Aeronautics and Astronautics Part 5 doc

Physico - Chemical Modelling in Nonequilibrium Hypersonic Flow Around Blunt Bodies 25 X/R Temperatures, K -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 0 2000 4000 6000 8000 10000 12000 T T T T v v e O2 N2 without correction with correction Fig. 9. Temperature along stagnation line with weakly ionized gas; M ∞ = 18 149 Physico - Chemical Modelling in Nonequilibrium Hypersonic Flow Around Blunt Bodies 26 Aeronautics and Astronautics X/R -0.15 -0.125 -0.1 -0.075 -0.05 -0.025 0 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 22000 Park 93 Gardiner Moss Modif. Dunn & Kang With Gupta curve fit constants and Park CVD T[°K] T T v N M =25.9 ∞ 2 Fig. 10. Temperature profile with Gupta curve fit constants, M ∞ =25.9 150 Aeronautics and Astronautics Physico - Chemical Modelling in Nonequilibrium Hypersonic Flow Around Blunt Bodies 27 θ 0 10 20 30 40 50 60 70 80 90 0 0.5 1 1.5 2 2.5 3 Park (93) Gardiner Moss Dunn & Kang With Park CVD With Hansen CVD Q(MW/m) w 2 With Gupta Curve fit Constants Modif. Dunn & Kang M =25.9 ∞ Fig. 11. Stagnation heat flux, M ∞ =25.9 151 Physico - Chemical Modelling in Nonequilibrium Hypersonic Flow Around Blunt Bodies 28 Aeronautics and Astronautics X/R Temperatures, K -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 0 4000 8000 12000 16000 20000 T T T T V V e O2 N2 Fig. 12. Temperatures distribution along the stagnation line, M ∞ =23.9 152 Aeronautics and Astronautics Physico - Chemical Modelling in Nonequilibrium Hypersonic Flow Around Blunt Bodies 29 X/R Ne 0 1 2 3 4 5 6 7 8 10 9 10 10 10 11 10 12 10 13 10 14 Mach=23,9; H=61 Km Experiment, H=61 Km Δ Δ Δ Δ Ο Ο Ο Ο Mach=25,9; H=71 Km Experiment, H=71 Km Δ Ο Fig. 13. Comparison with experiment of the peak of electron number density following the axial distance 153 Physico - Chemical Modelling in Nonequilibrium Hypersonic Flow Around Blunt Bodies 30 Aeronautics and Astronautics Dunn & Kang Dunn & Kang with Gupta Fig. 14. Dunn and Kang, and Modified Dunn and Kang Interferograms computed Fig. 15. Fringe patterns on 1 in diameter cylinder with Park(93) model and Exact equilibrium constant 154 Aeronautics and Astronautics Physico - Chemical Modelling in Nonequilibrium Hypersonic Flow Around Blunt Bodies 31 Fig. 16. Fringe patterns on 1 in diameter cylinder with Gardiner model and Exact equilibrium constant 155 Physico - Chemical Modelling in Nonequilibrium Hypersonic Flow Around Blunt Bodies 32 Aeronautics and Astronautics Chemistry of Gardiner Chemistry of Park 15° 60° M ∞ =9 Gardiner Park S/L P/P 0 0.5 1 1.5 2 0 100 200 300 400 500 ∞ Chemistry of Gardiner Chemistry of Park θ =15° θ =60° ∞ Μ=9 1 2 Fig. 17. Effect of chemical kinetics: a) Contours Mach number b) Surface pressure 6. Conclusion The hypersonic flow past blunt bodies with thermo-chemical nonequilibrium were numerically simulated. The dependence of solutions on available chemical models, allowing to assess the accuracy of finite rate chemical processes has been examined. The present results were successfully validated with the theoretical and experimental work for shock-standoff distances, stagnation point heat transfer and interferograms of the flow. Although all model describe the essential aspects of the nonequilibrium zone behind the shock, they are not accurate for the evaluation of the aerothermodynamic parameters. A comparative study of various kinetic air models is carried out to identify the reliable models for applications with a wide range of Mach number. The present study has shown that the prediction of hypersonic flowfield structures, shock shapes, and vehicle surface properties are very sensitive to the choice of the kinetic model. The large dispersion in the wall heat flux reaches 60 % as observed in the RAM-CII case. The manner in which the backward reaction rates are computed is quite important as indicated by the interferograms that were obtained. The model of Park (93) gives a better prediction of hypersonic flowfield around blunt bodies. Park(93) is identify as the model for hypersonic flow around blunt bodies with a confidence acceptable to a wide range of Mach number. There is also great sensitivity to the choice of chemical kinetics in flowfield around double-wedge. More numerical simulations compared with experiments need to be conducted to improve the knowledge of the thermochemical model of air flow around double-wedge. 