1 5 TH INTERNATIONAL CONGRESS OF THE AERONAUTICAL SCIENCES SIMULATION OF FLUID MECHANICAL AIRCRAFT SYSTEMS FROM CONCEPT EVALUATION TO QUALIFICATION TESTS Birgitta Latto, Has Ellströ, Söre Steikeller, Marti Jarelad Saab AB Keywords: siulatio, fluid, echaical, aircraft, syste Abstract This paper gives a overview of the odellig ad siulatio work for the ilitary aircraft JAS 39 Gripe s fuel syste. Fuel systes have several odellig challeges such as both copressible air ad less copressible fuel that give stiff differetial equatios, g-forces effects, oliear cavitatio ad saturatio. It is also a coplex syste that requires a odel with itegrated syste software. Dyaic odels based o physical differetial equatios have geerally bee used. The odellig work has bee doe i Easy5. Siulatios have bee doe durig the whole developet cycle of the aircraft fro cocept evaluatio to qualificatio tests. The paper gives soe exaples fro the siulatios where syste perforace ad the iteral states of the syste are calculated. Fially, the paper focuses o uerical istability of fuel systes. 1 Itroductio Saab has the ability to develop ad itegrate coplete aircraft systes. The Gripe, the world s first fourth-geeratio fighter aircraft i active service, is the ost powerful ad advaced aircraft Saab has ever built as well as the ost flexible ad cost effective. Saab has capability ad kow-how to take the overall resposibility as a tier oe supplier, through a overall approach, for aagig the coprehesive sub-tier supply chai, fro desig through developet, systes itegratio, validatio ad productio to life cycle support. Saab s expertise is withi safe, reliable, copact ad light, low power cosuig ad care-free systes solutios. Soe of the vehicle systes that are desiged ad itegrated i ilitary ad civil aircrafts by Saab are: Electric power syste Theral aageet syste Ati-ice ad de-ice Flight syste ad hydraulic ad electric actuators Fuel systes with i-flight refuellig Auxiliary power uit ad syste Hydraulic syste Ladig gear ad brake syste Egie syste Itegrated odular avioics for cotrol uits Cotrol ad oitorig software for systes Coplete systes, subsystes, equipet, cotrol uit s hardware ad software are itegrated with 60 years of experiece, curretly fro the ilitary fighter Gripe, the civil aircrafts Saab 340 ad 000, the traier Saab 105 ad UAVs. I order to achieve cost-effectiveess, odellig ad siulatio are used sice 1968 to develop the ost coplex vehicle systes. Geerally, odellig ad siulatio withi vehicle systes are used today for Total syste specificatio ad desig, e.g. fuctioality o groud ad i air 1
2 LANTTO, ELLSTRÖM Equipet specificatio ad desig Software specificatio ad desig Various siulators Test rig desig Vehicle aircraft systes are coplex systes. Coplex systes require coplex test rigs ad coplex istallatio of the equipet i test aircrafts. Durig the Gripe project it was soo foud that if oly oe ajor redesig of the fuel syste i a test aircraft could be spared, ot oly all odellig ad siulatio work for the fuel syste but also the eviroetal cotrol syste could be paid. Siulatio reduces the risk of detectig late desig faults i the developet work. Research has show that early detectio ad correctio of desig faults cost ties less tha late desig faults,  ad . See Figure 1. Usage 1:1000 Productio 1:100 Developet 1:10 Figure 1 Cost to correct desig faults durig the plaig, developet, productio ad custoer usage phases. The Four Fluid Mechaical Syste Models of JAS 39 Gripe Withi fluid echaical systes, Saab AB has developed four ajor total syste odels for Gripe i the coercial tool Easy5: Eviroetal cotrol syste (ECS) Hydraulic supply syste Fuel syste (FS) Auxiliary power syste Plaig 1:1 The odels are coplex aircraft syste odels which iclude equipet as well as the software cotrollig ad oitorig each syste. Aircraft systes have several odellig challeges such as odellig g-forces effects, ixig fuel ad air i fuel systes ad flight evelop ad eviroetal depedecy of the ECS. The odellig work has bee doe i Easy5. Figure The Saab fuel syste library. Fro . Depedig o the syste type, the odellig work has bee various. Withi hydraulics ad ECS, Easy5 subrouties of the equipet have bee used ad odified, while a ew uique library, Figure, had to be desiged by Saab AB, , i order to odel the fuel syste i Easy5. 3 Fuel Syste Model The fuel syste odel of JAS39 Gripe i Figure 3 has 300 copoets ad a cotrol uit with 70 iput sigals ad 80 output sigals. All copoets i the systes have bee physically odelled, such as valves, pipes, taks, sesors, heat exchagers. Each box represets a copoet i the syste. Each solid lie i the odel represets a power port, e.g. two fluid states (total pressure, ass flow) or electric states (curret, voltage).
