Two- and Three-Dimensional Validation of Icing Model

Transcription

1 APCOM & ISCM th December, 13, Singapore To- an Three-Dimensional Valiation of Icing Moel *Ryosuke Hayashi¹ an Makoto Yamamoto 1 Grauate School of Mechanical Engineering, Tokyo University of Science Niijyuku, Katsushika-ku, Tokyo, Japan Department of Mechanical Engineering, Tokyo University of Science *Corresponing author: j45173@e.tus.ac.jp Abstract Ice accretion is a phenomenon here super-coole ater roplets impinge an accrete on a boy. It occurs frequently on airplanes, inmills an conuctor cables. In particular, hen ice layer is forme on an aircraft ing, it affects on the aeroynamic performance by increasing rag an ecreasing lift, an it may cause a serious accient. On a jet engine, ice accretion isturbs the inlet flo, an separate ice pieces can amage to the compressor an the casing, hich leas to the severe performance egraation. There have been several accients ue to the ice accretion. Therefore, the estimation of ice accretion in the esign phase is necessary to avoi accients. The research on ice accretion phenomena has been conucte since early 199's. The first icing simulation moel as evelope by Messinger in This moel has been iely use in simulating ice accretion phenomena. Recently, Messinger moel as evelope by Ozgen an Canibek in 9. This moel is more sensitive than Messinger moel in suitably estimating the runback mass. The preictive performance for the runback mass has a huge influence on ice accretion phenomena in glaze ice conition. In this stuy, e conucte the valiation of these icing moels in to- an three-imensional fiel. Finally, e inicate Messinger moel is more superior to Messinger moel in simulating glaze icing. Keyors: Multiphysics CFD, Ice Accretion, Jet Engine, Messinger Moel Introuction Ice accretion is a phenomenon here super-coole ater roplets impinge an accrete on a boy. It has to types of ice shape. One is calle rime ice hich is generate at very lo temperature (less than -1 C). On the rime ice conition, roplets in the air instantly freeze at the impingement point. The other is calle glaze ice hich is generate at -1 to C. On the glaze ice conition, roplets graually freeze ith running along a boy (so-calle runback). This phenomenon is consierably important in simulating the glaze icing. When ice layer is forme on an aircraft ing, it affects on the performance by increasing rag an reucing lift, an it may cause a serious accient. On a jet engine, ice accretion isturbs the inlet flo, an separate ice pieces can amage to the compressor an the casing, hich leas to the severe performance egraation. There have been several instances of accients ue to ice accretion. Obviously, it is essential that the mechanisms of ice accretion are unerstoo. The estimation of ice accretion is necessary to avoi accients an useful to reuce the cost an the esign time in the esign phase of aircrafts an jet engines. Hoever, the experimental investigations are very ifficult, because it is not easy to set ice accretion conitions repeately in a in tunnel. Therefore, it is expecte computational flui ynamics (CFD) ill be a useful ay to preict ice accretion phenomenon. CFD research of ice accretion phenomena has iely been conucte by agencies an universities, such as NASA [1], ONERA [] an so on. 1

2 The first icing simulation moel as evelope by Messinger in 1953 [3]. This Messinger moel has been iely use in the major research institution such as NASA, DRA an ONERA. The results preicte ith the Messinger moel is in goo agreement ith the experimental ata in rime ice conitions. Hoever, in glaze ice conitions, the preictive performance of the Messinger moel is lo, because the mass of the runback is unerestimate. Therefore, the user specially moifie the Messinger moel in simulating glaze icing phenomena. Recently, Messinger moel as evelope by Ozgen an Canibek in 9. It is expecte that the Messinger moel is more sensitive to glaze ice conitions than Messinger moel, because it inclues phase change conition from rime ice to glaze ice. Hoever, the extene Messinger moel has not been extensively valiate yet. In this stuy, e conucte the valiation of these icing moels to- an three-imensional fiel. In the to-imensional valiation, e aopte the NACA 1 airfoil because a lot of experimental ata are available. In the three-imensional valiation, e aopte a fan rotor an FEGVs, because these components are easy to accrete ice. Finally, e inicate Messinger moel is more superior to Messinger moel in simulating glaze icing. Numerical Proceure Our icing simulation coe is compose of iterative computations for flui motion, roplet trajectory, thermoynamics an gri moification. Belo each computational etail is explaine. Flo Fiel The flo fiel is assume to be three-imensional, compressible an turbulent. The governing equations are Favre-average continuity, Navier-Stokes an energy equations. Coriolis force an centrifugal force are ae as boy forces. The Kato-Launer k- turbulence moel (Kato an Launer, [4]) is applie to estimate turbulence. The governing equations are iscretize using seconorer upin TVD scheme (Yee an Harten, [5]) for the invisci terms, secon-orer central ifference scheme for the viscous ones, an LU-ADI scheme (Fujii an Obayashi, [6]) for the time integration. Droplet Trajectory Droplet trajectory calculation base on a Lagrangian approach is performe to obtain the roplet collection efficiency on a boy. The calculation uses the folloing assumptions: 1. Droplet is spherical.. Droplet is sufficiently small, an thus it oes not break up. 3. Forces acting on the roplet are rag, centrifugal force an Coriolis force. 4. Droplets o not interact ith each other. 5. Droplets o not affect on the flo fiel (one-ay coupling). 6. Initial roplet velocity is equal to the gas velocity at the release point. The equation of roplet motion is U 3 f 1 CD U r U r U t 4 r here t is the time, Ur is the relative velocity beteen the gas an the roplet, is the roplet iameter, an f an are the gas an the roplet ensity. The secon term on the RHS represents (1)

