Component-level Modeling Technology and Optimization for Variable Cycle Engine

Transcription

1 Amercan Journal of Mathematcs and Statstcs 2013, 3(6): DOI: /j.ajms Component-level Modelng echnology and Optmzaton for Varable Cycle Engne hongzheng You Shangha Unversty of Engneerng Scence, Shangha, , Chna Abstract hs thess manly studes the mathematcal model of the varable cycle engne and ts optmzaton. he varable cycle engne workng process s very complcated. he workng process of t s not only a sngle component of thermal processes, but contans all the components and ther nteracton as awhole. All the components are nterrelated and nteract wth each other. he varable cycle engne s dvded nto general structure, each structure s typcal, ndependence, versatlty and connectvty, then the mathematcal model of the parts s establshed. Fnally smulaton wth MALAB software to solve the seven balance equaton of the varable cycle engne model under known the condton of external nput, and the model s evaluated. Keywords Varable cycle engne, Modularmodelng, Balance equaton 1. Introducton he varable cycle engne can work n the bg thrust wth hgh speed and lower fuel consumpton wth low speed at the same tme. he varable cycle engne has drawn the attenton of the varous avaton powers n many countres because of these advantages, and t s one of the mportant research drectons of arcraft engnes. 2. he Structure and Basc Prncple of Varable Cycle Engne 2.1. he Basc Structure he basc structure of the double duct varable cycle engne, as shown n fgure 1, fgure 2, he man components are: Inlet, Fan, Deputy external duct (DED), duct,, Man external duct (MED), he former mxer (FM), Hgh pressure compressor (HPC), Man chamber (MC), Hgh pressure turbne (HP), Low pressure turbne (LP), he after mxer (AM), afterburners, exhaust nozzle. he dgtal seral umbers n the fgure mean engne secton parameters he Workng Prncple Correspondng author: yzz2018@163.com (hongzheng You) Publshed onlne at Copyrght 2013 Scentfc & Academc Publshng. All Rghts Reserved Inlet Fan Hgh pressure he former Man compressor Low pressure mxer Man turbne external duct chamber afterburners Mode Deputy converson Hgh pressure he after external duct valve turbne mxer exhaust nozzle Fgure 1. he basc constructon of varable cycle engne he front fan Selector valve Deputy external duct Heart duct Man he after external duct mxer Fgure 2. he structure dagram of double duct varable cycle engne he connecton between the engne parts as shown n fgure 3, Varable cycle engne s a dual rotor motor, he fan s connected to the low pressure turbne, and Hgh pressure compressor also be connected tothe hgh pressure turbne, As shown n fgure 3.