7. References [1] Park, C. (1990). Nonequilibrium Hypersonic Aerothermodynamics. New York, Wiley. [2] Gupta, R. N., Yos, J. M., Thompson, R. A., and Lee, K. P. (1990). A Review of Reaction Rates and Thermodynamic and Transport Properties for an 11-Species Air Model for Chemical and Thermal Nonequilibrium Calculations to 30 000K", NASA RP-1232. [3] Vincenti, W. G., Jr.Kruger, C. H. (1965). Introduction to physical Gas Dynamics. Krieger, FL. [4] Gardiner, W. C. (1984). Combustion Chemistry, Springer-Verlag, Berlin. 156 Aeronautics and Astronautics Physico - Chemical Modelling in Nonequilibrium Hypersonic Flow Around Blunt Bodies 33 [5] Shinn, J. L., Moss, J. N., Simmonds, A. L. (1982). Viscous Shock Layer Heating Analysis for the Shuttle Winward Plane Finite Recombination Rates, AIAA 82-0842. [6] Dunn,M. G., Kang, S. W. (1973). Theoretical and Experimental Studies of re-entry Plasma, NASA CR-2232. [7] Park, C. (1993). Review of Chemical-Kinetic Problems of Future NASA Mission, I: Earth Entries", Journal of Thermophysics and Heat Transfer. Vol. 7, No. 3, pp. 385-398. [8] Hansen, C. F. (1993). Vibrational Nonequilibrium Effect on Diatomic Dissociation Rates". AIAA Journal, Vol. 31, No. 11, pp. 2047-2051. [9] Macrossan, N. M. (1990). Hypervelocity flow of dissociating nitrogen donwnstream of a blunt nose. Journal of Fluid Mechanics, Vol. 27, pp. 167-202. [10] Josyula, E. (2001). Oxygen atoms effect on vibrational relaxation of nitrogen in blunt body flows. Journal of Thermophysics and Heat Transfer, Vol. 15, No. 1, pp. 106-115. [11] Peter, A. G. and Roop, N. G. and Judy, L. S. (1989). Conservation Equation and Physical Models for Hypersonic Air flows in Thermal and Chemical Nonequilibrium. NASA TP 2867. [12] Knab, O. and Fruaudf, HH. and Messerschmid, EW. (1995). Theory and validation of the the physically consistent coupled vibration-chemistry-vibration model. J. Thermophys Heat Transfer,nˇr9, Vol.2, pp.219-226. [13] Tchuen G., Burtschell Y., and Zeitoun E. D. (2008). Computation of non-equilibrium hypersonic flow with Artificially Upstream Flux vector Splitting (AUFS) schemes. International Journal of Computational Fluid Dynamics, Vol. 22, Nˇr4, pp. 209 - 220. [14] Tchuen G., and Zeitoun D. E. (2008). Computation of thermo-chemical nonequilibrium weakly ionized air flow over sphere cones. International journal of heat and fluid flow, Vol.29, Issue 5, pp.1393 - 1401. [15] Tchuen G., and Zeitoun D. E. (2009). Effects of chemistry in nonequilibrium hypersonic flow around blunt bodies. Journal of Thermophysics and Heat Transfer, Vol. 23, Nˇr3, pp.433-442. [16] Burtschell Y., Tchuen G., and Zeitoun E. D. (2010). H2 injection and combustion in a Mach 5 air inlet through a Viscous Mach Interaction. European Journal of Mechanics B/fluid,Vol. 29, Issue 5, pp. 351-356. [17] Lee Jong-Hun. (1985). Basic Governing Equations for the Flight Regimes of Aeroassisted Orbital Transfer Vehicles. Thermal Design of Aeroassisted Orbital Transfer Vehicles, H. F. Nelson, ed., Volume 96 of progress in Astronautics and Aeronautics, American Inst. of Aeronautics and Astronautics, Vol. 96, pp. 3-53. [18] Appleton, J. P. and Bray, K. N. C. (1964). The Conservation Equations for a Nonequilibrium Plasma. J. Fluid Mech. Vol. 20, No. 4, pp. 659-672. [19] Tchuen, G., Burtschell, Y., and Zeitoun, E. D., 2005. Numerical study of nonequilibrium weakly ionized air flow past blunt body. Int. J. of Numerical Methods for heat and fluid flow, 15 (6), 588 - 610. [20] Blottner, F. G., Johnson, M., and Ellis, M., 1971. Chemically Reacting Viscous Flow Program for Multi-Component Gas Mixtures. Sandia Laboratories, Albuquerque, NM, Rept. Sc-RR-70-754. [21] Wilke, C. R., 1950. A viscosity Equation for Gas Mixture. J. of Chem. Phys. 18 (4), 517-519. [22] Ramsaw JD., and Chang CH., 1993. Ambipolar diffusion in two temperature multicomponent plasma. Plasma Chem Plasma process. 