3 the centrifugal force an Coriolis force, here is the rotational spee, an r is the raial position of the roplet. The rag coefficient CD is expresse as: CD Re () Re here Re is the Reynols number of the roplet base on the iameter an the relative velocity beteen the gas an the roplet. The roplet trajectory calculation is conucte to obtain the collection efficiency. The collection efficiency is folloe as: A U in in imp (3) MVD LWC here Ain is the roplet inlet area, Uin is the roplet inlet velocity, LWC is the liqui ater content, Nimp is the roplet impingement number, Nin is the roplet inlet number an Aimp is the roplet impingement area. The collection efficiency is one of the key parameters of the icing simulation. Messinger Moel The Messinger moel as evelope by Messinger in This moel is base on the mass an energy balance in a control volume. The governing equations is folloe as: Q im in m im in ac N N in e s A imp m m m, m (4) air fri ac e s out Q Q Q Q Q, Q Q (5) here mim, min, mac, mout an me,s are the mass of impingement, runback-in, accretion, evaporating (or sublimating) an runback-out, respectively; Qim, Qin, Qair, Qfri, Qac, Qe,s, Qout an Qcon are the energy of impingement, runback-in, air, friction, accretion, evaporating (or sublimating), runbackout an convection. The freezing rate f can be erive from Eqs. (4) an (5). out con f m m m ac (6) im in 1 f m im min me s m out, (7) if f = 1, all mass in the control volume accretes, on the other han, if f =, all mass in the control volume runbacks to the next cell. Messinger Moel Messinger moel has a problem in the preictive performance of the runback mass, because the phase change from rime ice to glaze ice is instant. To get over this problem, Messinger moel as evelope by Orgen an Canibak in 9 [7]. This moel is base on the Stefan problem, hich is a stanar metho of the phase change problem. The governing equations are expresse as: Ti t ki C i pi T h i (8) T t k C p T h (9) 3

4 B B i i mim min me, s (1) t t Bi Ti T ilf ki k (11) t h h here Eqs. (8) an (9) are the energy equations in the ice an ater layer respectively, Eq. (1) is the mass conservation equation an Eq. (11) is the phase change conition at the ice/ater interface. In these equations, Ti an T are the temperatures of ice an ater; Bi an B are the thicknesses of ice an ater layers; ki an k are the thermal conuctivities of ice an ater; Cpi an Cp are the specific heats of ice an ater; mim, min an me,s are impinging, runback an evaporating (or sublimating) ater mass flo rates for a control volume, respectively; i an are the ensity of ice an ater; LF enotes the latent heat of soliification of ater. Ice ensity is assume to have to ifferent values for rime ice r an glaze ice g. The coorinate h is normal to the all or ice surface. To-imensional valiation Computational Target an Gri We aopte a NACA 1 airfoil in the to-imensional valiation, because a lot of experimental ata are available in literatures. In this stuy, the overset gri metho is applie to clarify the icing area aroun the leaing ege, here it is easy to occur icing phenomena. The sub gri resolution is important for icing simulation. We checke relatively gri for the icing simulation by three type sub gris; the coarse gri resolution is 81 x 1, the meium gri resolution is 1 x 51 an the fine gri resolution is 31 x 81. The coarse gri has a margin of error in the icing limit point. Therefore, e aopte the meium gri in this stuy. The number of gri point in the main gri is 15,691 an that in the sub gri point is 1,51. The computational omain is chor chor. Computational Conition The computational conition is liste in Table 1. The LWC means the liqui ater content, an the MVD is the meian volume iameter of roplets. The number of valiation cases is six. The number of inlet roplets is 1,,.The bounary conitions are folloe as; in the inlet bounary, the flo angle, the volume flo rate an the total temperature are fixe an the Mach number is extrapolate ; in the outlet bounary, the static pressure is fixe an the others are extrapolate; in the all bounary, no-slip, aiabatic an all function conitions are applie. Uner the these conitions, e compare Messinger moel ith Messinger moel in the to-imensional valiation. Chor [m] Table 1. Computational Conition of D Valiation Angle of Static Static Velocity LWC Attack Temperature Pressure [m/s] [g/m [eg.] [ C] [kpa] 3 ] MVD [m] Exposure Time [s] Run Run Run Run Run Run

