obsevable element, Accounting of the mateial anisotopy, Accounting of the changing of the mateial popeties duing opeation, Accounting of the changing of the SSS duing flight cycles. 4. Radial gaps on tansient modes At the initial stage the design of tubines is caied out based on steady woking mode of the engine, fo example, at cuise mode. Expet values of adial gaps ove tubine blades ae accepted. Gasdynamic paametes on othe opeating modes ae defined on the same geometical model, at the same values of gaps, as at the design point. Fo ai system model expet values of adial gaps in labyinth seals ae also accepted. Steady themal and stength state of the tubine is calculated at the design point, and then the "cold" geomety is defined. Then coection of the tubine flow path geomety is pefomed fo othe woking modes unde the assumption about steady tempeatue fields. Howeve, as ou expeience shows, fo steady state fo many modes of flight mission is not ealized. L. L. L. L. Fig.4 Typical design of twin stage HPT tip. Fig. 5. Radial gap above the HPT blade fo flight missions at diffeent envionment conditions: - cold, nomal, 3 hot condition. 6

7 Take Off 8 TH INTERNATIONAL SYMPOSIUM ON FLOW VISUALIZATION (998) Simulation of the themal and stength state of the tubine fo the flight mission is pefomed and contol system of adial gaps is designed. Values of assembly gaps ae chosen. As esult the behavio of adial gaps in the tubine is defined. The geomety of the tubine flow path and othe tubine design elements is defined at woking steady and tansitional egimes in the flight mission. In the subsequent analysis moe accuate calculation of the tubine efficiency, themal state, axial foces ae pefomed fo the vaious time moments duing the flight mission. Figue 4 shows typical design of twin stage HPT tip. And figue 5 pesents the esults of adial gap calculation above the HPT blade fo genealized flight missions at diffeent envionment conditions. Designed contol system allows poviding minimal acceptable gaps duing cuise mode, avoiding cut-in of blade tip fo whole flight mission and thus deceasing degading of the tubine efficiency duing life time. Accoding to calculations the use of the contol system inceases HPT efficiency in ou example by 0.9% fo cuise. But at take off mode we have inceased gaps (by.5 times) in the tubine. It esults in gas tempeatue inceasing 5-0 K at most hot egimes. It should be taking into account at the design of the HPT. Figue 6 shows design of LPT stage tip with shouded blades. Typical behavio of the gaps is pesented in figue 7. Simila to the consideed above HPT minimal acceptable gaps take place duing the cuise mode and deceases fuel consumption fo this most continuous woking egime. Fig.6 Typical design of LPT intemediate stage tip. Inceased gaps occu at take off mode. It leads to LPT efficiency deceasing by -.%. P. Idle P. Climb Cuise Descent Fig. 7. Radial gap above the LPT blade fo flight missions.

8 S.V.KHARKOVS KY, R.Z.NIGMATULLIN, V.S. KINZBURS KY, V.V. S TARODUBTS EV Conclusion The pape pesents unified intedisciplinay mathematical models of gas dynamic, heat tansfe, stength, which takes place in high and low pessue tubines of moden aicaft engines. Along with stationay modes the developed models allow to calculate tansitional woking modes of the engines and to define thei chaacteistics efficiency, themal states, seconday ai system state, stain stess state. It is shown that fo typical design of HP and LP tubines active contol system allows poviding minimal acceptable gaps duing cuise mode, avoiding cut-in of blade tip fo whole flight mission and thus deceasing degading of the tubine efficiency duing life time. At take off mode thee ae inceased adial gaps in the tubine. It leads to necessay inlet gas tempeatue inceasing at most hot egimes. It should be taking into account at the design of the HP and LP tubines. Refeences [] Ivanov M.J., Nigmatullin R.Z. Simulation of Steady and Unsteady Woking Pocesses in Gas Tubine Engine. Some Aeo -Themo-Fluid Aspects in Aibeathing Populsion. CIAM, 00, pp. -7. [] Khakovskij S.V., Pochuev V. P, Bulchinskij J.S., Mukhin A.A., Rykachev J.J. Modelling of a themal condition of details and units of high-tempeatue GTE. The collection of aticles «the Scientific contibution to ceation of aviation engines» the Book. CIAM, 000. Copyight Statement The authos confim that they, and/o thei company o oganization, hold copyight on all of the oiginal mateial included in this pape. The authos also confim that they have obtained pemission, fom the copyight holde of any thid paty mateial included in this pape, to publish it as pat of thei pape. The authos confim that they give pemission, o have obtained pemission fom the copyight holde of this pape, fo the publication and distibution of this pape as pat of the ICAS 04 poceedings o as individual off-pints fom the poceedings. 8