Eects of Gas-Surface Interaction Model in Hypersonic Rareed Gas Flow

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1 4 D-5 Eects of Gas-Surface Interaction Model in Hypersonic Rareed Gas Flow,, 3--, 7-3-, Nobuyuki Tsuboi, Institute of Space and Astronautical Science, Yoshinodai 3--, Yoshinodai, Sagamihara, Kanagawa Yoichiro Matsumoto, Mechanical Engineering, The University of Tokyo, Hongo 7-3-, Bunkyo-ku, Tokyo A DSMC (direct simulation Monte Carlo) simulation using Dynamic Molecular Collision (DMC) model and Multi- Stage (MS) model based on Molecular Dynamics (MD) calculation is applied for solving the two-dimensional nonequilibrium hypersonic rareed ow over a at plate with angle of leading edge. Numerical results show that nonequilibrium between translational and rotational temperature are obtained behind the leading edge over the plate. Pressure, heat ux ratio on the plate and rotational temperature in the DSMC results agree well with those in the experimental results. The results also indicates that the eects of gas-surface interaction are revealed and correrated with a rarefaction parameter V.. strong interaction weak interaction rarefaction parameter V (= M p C=Re x ) > :5 DSMC(direct simulation Monte Carlo) Hypersonic Stream Kinetic Flow Transition Continuum Flow Wall Slip Merged Layer Strong Interaction Shock Wave Boundary Layer No Wall Slip Hypersonic Interaction Inviscid Weak Interaction Fig. : Schematic of viscous interaction near a sharp leading edge. DMC(Dynamic Molecular Collision) 4 MS(Multi-Stage) 5 DSMC 2. 2 DSMC Null-Collision 6 DSMC 7 MPI 2 DSMC DMC 2 2 DSMC Maxwell-Boltzmann (i) (ii)cercignani-lampis-lord(cll) 9 (iii)multi- Stage(MS) 5 3 Copyright c 2 by JSCFD

Tab. : Simulation conditions. No. 2 3 4 5 6 7 8 9 2 3 4 Leading Edge angle[deg.

5[m],2L=plate length) Wall temperature T w [K] Knudsen number Kn (based on L) 2 2.2 Nitrogen 3.5 5, 3.32.683,53 566 29.47 3 4.89 Nitrogen 983 669 5.8 2.2,72 77 29.

2 Tab. : Simulation conditions. No Leading Edge angle[deg.] Mach number M Working Gas Stagnation pressure p [Pa] Stagnation temperaturet [K] Freestream temperature T [K] Freestream pressure p [Pa] Freestream velocity V [m/s] Reynolds number Re (based on L=.5[m],2L=plate length) Wall temperature T w [K] Knudsen number Kn (based on L) Nitrogen 3.5 5, , Nitrogen , Wall boundary condition Diffuse MS CLL Diffuse MS CLL Accomm. coeff. n/ t/ r /.986/ /.986/ (a)computational grid system for No.-7 (b)computational grid system for No.8-4 Fig. 2: Computational grid systems. Maxwell-Boltzmann ( engineering surface ) CLL c i c r P (c i! c r ) 2 c it = p c 2 it + c2 iz c in P (c it! c rt) = p exp t(2 ; ) P (c in! c rn) = 2crn n " exp ; c rt ; ( ; t)c it t(2 ; t) 2 p ; nc in c rn I n 2 ; c2 rn +(; n)c 2 in n I t n # () (2) 2 P (E i! E r ) = p 2 ; r E i E r I c in c rn r r exp ; E i +(; r )E r (3) r r E CLL 2 3 Arkilic Cook /.7.95 MS (i) (ii) (iii) 3 MS Lengrand 2 / MS 2 Copyright c 2 by JSCFD

3 (a)diffuse,no. (b) (c) (d) (e) (f) Fig. 3: Density contours over the plate for M = 2:2. MS 5 3. Lengrand mm 2 No.7 58( )4( ), 48 no , M=2.2 Lengrand M =2:2 2 MS p/p Experiment[Lengrand et al.(992)] Y/L Experiment [Lengrand et al.(992)] ρ/ρ Fig. 4: Density proles over the plate at X=L=.5 for M =2: Fig. 5: Pressure distributions on the plate for M =2:2. 3 MS CLL 4 X=L =:5 CLL MS 5 MS CLL 3 Copyright c 2 by JSCFD