3 SIMULATION OF FLUID MECHANICAL AIRCRAFT SYSTEMS CVU FlightData FuelPup DropTaks FwdTak CetTak AftTak WigTaks FRTU & Trasferpup ARTU Refuelig GECU SysteBuild Model Figure 3 The fuel syste odel of Gripe Sice the lies represet pipes ad wires ad boxes copoets, the odel looks like the syste scheatics o the scree. The eviroetal coditios such as flight coditios (g-forces, altitude) are iputs to the odel. So are the iterfaces to other systes where eergy is trasferred ito the syste (fuel cosuptio of egie). Dyaic odels based o physical differetial equatios have geerally bee used. Black-box odels have bee used for soe equipet of ior iterest such as sesors. Tables have bee used for highly oliear pheoea such as cavitatio. The cotrol uit is represeted by the syste software odel i MatrixX/Systebuild. The syste software is icorporated as a subroutie which is autoatically geerated fro the software specificatio i MatrixX/Systebuild, Figure 4. To itegrate ew code takes 4h after a ior software redesig. The hardware of the cotrol uit has ot bee odelled i these odels. 3
4 LANTTO, ELLSTRÖM T1_T (G) Fid_Target NO_TANK (G) SOURCEABLE SOURCEABLE = = BAD_TRANSF STATPRESS 99 VOL_COR_CT1F TARGET_p OR Select_Speed SUPER BLOCK 90 Procedure 5 TP_CMD_pp 4 Flow to ad fro copoets Pressure before, iside ad after copoets Speed of egies, otors, pups ad cyliders Sesor sigals, cotrol sigals Iteral sigals i cotrol uits Others 4.1 Siulatio of Syste Perforace Fuel Cotet REG_ON Figure 4 Syste software i Systebuild 4 Fuel Syste Siulatios The objectives of the fuel syste s siulatios at Saab are to verify ad validate syste fuctio ad perforace durig Coceptual desig ad developet of ew systes for aircrafts, groud supply equipet. Also test rigs are siulated. Itegratio of ew equipet, such as pups, valves, etc i the syste. Developet of ew software for cotrol ad oitorig of the fuel syste. Tactical validatio; to check FS perforace. Flight ad rig testig; to coplete tests that caot be tested (e.g. qualificatio). Tak pressure Both syste perforace ad iteral states ca be siulated for Differet operatio coditios (egie or APU supply, etc) Differet operatio states (height, Mach o, teperatures, huidity) Fuel syste states ad variables that are siulated are: Figure 5 Refuellig siulatio results 4
5 SIMULATION OF FLUID MECHANICAL AIRCRAFT SYSTEMS FROM CONCEPT EVALUATION TO QUALIFICATION TESTS I Figure 5, the siulatio results whe refuellig the seve taks i JAS39 Gripe are show. The diagra shows the fuel cotet level accordig to the sesors i the taks as a fuctio of tie. The pressure levels i the taks are also show. 4. Siulatio of Syste Software Oe siulatio area which is particularly iterestig today is verificatio ad validatio (V&V) of the software cotrollig ad oitorig the fuel syste. I JAS 39 Gripe, it has bee show that siulatio with physical odels ehaces the quality of the software while reducig the tie. Today such software is ofte odelled i tools such as MatLab/Siulik, MatrixX/Systebuild ad SysUML i the aircraft idustry. V&V with siulatio is therefore easily doe withi fluid echaical ad electric power systes by itegratig autogeerated code ito physical odels such as Saab has doe i the Easy5 odels. Nz= cost while reducig the availability of the aircraft. To ehace the quality of oitorig software is therefore a highly