Numerical Simulation and Performance Analysis on Windmill Starting Process of Small Turbojet Engine

JOURNAL OF CHINA ORDNANCENumerical Simulation and Performance Analysis on WindmillStarting Process of Small Turbojet EngineYANG Xin-yi( 杨欣毅)', TIAN Yu( 田宇)”, ZHU Xu-cheng(朱旭程)'，ZHOU Yuan(周源)', LI Guan-jun(李冠军)'(1. Naval Aeronautical and Astronautical University, Y antai 264001，Shandong, China;2. Detachment 92, Unit No. 92941, Huludao 125001, Liaoning, China;3. Naval East China Sea Fleet 19 division, Ningbo 315122, Zhejiang, China)Abstract: A new simulation strategy is proposed for the starting process of missile turbojet engine windmill. The startingprocess of windmill before ignition is simulated using a radial basis function neural network ( RBFNN) , and the accelera-tion process after ignition which model is a set of nonlinear equations is solved using a particle swarm optimization ( PSO)algorithm. The introduction of PSO helped to tackle the problem of divergence caused by traditional iteration methods. Thecalculated result is in a great agreement with test data, which shows that the presented model has a high accuracy. Thestaring processes are simulated at dfferent ignition times, and the results are analyzed synthetically. The analysis showshow the ignition time ffects the starting performance of engine windmill. The method ofers a useful tool for ignition timeoptimization as well as engine starting performance analysis.Key Words: missile propulsion; turbojet engine ; windmill; moving least squares; particle sw arm optimizationCLC Number: V235. 1Document Code: AArticle ID: 1673-002X( 2011)03-0145-08state. The compressor can be test to obtain its lowIntroductionspeed range on special test beds2. It can be also ac-Small turbojet engine, such as missile main en-quired by extrapolating the existing characteristics mapgine, is usually started using a windmill. The engine isof high rotational speed. But the extrapolation methodfirst driven by using a booster to propel the windmill.needs detailed structure and size data of compressor' 3.Then it is ignited and acelerated into cruise stage.Windmill process is a complex nonlinear process. ADuring its starting process，the inlet and components’neural network is used to model the engine windmillconditions are changing rapidly, which, in turn， afsince it has ability to approximate the nonlinear func-fects the stability of engine and some malfunctions maytions. YU Da-ren43 used a radial basis function neuralhappen'. Therefore it is very necessary to study thenetwork ( RBFNN) to model the windmill of missilestarting process of missile turbojet engine theoretically.turbojet engine dynamically on the base of test data onSome problems exist in the modeling and simula-windmill starting. WU Zhi-wen' 5 made some improve-tion of starting start process of a missile turbojet en-ments on the neural network starting model of enginegine. In the windmill process before ignition, the pres-windmill. He used the relative priori knowledge tosure ratio of compressor is less than 1. The compressortransform the input viriable of network and reduce themanufacturer provided only the high rotational speednumber of input parameters. As a result, the generali-range of compressor without low rotational speed range.zing ability of the network is enhanced greatly evenThis makes it more difficult to model the windmillwhen the sample data is relatively few.中国煤化工Sponsored by the National Aeronautical Science Foundation of China( 20095584006 )Received 2011-04-07MHCNM HGBiography YANG Xin-yi(1978- ), male, lecturer, E-mail: jimyang2008@ 163. comJOURNAL OF CHINA ORDNANCE, 2011, Vol.7, No. 3The starting process model after ignition consistsand the characteristic curve of engine windmil. Theof nonlinear equations. These equations can be solvedfocus now is to obtain the parameters of compressorby Newton-Raphson ( N-R ) and Broyden method.outlet pressure, thrust and air flow.These methods are simple and widely used. But the it-As windmill start test is difficult to execute, theerative methods tend to be easily affected by the initialacquired test data are just a few curves of compressorconditions，and have some convergent problems. In theoutlet pressure and rotational speed. In the case, therecent years，some artificial intelligence methods, suchgenerality ability of traditional neural network tends toas Genetic algorithm and paricle swarm optimizationbe weak. In order to improve the generality ability of(PSO) algorithm, have been applied to solve the en-network, some relative priori knowledge, such as thegine dynamic model'- 1。