13 (3), 489-498. 157 Physico - Chemical Modelling in Nonequilibrium Hypersonic Flow Around Blunt Bodies 34 Aeronautics and Astronautics [23] Masson, E. A., and Monchick, 1962. Heat Conductivity of Polyatomic and Polar Gases. The Journal of Chemical. 36 (6), 1622-1640. [24] Ahtye, W. F., 1972. Thermal Conductivity in Vibrationnally Excited Gases. Journal of Chemical Physics, 57, 5542-5555. [25] Candler, G. V., and MacCormarck, R. W., 1991. Computation of weakly ionized hypersonic flows in thermochemical nonequilibrium. Journal of Thermophysics and heat transfer, 5 (3), 266-273. [26] Taylor R., Camac, M., and Feinberg, M., 1967. Measurement of vibration-vibration coupling in gas mixtures, In Proceeding of the 11th Intenational Symposium on combustion, Pittsburg, PA, 49-65. [27] Sharma, S. P., Huo, W. M., and Park, C., 1988. The Rate Parameters for Coupled Vibration-Dissociation in a Generalized SSH Approximation Flows. AIAA-88-2714. [28] Shatalov, O. P., and Losev, S. A., "Modeling of diatomic molecules dissociation under quasistationary conditions", AIAA 97-2579, 1997. [29] Roe, P., 1983. Approximate Riemann Solvers, Parameters vectors and difference schemes. Journal of Computational Physics, Vol. 43, 357-372. [30] Lobb, K., "Experimental measurement of shock detachment distance on sphere fired in air at hypervelocities", in The High Temperature Aspect of Hypersonic Flow. ed. Nelson W. C., Pergamon Press, Macmillan Co., New York, 1964. [31] Rose, P. H., Stankevics, J. O., "Stagnation-Point Heat Transfer Measurements in Partially Ionized Air". AIAA Journal, Vol. 1, No. 12, 1963, pp. 2752-2763. [32] Hornung, H. G., "Non-equilibrium dissociating nitrogen flow over spheres and circular cylinders". Journal of Fluid Mechanics, Vol. 53, 1972, pp. 149-176. [33] Joly, V., Coquel, F., Marmignon, C., Aretz, W., Metz, S., and Wilhelmi, H., "Numerical modelling of heat transfer and relaxation in nonequilibrium air at hypersonic speeds", La Recherche Aérospatiale, Vol.3, 1994, pp. 219-234. [34] Séror, S., Schall, E., and Zeitoun, E. D., "Comparison between coupled euler/defect boundary-layer and navier-stokes computations for nonequilibrium hypersonic flows, Computers & Fluids, Vol.27, 1998, pp. 381-406. [35] Fay, J. A., Riddell, F. R., "Theory of stagnation point heat transfer in dissociated air". J. Aero. Sciences, Vol. 25, 1958, pp. 73-85. [36] Walpot, L. M., "Development and Application of a Hypersonic Flow Solver". PhD thesis, TU Delft, 2002. [37] Soubrié, T., Rouzaud, O., Zeitoun, E. D., "Computation of weakly multi-ionized gases for atmospheric entry using an extended Roe scheme". ECCOMAS, Jyväskylä, 2004. [38] Candler, V. G., MacCormack, W. R., "The computation of hypersonic ionized flows in chemical and thermal nonequilibrium". AIAA 88-0511, 1988. 158 Aeronautics and Astronautics [...]... be solved numerically 176 Aeronautics and Astronautics Will-be-set-by-IN-TECH 18 Fig 6 RMS of the instantaneous pressure field near the profile using interpolation polynomials of degree p = 6, Pa 0.6 0 .56 p=3 p=4 p =5 p=6 0 .5 0 .55 0 .54 0 .53 prms, Pa prms, Pa 0.4 0.3 0.2 0 .52 0 .51 0 .5 0.49 p=3 p=4 p =5 p=6 0.48 0.1 0.47 0 0 50 100 150 200 250 300 350 0.46 30 35 40 θ, deg (a) 45 50 θ, deg (b) Fig 7 Directivity... to ρt ∞ = 1.2 25 Kg/m3 In the second one, condition B, the external flow is at rest, c∞ = 340.17 m/s and ρ∞ = 1.2 25 Kg/m3 , whereas there is a mean velocity both inside the by-pass duct and inside the core duct Flow properties at duct’s inlet are the following: cfan = 353 . 15 m/s, ρt fan = 1.327 Kg/m3 , and Mfan = 0. 35 for the by-pass duct and cturb = 50 8. 