iterestig area to focus o. Moitorig software is ot siple to verify ad validate i test rigs ad aircrafts sice faults should be itroduced i the syste. To itroduce faults i a test rig icreases the risk to daage the test rig. That ca be severe for the tie schedule i a developet project. Itroducig faults i a aircraft ay lead to a situatio where air worthiess is ot achieved. Siulatio is therefore a powerful tool. 5 Fuel Systes ad Nuerical Istability 5.1 Nuerical Istability Modellig oliear coplex systes such as a fuel syste require hadlig of stiff differetial equatios. Stiff differetial equatios ay result i uerical probles such as uerical istability whe the differetial equatios are itegrated. 1.5 TP cd X h ω I(h*λ) 0 O ±arccosδ Trasfer ode Noral HCT Noral Figure 6 Siulatio of syste software X Figure 6 shows a siulatio exaple where the trasfer odes i the fuel syste cotrol software has bee siulated. Especially the quality of oitorig software for fault detectio ad isolatio ca be ehaced if siulated with such accurate odels. Accordig to , the literature shows that about 50% of the lie replaceable uits reoved fro aircraft are classified as o fault foud (NFF). NFF both icreases the uscheduled aiteace cost ad the spare Re(h*λ) Figure 7 Stability area for Eq. (1) itegrated with Euler s ethod. Stiff differetial equatios are geerally achieved whe the differetial equatios that odel the syste have large differeces i each equatio s badwidth. Also discotiuous 5
6 LANTTO, ELLSTRÖM oliearities ay result i stiff differetial equatios. Here, ethods to iprove cotiuous stiff differetial equatios will be discussed. Basically, there are three differet strategies to stabilize stiff differetial equatios. These strategies are illustrated i Figure 7, based o . The stability area of the syste i Eq. (1) has bee plotted there whe itegrated with Euler s ethod. x = λ x where x( 0) = 1 (1) I the figure, the two poles to the secod order differetial equatio, Eq. (), are show with X. If the poles of a differetial equatio of a stable syste are withi the stability area of the itegratio ethod used, uerical stability will be achieved. Otherwise, uerical istability is achieved. y + δ ω y + ω y = ω bu () The two poles are foud o a radius of h ω at the agles ± arccosδ for dapig ratios δ < 1, see also Figure 7. If δ > 1, the syste becoes two first orders systes with poles i ( hω ( δ + δ + 1), 0 j) ad i 1 ( hω, 0 j). δ + δ + 1 For the first order syste i Eq. (3), oe pole is foud at ( hω, 0 j). See the O i Figure 7. y + ω y = ω bu (3) The first strategy to stabilize the itegratio of a differetial equatio is to replace the itegratio ethod. It should be replaced with a itegratio ethod with a stability area that covers the poles of the odelled differetial equatios. Secodly, the tie step of the itegratio ethod ca be reduced util the poles are withi the stability area. Thirdly, the odel of the syste ca be altered, e.g. the atural frequecy ca be decreased util the poles are withi the stability area. For the iexperieced siulatio egieer, this ethod ay see iexact sice the odel will ot exactly represet the real syste the. However, if the odel s frequecy rage has bee specified, as described i , with a odel badwidth ω, there is o poit i odellig dyaics higher tha ω. Therefore, the dyaics ca either be reoved fro the differetial equatio i (1) ad () so the equatios becoe algebraic equatios (uerically stable) such as i Eq. (3) y = bu (3) Whe dyaics are required i the odel, ca istead be approxiately reduced to ω > 0. 