2 Amercan Journal of Mathematcs and Statstcs 2013, 3(6): Montor Fuel tank Man fuel valve Fuel ol controller Strength fuel valve Man chamber Inlet Fan Hgh pressure compressor Hgh pressure turbne Low pressure turbne he after mxer Fgure 3. he dagram of a varable cycleengne workng prncple After-burners Exhaust nozzle here are two knds of workng mode about the varable cycle engne, turbojet and turbofan, as n[1]. When engne workng n subsonc cruse low power state, the mode converson valve open, make more ar nto the deputy external duct, at the same tme the former mxer s wde opened. Open the after mxer, ncreasng the bypass rato; reduce fuel consumpton, the engne workng at the model of turbofan ths tme. When engne workng n the state of supersonc cruse, acceleraton and clmbng, the former mxer s smaller, selector valve closed, most of the gas forced nto the core engne, produce hgh thrust, the engne workng at the model of turbojet ths tme. 3. Component Modelng Method of Varable Cycle Engne he characterstcs of the varable cycle engne can be acheved by experment method and the calculaton method. But the experment method needs to develop sophstcated equpment, nvest a huge sum of money and huge energy consumpton. Because of ths, the experment method s often adopted. Wth the contnuous mprovement of computng power and the deepenng of the research engne mathematcal model, computer smulaton accuracy has been mproved to some extent make up for the defcency of the expermental method. he varable cycle engne s composed of nlet, compressor, combuston chamber and turbne, nozzles and other components. Wth the computer smulaton of these components, we can get the smulaton of the engne he Modular Model From the fgure of the prncple of varable cycle engne, we know that the workng process of the varable cycle engne s very complex, and the characterstcs of the components have a very close relatonshp wth the characterstcs of the engne. So we must study the characterstcs of components before we study the propertes of the engne and then establsh ts mathematcal model. And buld a mathematcal model of the whole system bass on the mutual restrcton relatons between varous components. Decomposablty of the system s the base of modularzed modelng. hat means the system can be decomposed nto several subsystems. For each subsystem we bult a model. Dvdng accordng to the actual physcal system module, make a module has the relatve ndependence of physcal, namely to complete a separate physcal functon, at the same tme ensure that each module has the ndependence of the math. hat means all of the equatons descrbng the physcal component characterstcs and calculaton are ncluded n the module wthn the program. hs makes the modelng and smulaton process becomes natural, ntutve, and the gap between the physcal model and computatonal model narrow. At the same tme can make sub models for repeated use, greatly shorten the tme of the modelng and smulaton. So, accordng to the actual physcal devce to separate modules, has become the prncple of modular modelng of module partton. o the system we study should make reasonable modular decomposton and the module have the followng features: 1. he module s the base of the basc unt of the system model, t can no longer small, and the system dynamc model program s composed of the basc module subroutne. 2. Modulepartton s based on completely ndependent of the physcal devce and the component. hey have clear physcal boundares and enough physcal ndependence. 3. Module wth hgh mathematcs ndependence. It stpulates that all of thee equatons descrbng the part feature are contaned nsde the module, theoutput of the module accord to the module tself, energy, mass and momentum to calculate flud propertes, on the sde of the change and not as a functon of the other varables n a module to calculate. It can be used as a basc unt to attend to a larger system, and can also be used separately whch do not add any other smulaton module to determne the physcal devce.

3 Inlet exhaust nozzle after-burners AM LP HP MC HPC Fan Inlet 430 hongzheng You: Component-level Modelng echnology and Optmzatng for Varable Cycle Engne p 225, 225 ode225 ode125 p 125, 125 Deputy duct Duct ode62 p 62, 62 W g 225 W g125 W g 62 ode0 p 0 0 ode1 ode21 ode25 ode3 ode4 ode45 ode61 ode6 p 1 p 21 p 25 p 3n p 4 p 45 p 61 p 6n n n W a1 Wa21 W Wa 3n Wa 4 Wa 45 W g 61 W a25 g 6 n ode8 p 8 8 W g8 hgh pressure axal low pressure axal Fgure 4. he flow dagram of the engne 4. he module has good compatblty;t s the key to the modular modellng, as n[2]. he dffculty of modular modellng s nteractve and the couplng wthn the system. In the model system of modularzaton, the module desgn goal s to reduce the couplng between modules, ncrease module coheson. In order to acheve the desgn goal, we need to make sure that physcs and mathematcs ndependence of the module. he flow dagram that adoptng modular decomposed about varable cycle engne shown n fgure he Relevant Data n the Model he nput parameter of an engne mathematcal model s the flyng heght ( H ), Mach number ( Ma ), the man fuel flow (WFB ), the strength of fuel flow (WFA ) and the nozzle area ( A 8 ). Under the condton of guarantee engne work output parameters are the motor rotor speed, the cross secton of aerodynamc parameters and performance. Accordng to the modular modelng, descrbe the workng process of the engne component level model manly ncludes the followng three aspects: 1. Accordng to the aerothermodynamcs propertes and component propertes of the engne establsh mathematcal model, as n[3]. 2. Accordng to the engne nternal flow channel, traffc, power balance and rotor dynamc prncple to buld models whch reflect the workng process of engne stablty, dynamc mathematc, and t means some equatons to descrbe a seres of nteractons about the components work together. 3. Usng a numercal method to solve the work equatons to dentfy the common workng pont and get the engne performance parameters. When we get some of the results about above, we can buld engne module correspondng database, and t can be used n the back of the calculaton Engne umercal Smulatons and the Soluton of the Common Workng Pont When the engne workng on parts matchng, t's condtoned by the followng seven balance equaton, as n[4]: Power balance equaton of low voltage axal: 0 (1) CL L ml CL s the fan consumed power, L pressureturbne power, ml 0.99 s the low s the ntermedate shaft mechancal effcency. Power balance equaton of hghpressure axal: 0 (2) CH H mh CH and are the power whch the hghpressure compressor and consumed, H the power of the hgh pressure turbne, mh 0.99 mechancal effcency of the hgh-speed shaft. he balance equaton of hgh pressure turbne nlet flow: Wg 41 W g 41 W g41 g41 0 s s the W (3) s the hgh pressure turbne nlet secton gas flow, s the hgh pressure turbne flow whch gets from the hgh pressure turbne of characterstc data about hgh