And the methods have betterrelation between residual power and acceleration, isperformance than the traditional iteration methods.used to transform the network input parameters.When the oil control of engine is definite, the ig-A mathematical model of windmill start is estab-nition time becomes very important to windmill start- lished using the neural network. If the rotor inertia ising. Different ignition time results in different startingconsidered and the engine thermal inertia is ignored ，performance. The ignition time is usually determinedthe relationship between rotational speed n and the in-by tests. The efcts of ignition time on stability marginlet pressure P. and outlet pressure P, of compressor isof compressor, temperature of combustion chamber and given bystarting time has never been analyzed theoretically.sdn = ow,dt 30In this paper, the start process of a missile turbo-jet engine is divided into two parts: windmill processwhere J, engine rotor inertia, is a constant.△W is thebefore ignition and aceleration process after ignition.acceleration moment of engine: .The windmill process before ignition is simulated byoW =g(P, ,Pr ,n).(2)neural networks, and the nonlinear functions of acce-The network which needs training is as followsleration process after ignition are solved by PSO algo-d1 =f(P, ,Pn,n). .(3)rithm. The whole rotational speed range of compressor. It can be seen from Eq. (3) that the input pa-is obtained using moving least squares ( MLS) on thebasis of test data. The effect of ignition time on enginerameters of network are Pi，n and Pr, and the outputstarting performance is obtained using the proposedparameters is dn/dt. The input variables are recom-bined using the priori knowledge. If Pn and Pn can bemethod.replaced by pressure ratio , then the network becomes1 Modeling of Engine Starting Process=f(πc,n).(4)1.1 Modeling of Windmill ProcessRotational speed is strongly depend on pressureThe engine is not ignited during the windmillratio, thus the input parameters can be transferred far-process. Therefore not all the parameters need to bether. The rotor is accelerated by the residual powersolved. Attention is paid on the parameters such as ro-ON:tational speed, compressor outlet pressure, thrust andair flow, which have great influence on engine perform-Jn dnn =ON.(5)It can be seen from the compressor characteristicThe turbojet engine is driven into windmill processmap that the unit power of compressor is dependent onwith the aid of the propulsion of missile booster. So ,π。and中国煤化工rotational speed on-the inlet has the same Mach number as the misile.ly affects:MYHCN M H Gnd the right part ofThe rotational speed during windmill process can beEq. (5) Is the tuncton ot π。. Ihen Eq. (5) is writtencalculated from the Mach number curve of missile'*]s一146一YANG Xin-yi, et al. 1 Numerical Simulation and Performance Analysis on Windmill Starting Process of Small Turbojet EngineJrh=ON=g(π.).(6)Z=p, -P'.(11)Htwhere PExτ is the power extracting value, ( 9mgeur )atAs a result Eq. (4) can be rewritten asand (9mgor)的g are the calculated air flow of turbine in-(7)let and the value read from the turbine characteristicsmap， respectively, P,. and p', are the turbine outletNow the network output is the differential coffi-pressure calculated by different ways, P。is calculatedcient of n', we can easily get n from n2 by its integraland extraction. As n is known, the input and output offrom the component modules before nozzle, and p', isEq. (7) are exchanged to obtain the relation betweencalculated from nozzle module.1.2.2 Extension of Compressor Characteristics Mapπ。and n:The compressor characteristics map on the wholedn2*)π。=f(].(8)range of rotational speed is necessary for the simulationWhen the network is trained, the input sample isof engine starting. While the known map has only thed(n2 )/dt = 2n( dn/dt)，the rotational speed curvescharacteristics data of high speed, it is required to ex-need to be differentiated smoothly, and dn/dt is re-tend the map to low rotational speed.placed with On/ Ot. .The test data is necessary to obtain a map of wholeIn this paper the RBF network is used to modelrotational speed range. And some parameters of com-the windmill starting. Because the priori knowledge ispressor can be extracted from test data. These data andused, the network has better generality ability. Thethe data in the known map are used to obtain the mapnetwork training is performed by Matlab toolbox.of the whole speed range by a surface fitting tech-The thrust and air flow during the windmillniqueprocess are calculated by the method presented in Ref.The compressor parameters can be extracted from[9- 10]. .test data which is obtained on ground test bed or alti-1.2 Modeling of Acceleration After Ignitiontude test bed. Below are the equations used for param-1.2.1 Dynamic Model of Accelerationeter extraction.In a short time after ignition, the flame flows intoneon=n√288. 