4 CH Experiment[Lengrand et al.(992)] Fig. 6: Heat transfer rate distributions on the plate for M =2:2. Cf Fig. 7: Skin friction distributions on the plate for M =2:2. Ttr/T Fig. 8: Translational temperature distributions on the plate for M = 2:2. Trot/T Fig. 9: Rotational temperature distributions on the plate for M = 2:2. CLL (No.3) CLL.7 =3 DSMC 6 MS CLL (No.3) MS CLL (No.3) MS CLL.7 MS 7 CLL (No.7) MS CLL (No.3) 8 MS CLL (No.3) MS 2 9 MS CLL (No.3).9 DSMC DSMC X=L >.5 CLL (No.3) MS 4 Copyright c 2 by JSCFD

5 (a)diffuse,no.8 (b) (c)cll,no. (d)cll,no.2 (e) (f) Fig. : Density contours over the plate for M = 4:89. MS,CLL (No.3) 3.2 M= p/p CLL,No. CLL,No. CLL,No Fig. : Pressure distributions on the plate for M =4:89. MS CLL MS CLL CH CLL,No. CLL,No. CLL,No Fig. 2: Heat transfer rate distributions on the plate for M =4:89. M =2:2 Kn MS CLL (No.) 2 3 CLL.95 No.8 CLL (No.4) 4,5 mm 4 5 2mm(X=L =:4) 3 5 Copyright c 2 by JSCFD

6 Cf CLL,No. CLL,No. CLL,No Fig. 3: Skin friction distributions on the plate for M =4:89. Ttr/T CLL,No. CLL,No. CLL,No Fig. 4: Translational temperature distributions at Y=mm over the plate for M = 4:89. Trot/T Experiment[Tsuboi et al.(2)] CLL,No. CLL,No. CLL,No Fig. 5: Rotational temperature distributions at Y=mm over the plate for M = 4:89. X=L =: MS CLL (No.) No.8 CLL.8 CLL (No.4) CLL 5mm,2mm(X=L =: :4) 6,7 MS CLL (No.) CLL.95 Y/L Experiment[Tsuboi et al.(2)] CLL,No. CLL,No. CLL,No Trot/T Fig. 6: Rotaional temperature proles at X=L = : for M =4:89. Y/L Trot/T Experiment[Tsuboi et al.(2)] CLL,No. CLL,No. CLL,No.2 Fig. 7: Rotaional temperature proles at X=L = :4 for M =4:89. 6 Copyright c 2 by JSCFD

7 3.3 Rarefaction parameter V 8,9 M =2:2 2 M =4:89 strong interaction theory weak interaction theory 6 7 merged layer. Experiment[Lengrand et al.(992)].5 M 3 CH/ χ... Experiment[Lengrand et al.(992)] Merged Layer Regime p/p χ.. Merged Layer Regime.. V.. V Fig. 8: Rarefaction eects for pressure distributions on the plate for M =2:2. DSMC strong interaction theory weak interaction theory merged layer CLL merged layer CLL 4. 2 DSMC () DSMC 2 DSMC (2) 2 DSMC CLL MS Fig. 9: Rarefaction eects for heat transfer rate distributions on the plate for M = 2:2. χ p/p. CLL,No. CLL,No. CLL,No.2 Merged Layer Regime. V Weak interaction theory Fig. 2: Rarefaction eects for pressure distributions on the plate for M =4:89. 7 Copyright c 2 by JSCFD

8 M =2:2 MS M =4:89 (3) merged layer A.E.Beylich. Stollery JL, Kumar D, Atclie PA, Theoretical and Experimental Methods in Hypersonic Flows, AGARD- CP-54 (993), 5- { Bird, G.A., Molecular Gas Dynamics, Clarendon Press, Oxford (976). 3. Nanbu, K., J Phys. Soc. Jpn., Vol. 49(99), Tokumasu, T. and Matsumoto Y., Phys. Fluids, Vol., No.7(999), 97{ Yamanishi, N. and Matsumoto, Y., Phys. Fluids, Vol., No.(999), 354{ Koura, K., Phys. Fluids, 29 (986), 359{ ,B(993), 7{ ,B(2), 7{ Lord, R.G., Proceeding of the 6th International Symposium on Rareed Gas Dynamics(988), 427{ Arkilic, E.B., Schmidt, M.A. and Breuer, K.S., Proceeding of the 2th International Symposium on Rareed Gas Dynamics(996), 983{988.. Cook, S.R. and Hobauer, M.A., Proceeding of the 2th International Symposium on Rareed Gas Dynamics(996), 467{ Lengrand, J.C., private communication, Lengrand, J.C. et al., 8th Int. Symp. on Rareed Gas Dynamics (992), 276{ (2), (2). 6. Anderson, J.D., Jr., Hypersonic and High Temperature Gas Dynamics, McGraw-Hill Book Co., New York(989). 7. Vidal, R.J. and Wittli, C.E., Proceeding of the 3rd International Symposium on Rareed Gas Dynamics(963), Copyright c 2 by JSCFD

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