5 Result an Discussion We valiate our icing simulation coe by use of the NASA, DRA an ONERA simulation ata an the experimental ata [8]. These simulations ere conucte by Messinger moel. The ice shapes are seen in Fig. 1; (a)-(c) are uner the rime ice conition, ()-(e) are uner the glaze ice conition. In the rime ice conition, the noticeable ifference of the preictive performance beteen Messinger moel an Messinger moel oes not appear. This is hy the runback phenomenon oes not occur in the rime ice conition. On the other han, there is consierable isagreement in the glaze ice conition. Messinger moel gives the results closer to the experimental ata than Messinger moel, because it is sensitive to the runback mass. Hoever, the simulation results of NASA, DRA an ONERA can reprouce the glaze icing even if they use Messinger moel. The reason hy our icing simulation coe of Messinger moel is not moifie unlike their icing moels. Therefore, Messinger moel nee to be moifie hen simulate the glaze icing. Three-imensional valiation Computational Target an Gri We valiate our icing simulation coe by use of a jet engine. The icing components of jet engine are the rotor fan, FEGV (fan exit guie vane), nose cone, splitter an lo pressure compressor. In this stuy, e focuse on a fan blae an FEGV, because these are more accrete ice area. The jet engine use in this stuy has tenty-four rotor blaes an sixty stator vanes. For simplicity, only one rotor blae an to stator vanes are simulate, assuming the geometrical perioicity. The computational gri base on an overset gri metho an a multi block metho is exhibite in Fig. ; (a) is the main.1 Exp. NASA ONERA DRA.1 Exp. NASA ONERA DRA.1 Exp. NASA ONERA DRA (a) Run 1 (b) Run (c) Run 3 Exp. NASA Exp. NASA Exp. NASA ONERA.1 ONERA.1 ONERA DRA DRA DRA () Run 4 (e) Run 5 (f) Run 6 Figure 1. Icing Shape of D Valiation 5

6 gri for the passage, (b) is the sub gri aroun the blae. The total number of the gri points is about.8 million. Computational Conition Computational conitions in this stuy are summarize in Table. We set three cases ith ifferent total temperature. In all cases, the mass flo rates are same. The roplet trajectory simulations are conucte for 1,, roplets ranomly an spatially istribute at the computational upstream bounary. The initial roplet velocity is equal to the local gas velocity. Total pressure, total temperature an flo angle are impose, an Mach number is extrapolate at the upstream inflo bounary. The inflo turbulent kinetic energy is assume by the.1 % turbulence of the free stream. Aiabatic, no slip an all function bounary conitions are prescribe on the stationary an rotating surfaces. The exit static pressure is specifie. Result an Discussion Fig. 3 shos the static temperature istribution at the rotor mispan, hich is a pitch-average. Aroun the leaing ege of the rotor suction sie, the static temperature is consierably lo (about K, Run 1) ue to the high Mach number region. Even in the high temperature region such as the rotor ake, the stagnation point an the pressure surface on the FEGV, the temperature is belo the freezing point. Therefore, ice accretion can occur if the super-coole roplet impinges on the blae surface. Fig. 4 inicates the collection efficiency in Run 3. A lot of roplets impinge on the rotor suction sie, particularly, at the hub sie. There are no impingement roplets on the rotor suction sie. Some roplets impinge on the pressure sie of the FEGV. Other simulation cases have a same tenency. Finally, e sho numerical results of the ice accretion. Ice thickness istributions are exhibite in Fig. 5. These figures are for the suction sie of the rotor fan, because this is the thickest icing area. In all Messinger moel cases, icing area expane to the tip sie ue to the centrifugal force. (a) Main Gri (b) Sub Gri Figure. Computational Gri of 3D Valiation Rotational Spee [rpm] Table. Computational Conition of 3D Valiation Total Total Mach LWC Pressure Temperature Number [g/m [MPa] [K] 3 ] 6 MVD [m] Exposure Time [s] Run Run Run