15/T,(12)the turbine rapidly and drives it to rotate. The turbineoutput power rises greatly and drives the compressor towork. Meanwhile the operating temperature rise of tur-_2kbine decreases the flame density and the air flow.9Gcor =Ap。RT(h-1)(,)-(问)小.w hile the pneumatic thermal parameters change faster(14)than the rotational speed, resulting in the sudden upwards of engine working line on the compressor charac-(;)-1teristics map. The working line goes upwards from aηe =-(15)point which pressure ratio is less than 1 to a new point(号)which pressure ratio is bigger than 1 ，while the rota-tional speed keeps unchanged.where norr is the corrected rotational speed, Gacor is theIn order to get the whole working line, the acce-corrected air flow, η。is the compressor ' s efficiency,leration after ignition needs to be modeled. The dy-Ti, P and P are the total temperature, total pressurenamie model of acceleration process consists of the fol-and pressure of compressor inlet, and Tr,Pr are thelowing three equations:total tem中国煤化工of compresor out-let.z,=P,-P.-Pxr-(n)ndn,at’ThecaJ.H.pressure Iaius and the corrected airCNMHG2z2=(9ro.r)a- (9mon)ng,(10) .flows at 10% ，30% and 50% corrected rotational-147-JOURNAL OF CHINA ORDNANCE, 2011, Vol.7, No.3speeds are listed in Tab. 1.4.0Tab.1 Charateristies data calculated from test data10%30%50%3.No.9reer。T。0.491.022.01 1.13 3.34 1. 45e 2.53.32 1. 512.00.39 1.031.61 1.213.23 1. 581.50.37 1. 041.57 1.233.18 1. 611.(0.60.40.200030.609It is convenient to transfer the planar compressorcharacteristics map into a spatial surface. The charac-Fig.2 Fit surface of compressor pressure ratioteristic data points are used to fit a surface. The distri-(N-R) method. But these methods are very sensitivebution of test data points is shown in Fig. 1.to the initial values and need to calculate the differenti-4.al coefficients of the equations at every iterative time-4step. These characteristics often lead to the divergence3.2of the model solution.3.02.5-Recently particle sw arm optimization( PSO) algo-rithm has shown its advantage in the engine model so-lution. PSO algorithm is a bionic optimization algorithm1.firstly put forward by Kennedy and Eberhart12]. In0.5PSO algorithm, a population of particles is initialized1.0080.6040200firstly, and then the particles are iterated to get the op-”n..timum solution. When iterated, a particle updates it-Fig.1 Distribution of domain nodes at spaceself by two“best solutions". One is the best solutionThe traditional least squares(LS) method is usedobtained by the particle itself ( called personal best,difficult to fit a surface based on these points becausepbest. ), the other is the best solution obtained by thethe distribution of data points at space is complex. Inwhole population( called global best, gbest). All parti-this paper a moving least squares ( MLS) method iscles are set into a D-dimension solution space and theused to approximate the compressor characteristics sur-number of particles is n. The ith particle flies in theface.solution space with a certain velocity. And this velocityMLS is different from traditional Is. It consists ofis adjusted dynamically with the paricle' s own experi-a coefficient vector a(x) and a base vector p(x). Theence and other particles ’experience. The position ofconcept of compact support is introduced. This meansthe ith paricle is X =(xu，xp,...,xp) and its per-that a(x) is a function of coordinate x and is constantsonal best( pbest) is P: = (Pa，Pa.., P:o). Theonly in the interpolation dormain of base points. MLSglobal best (gbest) of the whole population is P, =makes it easier to approximate the compressor charac-(Pn, Pe2,"", Pgn). The velocity of the i-th particle isteristics surface than the traditional LS. The approxi-mated surface is ilustrated in Fig. 2.For any particle, its dth dimensional(1≤d≤D)1.2.3 Solution of Model Nonlinear Equationsvelocity中国煤化工the followThe dynamic model of engine starting is a nonli--xu) +YHCNMHG'near equation set. These equations are usually solved(16)by some numeric iterate method like Newton-Raphsonxu =xu +0ia.