4 Amercan Journal of Mathematcs and Statstcs 2013, 3(6): pressure turbne. he balance equaton of low pressure turbne nlet flow: W Wg 45 W W (4) g45 g45 0 s the hgh pressure turbne nlet secton gas flow, g45 s the hgh pressure turbne flow whch gets from the hgh pressure turbne of characterstc data about hgh pressure turbne. he statc balance equaton of the after mxer: p61 p62 0 (5) p61 and p62 are statc pressure of wthn mxer and external duct, they should be balanced. he balance equaton of exhaust area: A8 A 8 0 (6) A8 s the area of the gven varable nozzle 8, and A 8 = e 003. A 8 s the area of nozzle 8 whch calculate from the formula. he balance equaton of fan outlet flow: Wa 2 Wa 21 Wa 13 0 (7) Wa2 s the flow of fan outlet, Wa 13 s the flow of W Deputy external ductand a21 output he decomposton of engne system Buld a mathematcal model Buld a module lbrary he smulaton model he parameters of the model s the nlet flow of. lbrares avalable Matlab Fgure 5. he flow chart of buldng engne system model Each node n the flow dagram of engne can be obtaned whch contan the total temperature, total pressure and flow rate when we know the nput data, as n[5]: n,,, CH, 4, H, L. When engne workng n steady state, t means 1 V M E, Workng equatons and the characterstcs of components reflects the engne nternal aerodynamc and thermodynamc property together, s the descrpton of the engne nternal complex pneumatc thermal abstract mathematcal process, and also has a clear physcal meanng. In order to obtan the thermal parameters of the L CL engne through the mathematcs descrpton, the problem s converted nto workng out the equatons of components workng together as a system whch s the essence of engne component level model modellng. herefore, to determne the cooperatng ponts of engne problems are summed up nsolvng the equatons. But the nonlnear equatons have no obvous mathematcal expresson, so we can't get the analytc soluton. We use numercal methods to solve the nonlnear mathematcal model of the engne.in the frst, ntal values of ndependent varables are gven: X 1, X 2,, substtutng the values n the engne model, then parameters are calculated along the engne process, after that Check whether equatons satsfy common workng condtons and the control scheme be selected. If they satsfed, workng pont of each part under the ntal values s the common workng pont of the engne. Instead we get a set of resdual equaton. We use the vector represents some ntal values: X X1 X 2 X m (,,... ) (8) We use the vector represents some parameter: E (e 1,e 2,...e m) (9) Obvously, the vector E s a functon of ntal values, namely: E F( X ) (10) hs non-lnear equaton can't be expressed explctly, but only can be calculated accordng to the relatonshp ofthe engne thermodynamc model to get the relatonshp between the resdual E and ntal value vector X. Solvng equatons: F( X) 0 (11) We use the ewton-raphsonmethod to solve the nonlnear equatons. ake seven parameters: the speed of hgh pressure n H, pressure rato of fan CL, pressure rato of compressor CH combuston chamber turbne H, pressure rato of hgh pressure, the outlet temperature of man 4, pressure rato of hgh pressure, pressure rato of low pressure turbne L. he nonlnear equatons: E ( V, V,... V ) ( 1,2...7) So: V ( V, V,... V ) (12) Assume that the ntal value are: V ( V, V,... V ) ( 0) ( 0) ( 0) ( 0) Iteratve calculaton to step K: V ( V, V,... V ) (K) (K) (K) (K) 1 2 7