7 (4) ω ω 5. Exaple: Fuel tak with pressurized air Fuel systes with its two differet edia, fuel ad air, have by default stiff differetial equatios. Fuel is approxiately 10 ties less copressible tha air. Therefore, a tak filled with oly fuel has a atural frequecy that is app. 10 ties higher tha a tak filled with air. Figure 8 Fuel syste tak with air ad fuel. Therefore, the fuel taks have bee odelled for JAS39 Gripe with a low order odel where oly the dyaics of the air has bee odelled. To show this with a exaple, the low frequecy dyaics of the air for a airfilled tak i Figure 8 ca be odelled with the followig differetial equatio. RT p = ( i out ) (5) V The differetial equatio of the fuel for a fuel-filled tak i Figure 8 with high frequecy 6
7 SIMULATION OF FLUID MECHANICAL AIRCRAFT SYSTEMS FROM CONCEPT EVALUATION TO QUALIFICATION TESTS dyaics ca be siplified to the algebraic equatio i Eq. (6) sice p β ρv e = ( i out ) i = out β e RT <<. ρ (6) However, discotiuous effects such as the saturatio of the tak ust also be odelled correctly. I , the odellig work has bee show. 6 Model badwidth, itegratio ethod ad tie step I(h*λ) O Figure 9 Illustratio of Eq. (5) ad (6). Figure 9 ca be used to estiate which tie step h that is suitable for a syste odel. Whe the syste is a first order syste, such as the taks i a fuel syste, ad Euler s ethod is used, the tie step should be chose as (5) h << ω b ± arccos0.1 See also O i the figure. If the syste is a secod order syste with low dapig, such as i hydraulic actuators, where dapig ca be as low as δ = 0. 1, Figure 9 shows that that if Euler s ethod is used, the tie step should be chose as X X Re(h*λ) 0.1 (6) h << ω b See X i the figure. Sice the odel will be proe to istability, Euler s ethod caot be recoeded for secod order systes with low dapig. Noeclature b Coefficiet h Tie step j Iagiary uber i Ilet ass flow of tak out Outlet ass flow of tak p Total pressure i tak R Specific gas costat of air i tak T Teperature of air i tak u Iput sigal V Volue of tak x States y Output sigal β e δ λ ρ ω b ω ω Refereces Effective copressio odulus of fuel ad tak Dapig ratio Coplex uber Desity of fuel Model bad width Natural frequecy Model badwidth  Berga B ad Klefsjö B. Kvalitet frå behov till avädig. d editio, Studetlitteratur, I Swedish.  Backlud G. The Effects of Modellig Requireets i Early Phases of Buyer-Supplier Relatios. Liköpig Studies i Sciece ad Techology, Thesis No. 81, Liköpig, 000.  Ellströ H ad Steikeller S. Modellig of pressurized fuel systes i ilitary aircrafts. Proc. Siulatio of Oboard systes, Royal Aeroautical Society, Lodo, 004.  Ljug L ad Glad T. Modellbygge och siulerig. Studetlitteratur, I Swedish.  Söderhol P. Maiteace ad Cotiuous Iproveet of Coplex Systes, Likig 7
8 LANTTO, ELLSTRÖM Stakeholders requireets to the Use of Built-i Test Systes. Doctoral Thesis, Luleå Uiversity of Techology, Luleå, 005.  Latto B, Ellströ H, Gavel H, Jarelad M, Steikeller S, Järlestål, A ad Ladberg, M. Modellig ad siulatio of Gripe s fluid power systes. Proc. of Recet Advaces i Aerospace Actuatio Systes ad Copoets, Noveber 4-6, Toulouse, Frace,