(17)-148-YANG Xin-yi, et al. / Numerical Simulation and Performance Analysis on Windmill Starting Process of Small Turbojet Enginewhere i=1, 2,.，n; d=1, 2,., D; w is the iner-that the simulated total pressure of compressor outlet istia weight; which is often used as a parameter to con-also close to the test curve, and the maximum error istrol exploration in the search space. Ci and C2 are the5.2%. When the engine is ignited, the outlet pressureacceleration constants( usually set Cq = C2 = 2)，andrises abruptly. It can be seen from Fig.5 that the tem-particles’maximum velocity is limited by ug*. Whenperature of combustor rises suddenly, and it rises ra.PSO algorithm is applied to solve engine nonlinear epidly as the oil is supplied to the combustion chamber.quations, the particles are equation ’s candidate solu-0.6rtions, gbest is the best solution until current iteration“-- experimental0.5 _ caclaedand the fitness function is Z=F(X).As PSO is insensitive to initial condition values ,0.4-the algorithm has better convergence performance thanthe traditional iteration methods when the engine modelis solved. In this paper the equations of engine starting0.2model are solved using PSO algorithm.34562 Simulation of Engine Starting ProcessFig.4 Pressure curve of compressor outletThe whole engine starting process is simulated byduring starting processthe methods mentioned above. The simulated windmillstarting time is the time when the rotor begins to rotate.1100The engine ignites 1.99 s after the windmill starts,1 0000which is also the starting time of acceleration process.900800The engine start model is solved by PSO. Some simula-700ted parameters as the rotational speed, the total pres-600sure and total temperature of combustor outlet are500shown in Fig. 3 to 5. As only a few parameters are400measured remotely， the measured parameters which300can be compared with the simulated ones are rotational204-5一后speed and compressor outlet pressure..0一Fig.5 Temperature curve of combustor outlet.5 --- experimerntal一- calculatedFig.6 is the simulated working line of engine. It. 2.0can be seen from Fig. 6 that the compressor pressure1.5-ratio is less than 1 during windmill stage as the com-鲁10pressor is driven by the inlet air flow. After ignition ,0.5-the working line turns upwards along the same rotation-al speed line as the thermal parameters change rapidlywhile the rotational speed keeps stable. Afterwards,the rotational speed rises with increase in oil supply. ItFig.3 Rotor speed-time curve during starting processP. 6 thal the srge margin reachesIt can be seen from Fig.3 that the simulated rota-the least中国煤化工ition, the workingtional speed curve is very close to the test curve. Theline keepTYHCN M. H Gor the engine start-maximum error is 3. 6%，From Fig. 4 we can knowing process, the ignition time is the most important.一149--JOURNAL OF CHINA ORDNANCE, 2011, Vol.7, No.3When an ignition time is selected, the surge margin ofspeed at six ignition times are listed in Tab. 2.compressor must be considered and kept in a safeTab.2 Efect of ignition time on starting timerange. For the simulated engine staring, the ignitionio.123456( rotational speed is 4 951 r/min) surge margin isignition time/s 1.776 1.99 2.238 2.751 3.112 3. 54615.98%，which meets the safety requirement of en-speed/(r-min-') 4000 4951 6000 7000 8000 9000gine.start time/s 5.283 4.975 4.292 4.128 4.047 4. 012.0-To compare the difference between the starting.5-processes, the rotational speed curves under differentcondition are listed in a three dimensional space withx 2.5-three coordinates: time, ignition time, and rotational.0speed. As shown in Fig. 7, the starting process of en-1.5-gine is different at a diferent ignition time. The laterthe ignition time is, the shorter the engine starting time0.s十之当is. As shown in Tab.2, when the engine is ignited at3. 546s, the starting time is 19. 36% shorter than theFig.6 Operation line on compressor map duringnormal starting time.starting process3.0The starting time of missile turbojet engine is de-fined as the time from 0 to 90% maximum rotational含2speeds. By this definition, the starting time of engineis 4.975 s. During starting process， the combustortemperature suddenly rises after ignition, and the high-0,est temperature reaches 1 032. 