5 432 hongzheng You: Component-level Modelng echnology and Optmzatng for Varable Cycle Engne he partal dfferental equatons for nearby the nonlnear equatons V (K) : E de dv j n j ( 1,2...7) (13) j 1 V j Usng the dfference quotent nstead of dervatve: Also lke ths: M : V n E n E j 1 V j 1 V M E (14) order coeffcent matrx : he soluton vector. V j E V j n m So we get the values of varables: ( k 1) ( k) j j j V and the values of the V V V (15) We repeated teraton lke ths, contnuously revsed the ntal value, untl the error can be satsfed by the requrements of the accuracy of the balance equaton. And the numercal soluton was obtaned through the correspondng procedure wth MALAB whch s the cooperatng pont of the engne, as n [6]. he ntal values are: =0.173 CL, =0.485, =0.109 CH =0.121 H, =0.106, n =0.179, 4 = Runnng smulaton program we get results and graphcs as follows: H L Data nput Calculates the parameters of the atmosphere Intal values Calculaton of fan Calculaton of he flow resdual of hgh pressure rotor Calculaton of compressor Calculaton of MC he resdual of the power about hgh pressure rotor he flow resdual of low pressure rotor Calculaton of HP Calculaton of LP he resdual of the power about low pressure rotor Calculaton of FM Calculaton of duct he statc resdual of choosng valve and mxer he statc balance resdual of nsde and outsde duct Calculaton of AM Calculaton of afterburners Calculaton of nozzle Yes resdual<ɛ Data output he flow resdual of nozzle o Fgure 6. he dagram about smulaton of engne

6 Amercan Journal of Mathematcs and Statstcs 2013, 3(6): (a) (b) (c)

7 434 hongzheng You: Component-level Modelng echnology and Optmzatng for Varable Cycle Engne (d) (e) (f)

8 Amercan Journal of Mathematcs and Statstcs 2013, 3(6): (g) Fgure 7. he results of equatons after steady state teraton As you can be seen n the above fgures, the system acheved a stable state after about 160 tmes of teraton. Even n the ntal state devaton from steady state pont, the system can quckly return to the steady state. he steadystate value are: =0.813 CL, CH =0.235, L =0.609 =0.721 H, =0.686, n H =0.902, 4 = reached (ote: when resdual of equatons 0.05 convergence) hese are the solutons of seven nonlnear equatons. 4. Evaluaton of the Model Varable cycle engne s a very complex power plant, nvolvng flud mechancs, structural mechancs, heat transfer, combuston control and many other subjects, as n[7]. Mathematcal modellng plays an mportant role n ths research. Modellng s a very mportant n the smulaton experment, advanced modellng method s the mportant support of advanced technology. Modular modellng s a knd of advanced modellng method has been gradually appled n the smulaton feld whch has hgh value n practcal applcaton. he work n ths paper s just at the begnnng stage, and t has not done the mcroscopc arrangement job, and the model can be mproved from several respects: 1. Consderng more about the physcal characterstcs of the components, reducng the degree of model smplfcaton to mprove the smulaton accuracy. 2. Makng the model lbrary perfect and n detal, such as establshng the model of a centrfugal compressor, the model of coolng chamber and the model of export adjustable tal nozzle. REFERECES [1] GOU Xue-zhong, HOU Wen-Xang, HUAG Jn-quan, Component-level modelng technology for varable cycle engne, Journal of Aerospace Power, 2013, 28(1): [2] LIU Hong-bo, WAG Rong-qao, Investgaton of General Structure andmode ranstonmechansm of Varable Cycle Engne, Aeroengne, 2008, 34: 1-5. [3] LIU eng-wen, WAG han-xue, HUAG Hong-chao, CAI Yuan-hu, umercal smulaton onperformance of varable cycle engnes, Journal of Aerospace Power, 2010, 25(6): [4] FAG Chang-de, Varable Cycle Engnes, Gas urbne Experment and Research, 2004, 17(3): 1-5. [5] WAG Yuan, LI Qu-hong, HUAG Xang-hua, Research of varable cycle engne modelng technque, Journal of Aerospace Power, 2013, 28(4): [6] HAG Rong, YE h-feng, XUE Y-chun, Smulaton Research on Adjustment Plan to Mode ranston of Varable Cycle Engne, Measurement & Control echnology, 2011, 30: [7] XI Wang, MODULAR MODELIG AD SYSEM- LEVER SIMULAIOO AEROEGIE, Doctor Degree thess. Shangha, Chna, Shangha Jao ong Unversty