7 P.S. This tenency cannot be confirme by use of Messinger moel. This is cause by the preictive performance of the runback ater. In the case of Messinger moel, the higher inlet temperature becomes, the more the runback mass becomes an the larger the icing area is. The ice volumes of all computational conitions are summarize in Fig. 6. In the lo inlet temperature case, the icing moels make no ifference of the ice volume. Hoever, in the high inlet temperature case, the ifference beteen both icing moels can be confirme on the rotor fan icing. On the other han, the icing on the FEGV is little istinction, because the runback harly occur at the FEGV. Therefore, e recommen Messinger moel in simulating the ice accretion, because this moel can reprouce runback phenomena in glaze ice conitions. Conclusion We valiate Messinger moel an Messinger moel. The knolege obtaine in this stuy is escribe belo: (1) In to imensional valiation, the icing moel makes no ifference on the icing phenomenon in the rime ice conition. () In to imensional valiation, Messinger moel is better agreement ith the experimental ata ue to the higher preictive performance of the runback mass than Messinger moel. (3) In three imensional valiation, there is no ifference beteen Messinger moel an Messinger moel in lo inlet temperature case. (4) In three imensional valiation, Messinger moel can reprouce the span irection ier icing area in the spanise irection on the rotor fan ue to the centrifugal force in high inlet temperature case. (a) Run 1 P.S. S.S. S.S. (a) Rotor Fan (b) Run (c) Run x x 1 1 [K] [1/(m s)] Figure 3. Static Temperature at Rotor Mispan 7 (b) FEGV Figure 4. Collection Efficiency

8 Span Span Span (5) We recommen Messinger moel in simulating the icing phenomenon, because this moel is superior to Messinger moel in terms of the preictive performance of the runback mass. References [1] Biell, C. S. an Potapczuk, M. G., (1993), Users Manual for the NASA Leice Three-Dimensional Ice Accretion Coe (LEWICE3D), NASA TM [] Hee, T. an Guffon, D., 1995, ONERA Three-Dimensional Icing Moel, Journal of AIAA, Vol. 33, No. 6, pp [3] Messinger, B. L., (1953), Equilibrium Temperature of an Unheate Icing Surface as a Function of Airspee, Jounal of the Aeronautical Sciences, vol., no.1, pp [4] Kato M., Launer B. E., (1993), The moeling of turbulent flo aroun stationary an vibrating square cyliner, Proceeings of 8th Symposium on Turbulent Shear Flos, [5] Yee H. C., (1987), Upin an symmetric Shock-Capturing Schemes, NASA TM [6] Fujii K. an Obayashi S., (1987), Practical application of improve LU-ADI scheme for the three-imensional Navier-Stokes computations of transonic viscous flos, AIAA Paper, [7] Ozgen S., Canibek M., (9), Ice accretion simulation on multi-element airfoils using extene Messinger moel, Heat an Mass Transfer, Vol. 45, pp [8] William B. Wright, P. W. Gent an Diier Guffor, (1997), DRA/NASA/ONERA Collaboration on Icing Research, NASA CR (a) Run 1 (b) Run (c) Run 3 Figure 5. Ice Thickness at Suction Sie of Rotor Fan. [mm] Ice Volume on FEGV [x 1 mm 3 ] Ice Volume on FEGV [x 1 mm 3 ] Ice Volume on FEGV [x 1 mm 3 ] 1 [11 8 ] 1 [11 8 ] 1 [11 8 ] (Rotor Fan) (Rotor Fan) (FEGV) (FEGV) 4 6 Ice Volume on Rotor Fan [x 1 8 mm 3 [11 7 ] 4 6 Ice Volume on Rotor Fan [x 1 8 ] mm 3 [11 7 ] 4 6 ] Ice Volume on Rotor Fan [x 1 8 mm 3 [11 7 ] ] (a) Run 1 (b) Run (c) Run 3 Figure 6. Ice Volume 8