6 K, which is lower thanthe restricted temperature of combustor outlet.Num.3 Effect of Ignition Time on StartingFig.7 Rotational speed lines at different ignition timesPerformance3.2 Effect of Igntion Time on Compressor SurgeThe main factors affecting the engine starting per-Marginformance include oil control law and ignition time. UnFor the selection of ignition time, only the startingder the condition of a fixed oil control law, the ignitiontime should be not considered , but the effect of ignitionis a key to the starting performance. For the missiletime on the stability of compressor during staringturbojet engine under study, its ignition time is deter-process is also considered. As described in Sectionmined by test. Though the present ignition time guar-3.1, the surge margins of six ignition times are calcu-antees the successful starting of engine, few researcheslated and listed in Tab. 3, and the six working lines arehave been done on the effect of ignition time on enginelisted in Fig. 8 with its three coordinates, including airstarting performance. In this paper, the effect is stu-flow rate, ignition time, and pressure ratio.died theoretically in detail.Form Fig. 8 we know that the upward step of3.1 Effect of lgnition Time on Accelerationworking lines become more evident with the later igni-In order to investigate the effect of ignition time onion ti中国煤化工e surge margins de-acceleration performance, six different ignition timescrease.IYHCNMHGtthesurgemarginisare selected (No. 1 -6). Starting time and rotationalmnly 9.22%，which is 42.3% less than the normal-150--YANG Xin-yi, e al. / Numerical Simulaion and Peformance Analysis on Windmill Saring Proces of Small Turbojet Enginepart corresponds to 1.91 -3. 02 s. If the ignition timeis within this part, the engine has a short acceleration.03.5--time and provides the surge margin..2.52.01.5-.0-置5.0Numn.Fig.8 Working lines vs. ignition times4550.20? 4.00.153one when it is ignited at 3. 546 s.0.05 1.5Tab. 3 Effect of ignition time on surge marginFig.9 Acceleration performance vs. ignition timesN4Conclusionignitin time/s 1.776 1.99 2.238 2.751 3.112 3.546 .sped(rmin-1) 4000 4951 6000 7000 8000 9000In this paper , the starting process of a missile tur-surge margin/% 21.02 15.98 12.71 10.39 9.87 9.22bojet engine is simulated. The starting process of en-gine is divided into two parts: windmill and accelera-3.3 Effect of Ignition Time on Combustor Outlettion after ignition. The former is simulated by neuralTemperaturenetworks and the later nonlinear equations are solvedUsually the temperature of combustor outlet is re-using the particle swarm optimization algorithm. Thstricted during starting process. The calculated resultoptimization algorithm has greater convergence perfor-shows that the temperature of combustor outlet suddenlymance than the traditional iteration methods and im-rises after ignition. The later the ignition time is, theproves the modeling accuracy of engine staringgreater the rise in temperature is. But the temperatureprocess.Agreement between simulated results and testeurves of different ignition times all tend to 1 032 Kdata suggests that the proposed mathematical method iswhich is less than the restricted temperature ( 1 143very useful for the simulation of missile turbojet wind-K). It is concluded that the ignition time has a litlemill starting. The effect of ignition time on engineinfuence on the temperature of combustor outlet, andstarting performance is obtained by modeling the star-its temperature won't exceed the restricted value.ing process at six different ignition times. This providesIn general, the ignition time does have influencea research method and useful tool for the analysis ofon engine starting perormance. The later the ignitionengine performance and the determination of ignitiontime is, the shorter the start time is, while the surgetime.margin decreases. The ignition time has litte influenceon the temperature of combustor outlet. As a result,Referencesthe determination of ignition time should consider the[1] YU Jun, YU Shou-zhi. Starting and accelerating model ofstarting time and surge margin synchronously. The re-missile turbojet engine in fnight test[J]. Journal of Pro-lationship between ignition time and starting perfor-pulsion Technology, 2001, 22(6): 454 -457. (in Chi-mance can be given by a curve shown in Fig. 9. Thisnese )curve is helpful for determination of ignition time. 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Efctral Networks, Piscataway: IEE Serice Center, 1995,of turbine efficiency changing on turbo engine' s accelera-4: 1942 - 1948.中国煤化工MYHCNMHG.一152一