75 m/s, ρt turb = 0 .59 8 Kg/m3 , and Mturb = 0.29... inside the by-pass and the core duct 180 Aeronautics and Astronautics Will-be-set-by-IN-TECH 22 50 Numerical Results SPL * sin(α), dB 40 30 20 10 0 50 40 30 20 10 0 10 20 30 40 50 SPL * cos(α), dB (a) (b) Fig 13 Engine exhaust, flow condition B, mode (4, 1), f = 7981. 25 Hz; (a) near-field solution: real part of Fourier pressure coefficient, Pa; (b) far-field solution: SPL directivity 5 Conclusions A numerical... assemble and solve a system matrix which contains only the degrees of freedom associated with the element boundary nodes [Karniadakis & Sherwin (20 05) ] Distinguishing between the boundary and interior components of the vectors ue and e e f e using ue , ui and fb , fie respectively, that is b u= ub ui f = , fb fi , (57 ) the DGM linear system (38) can be written as Kb Kc1 Kc2 Ki ub ui = fb fi (58 ) 172 Aeronautics. .. near-field domain, and then the far-field solution is evaluated for the near-field one using the three-dimensional integral formulation of the wave equation proposed by Ffowcs Williams and Hawkings [Iob et al (2010)] The far-field results are then compared with the analytical solution The LEE computational domain extends for z ∈ [−2 .5 m; 5. 5 m] and for r ∈ [0.0 m; 3.9 m] and is surrounded by vertical and horizontal... 10], y ∈ [0, 10] and is surrounded by a PML region with a thickness equal to 0. 75 The domain is discretized with an unstructured grid, figure (1), of about 27, 000 elements (both triangles and quadrangles) and on each element Lagrangian basis of degree p = 4 are used Fig 1 Mesh of the internal (red) and PML (blue) domains Fig 2 RMS of the fluctuating pressure field 174 Aeronautics and Astronautics Will-be-set-by-IN-TECH... airfoil based on the RA16SC1 profile, with the slat and flap deflected by 30 deg and 20 deg, respectively The chord in fully retracted configuration is 0.480m Mean flow is at rest with a speed of sound equal to c0 = 340.17 m/s and a density equal to ρ0 = 1.2 25 Kg/m3 The computational domain extends for ( x, y) ∈ [−0. 85 m; 0. 85 m] and it is surrounded by vertical and horizontal PML layers with a thickness of... jet pipes: Far- and near-field solutions, J Fluid Mech 54 9: 3 15 341 Giles, M B (1990) Non-reflecing boundary conditions for Euler equation calculations, AIAA Journal 28(12): 2 050 –2 058 Goldstein, M (1976) Aeroacoustics, McGraw-Hill Hesthaven, J S (1998) From electrostatics to almost optimal nodal sets for polynomial interpolation in a simplex, SIAM Journal on Numerical Analysis 35: 655 –676 Hu, F Q (1996)... exhaust, flow condition A, mode (4, 1), f = 7981. 25 Hz; (a) near-field solution: real part of Fourier pressure coefficient, Pa; (b) far-field solution: SPL directivity near-field domain is discretized with an unstructured grid of 3, 800 elements and, in the external region, it extends for z ∈ [−0.44 m; 0. 95 m] and for r ∈ [0.0 m; 0.7 m] and is surrounded by vertical and horizontal PML domains with a thickness... 10(a) and 10(b), instantaneous pressure field and directivity (a) (b) Fig 8 Circular duct; (a) geometry; (b) domain discretization and boundary conditions 178 Aeronautics and Astronautics Will-be-set-by-IN-TECH 20 Analytical Results Numerical Results SPL * sin(α), dB 100 80 60 40 20 0 100 80 60 40 20 0 20 40 60 80 100 SPL * cos(α), dB (a) (b) Fig 9 Circular duct, M1 = 0.0, M2 = 0.0, mode (0, 1), f = 956 . 57 , 55 42 -55 55. [ 25] Candler, G. V., and MacCormarck, R. W., 1991. Computation of weakly ionized hypersonic flows in thermochemical nonequilibrium. Journal of Thermophysics and heat transfer, 5. Nelson, ed., Volume 96 of progress in Astronautics and Aeronautics, American Inst. of Aeronautics and Astronautics, Vol. 96, pp. 3 -53 . [18] Appleton, J. P. and Bray, K. N. C. (1964). The Conservation. Modelling in Nonequilibrium Hypersonic Flow Around Blunt Bodies 26 Aeronautics and Astronautics X/R -0. 15 -0.1 25 -0.1 -0.0 75 -0. 05 -0.0 25 0 0 2000 4000 6000 8000 10000 12000 14000 16000 18000 20000 22000 Park