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RAREFACTION EFFECTS IN HYPERSONIC AERODYNAMICS

Daniel Webster College, Nashua, NH, March 24, 2012. July 10—15, 2010 ~ Asilomar Conference Grounds ~ Pacific Grove, California, USA. RAREFACTION EFFECTS IN HYPERSONIC AERODYNAMICS. Vladimir V. Riabov, Ph.D. Professor of Computer Science & Math Rivier College Nashua, New Hampshire

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RAREFACTION EFFECTS IN HYPERSONIC AERODYNAMICS

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  1. Daniel Webster College, Nashua, NH, March 24, 2012 July 10—15, 2010 ~ Asilomar Conference Grounds ~ Pacific Grove, California, USA RAREFACTION EFFECTS IN HYPERSONIC AERODYNAMICS Vladimir V. Riabov, Ph.D.Professor of Computer Science & Math Rivier College Nashua, New Hampshire vriabov@rivier.edu http://www.rivier.edu/faculty/vriabov/

  2. Topics for Discussing • Experimental and numerical simulation of hypersonic rarefied-gas flows in air, nitrogen, carbon dioxide, argon, and helium; • Study of aerodynamics of simple-shape bodies (plate, wedge, cone, disk, sphere, side-by-side plates and cylinders, torus, and rotating cylinder); • Analysis of the role of various similarity parameters in low-density aerothermodynamics; • Evaluation of various rarefaction and kinetic effects on drag, lift, pitching moment, and heat transfer. Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  3. Techniques & Tools • Experiments in hypersonic vacuum chamber; • Direct Simulation Monte-Carlo technique: • DS2G (version 3.2) code of Dr. Graeme A. Bird • Knudsen numbers Kn∞,L from 0.01 to 10 • (Reynolds numbers Re0,L from 200 to 0.2); • Solutions of the Navier-Stokes 2-D equations; • Solutions of the Thin-Viscous-Shock-Layer equations; • Similarity principles applied to hypersonic rarefied-gas flows. Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  4. Earth and Mars Atmospheric Parameters Pressures and temperatures in Mars and Earth atmospheres. From D. Paterna et al. (2002). Experimental and Numerical Investigation of Martian Atmosphere Entry, Journal of Spacecraft and Rockets, Vol. 39, No. 2, March–April 2002, pp. 227-236 Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  5. Entry velocity envelopes for Earth & Mars missions Earth Entry Mars Entry Entry velocity envelopes for Earth & Mars missions with return to Earth. From “Capsule Aerothermodynamics,” AGARD Report No. 808, May 1997 Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  6. Typical trajectories of hypersonic spacecraft From: J. J. Bertin and R. M. Cummings, “Critical Hypersonic Aerothermodynamic Phenomena”, Annual Review of Fluid Mechanics, 2006, Vol. 38, pp.129-157 Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  7. European Space Agency Projects Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  8. Flow regimes and thermochemical phenomena Flow regimes and thermochemical phenomena in the stagnation region of a 30.5 cm radius sphere flying in air. From R. N. Gupta et al. NASA-RP-1232, 1990. Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  9. Estimating Transport Coefficients From Journal of Chemical Physics, 2004, Vol. 198, p. 424; Riabov’s data from Journal of Thermophysics & Heat Transfer, 1998, Vol. 10, N. 2 Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  10. Similarity parameters • Knudsen number, Kn,L= λ /L • or equivalent Reynolds number, Re0,L= ρU∞L/μ(T0) ~ 1/Kn,L • Interaction parameterχfor pressure approximation: • Viscous-interaction parameterVfor skin-friction approximation: • Temperature factor, tw= Tw/T0 • Specific heat ratio, γ= cp/cv • Viscosity parameter, n: μ Tn • Upstream Mach number, M∞ • Hypersonic similarity parameter, K∞= M∞ × sinθ • Spin rate, W = ΩD/2U∞ Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  11. Choosing a Mathematical Model The validity of the conventional mathematical models as a function of the local Knudsen number. From J. N. Moss and G. A. Bird, AIAA Paper, No. 1984-0223. Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  12. Estimating the local Knudsen number VSL Kn, local DSMC Density distribution along the stagnation streamline of the reentering Shuttle Orbiter at 92.35 km altitude (Kn∞,R = 0.028). From G. Bird, AIAA Paper No. 1985-994. Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  13. Modeling of Hypersonic Flight Regimes in Wind Tunnels The catalogs “Wind Tunnels in the Western and Eastern Hemispheres” (U.S. Congress, 2008) profiles 65 hypersonic wind tunnels used for aeronautical testing. The countries represented in the catalogs include those in America (Brazil [1] and USA [12]), Asia (Australia [7], China [5], and Japan [4]), Europe (Belgium [2], France [5], Germany [2], Italy [1], the Netherlands [1], and Russia [21]), and the Middle East and Central and South Asia (India [3] and Israel [1]). Nozzle and test chamber of the H2K hypersonic wind tunnel, Germany T-117 hypersonic wind tunnel, TsAGI, Moscow region, Russia Aerial view of the Thermal Protection Laboratory at NASA Ames, California Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  14. Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  15. Research on Hypersonics in TsAGI (Moscow region, Russia) Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  16. Studies of “Buran” Aerothermodynamics (TsAGI, Russia) Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  17. International Cooperation: Space Projects British HOTOL and Mriya-225 Launcher tested in T-128 TsAGI Wind Tunnel, Moscow region, Russia Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  18. Ground based testing in Germany Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  19. Ground based testing in Germany Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  20. HERMES Project, Germany & France, 1987-1992 HERMES-Columbus Project, Germany & Italy, 1987-1992 Testing ranges of some facilities (after Walpot L, Tech. Rept. Memo. 815, Univ Delft, NL, 1997). Bold lines indicate the individual range of each facility. Note that the times given are maximal run times and not necessarily testing times for constant conditions in all cases. Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  21. The International Space Station Mission The ISS effort involves more than 100,000 people in space agencies and at 500 contractor facilities in 37 U.S. states and in 16 countries. http://www.boeing.com/defense-space/space/spacestation/gallery/ Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  22. The International Space Station Mission World ISS Team: USA, Canada, ESA (Belgium, Denmark, France, Germany, Italy, the Netherlands, Norway, Spain, Sweden, Switzerland, the United Kingdom), Japan, Russia, Italy, and Brazil http://science.nationalgeographic.com/science/space/space-exploration/ Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  23. Space Shuttle Orbiter approximate heat-transfer model A) Representative flow models B) Heat flux on fuselage lower centerline From: J. J. Bertin and R. M. Cummings, Critical Hypersonic Aerothermodynamic Phenomena, Annual Review of Fluid Mechanics, 2006, Vol. 38, pp.129-157 Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  24. Applications of Underexpanded Jets in Hypersonic Aerothermodynamic Research • A method of underexpanded hypersonic viscous jets has been developed to acquire experimental aerodynamic data for simple-shape bodies (plates, wedges, cones, spheres and cylinders) in the transitional regime between free-molecular and continuum regimes. • The kinetic, viscous, and rotational nonequilibrium quantum processes in the jets of He, Ar, N2, and CO2 under various experimental conditions have been analyzed by asymptotic methods and numerical techniques. • Fundamental laws for the characteristics and similarity parameters are revealed. • In the case of hypersonic stabilization, the Reynolds number Re0 (or Knudsen number Kn) and temperature factor are the main similarity parameters. • The acquired data could be used for research and prediction of aerodynamic characteristics of hypersonic vehicles during their flights under atmospheric conditions of Earth, Mars, and other planets. Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  25. Underexpanded Hypersonic Viscous Jet Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  26. rd/rj = 1.34 (ps/pa)½ (1) Inviscid Gas Jets • Ashkenas and Sherman [1964], Muntz [1970], and Gusev and Klimova [1968] analyzed the structure of inviscid gas jets in detail. • The flow inside the jet bounded by shock waves becomes significantly overexpanded relative to the outside pressure pa. • If the pressure pj » pa , the overexpansion value is determined by the location of the front shock wave ("Mach disk") on the jet axis rd [Muntz, 1970]: Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  27. u'=u0+u1×z2(γ-1)+...; z=r*'(φ)/r' u0=[(γ+1)/(γ-1)]½ (2) (7) v'=v1×z2(γ-1)×d/dφ[lnr*'(φ)] +... u1=-θ1/(γ2-1)½ (3) (8) v1=-2θ1/{u0[1-2(γ-1)]} ρ'=1/u0×z2 +... (9) (4) θ1=1/(u0)(γ-1) T'=θ1×z2(γ-1) +... (5) (10) p'=θ1/u0×z2γ +... (6) r*'(φ)= r*(φ)/rj (11) The asymptotic solution [Riabov, 1995] of the Euler equations in a hypersonic jet region: Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  28. Mach number M along the axis of axisymmetric inviscid jets of argon (or helium), nitrogen, and carbonic acid:M=(u0)0.5(γ+1)×[ r'/ r*'(0)](γ-1) Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  29. W=(u' - u0)/ξλ, λ=2ω(γ-1) W=-Θ/[u0(γ-1)] - u0Θn/(r02X) (13) (18) V=v'/ξλ (14) Θ={γ(γ+1)(1-n)ω/(r02X) +θ11-n(r0X)(1-ω)/ω}1/(1-n) (19) Θ=T'/ξλ (15) r02(∂V/∂X-V/X)-(γu0X)-1∂(r02Θ)/∂φ+nu0Θn-1(2X2)-1∂Θ/∂φ = 0 (20) X=r*'(0)/(r'ξω) (16) r0 =r*'(φ)/[r*'(0)] (21) ξ=4/[3Rej r*'(0)], ξ → 0 (17) The asymptotic solution of the Navier-Stokes equations in a hypersonic viscous gas jet region[from V. V. Riabov, Journal of Aircraft, 1995, Vol. 32, No. 3]: r' = O(Rejω), ω = 1/[2γ-1-2(γ-1)n] Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  30. Mach number M along the axis of axisymmetric viscous jets of argon, helium, nitrogen, and carbonic acid. Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  31. Translational Relaxation in a Spherical Expanding Gas Flow Parallel (TTX) and transverse (TTY) temperature distributions in the spherical expansion of argon into vacuum at Knudsen numbers Kn* = 0.015 and 0.0015. [From V. V. Riabov, RGD-23 Proceedings, 2002] Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  32. Rotational Relaxation in a Freely Expanding Gas Relaxation time τR of molecular nitrogen vs. kinetic temperature Tt: solid line - Parker's model [1959]; open symbols - quantum rotational levelsj* = 4, 5, and 6 [Lebed & Riabov, 1979]. Experimental data from Brau, Lordi [1970] Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  33. Rotational temperature TR along the nitrogen-jet axis Experimental data from Marrone (1967) and Rebrov (1976): K* = ρ*u*r*/(pτR)* = 2730, psrj = 240 torr·mm and Ts = 290 K (nitrogen) Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  34. Rotational Relaxation in Viscous Gas Flows Rotational TR and translational Tt temperatures in spherical flows at different pressure ratios P = p*/pa under the conditions: Re* = 161.83; K* = 28.4; Pr = n = 0.75; Tsa = 1.2T*. Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  35. Similarity Criteria for Aerodynamic Experiments in Underexpanded Jets The interaction parameter χ for pressure approximation: χ=M∞2/[0.5(γ-1)Re0)]0.5 The viscous-interaction parameter V for skin-friction approximation: V=1/[0.5(γ-1)Re0)]0.5 The value of the Reynolds number, Re0, can be easily changed by relocation of a model along the jet axis at different distances (x) from a nozzle exit (Re0 ~ x--2). Other criteria: Mach number M∞, temperature factor tw; specific heat ratio γ; and parameter n in the viscosity coefficient approximation µ ~ Tn. Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  36. The Results of Testing: Influence of Mach Number M∞ Normalized drag coefficient vs. hypersonic parameter K = M∞sinα for the blunt plate (δ = 0.06) in He (γ = 5/3) at Re0 = 2.46. Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  37. The Results of Testing: Influence of Mach Number M∞ Normalized lift coefficient vs. hypersonic parameter K = M∞sinα for the blunt plate (δ = 0.06) in He (γ = 5/3) at Re0 = 2.46. Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  38. The Results of Testing: Influence of Mach Number M∞ Drag coefficientcx of the wedge (2θ = 40 deg) in helium at Re0 = 4 and various Mach numbers M∞ Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  39. The Results of Testing: Influence of Mach Number M∞ Lift coefficientcy of the wedge (2θ = 40 deg) in helium at Re0 = 4 and various Mach numbers M∞. Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  40. The influence of the specific heat ratio γ Drag coefficient cx of the wedge(2θ = 40 deg) for various gases vs. the Reynolds number Re0. Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  41. The influence of the specific heat ratio γ Lift coefficient cy of the wedge (2θ = 40 deg) at Re0 = 3 and various gases. Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  42. The influence of the specific heat ratio γ Lift-drag ratioof the blunt plate (δ = 0.1) at α = 20 deg in Ar and N2 vs. Reynolds number Re0. Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  43. The influence of the specific heat ratio γ: Drag coefficient cx of the disk at α = 90 deg for argon and nitrogen vs. the Reynolds number Re0 Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  44. The influence of the viscosity parameter n: µ ~ Tn Drag coefficient cx of the plate at α = 90 deg in helium and argon vs. the Reynolds number Re0. Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  45. The influence of the temperature factor tw Lift-drag ratiofor the blunt plate (δ = 0.1) vs. Reynolds number Re0 in nitrogen at α = 20 deg and various tw Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  46. Direct Simulation Monte-Carlo (DSMC) method • The DSMC method [G. Bird, 1994] and DS2G code (version 3.2) [G. Bird, 1999] are used in this study; • Variable Hard Sphere (VHS) molecular collision model in air, nitrogen, carbon dioxide, helium, and argon; • Gas-surface interactions are assumed to be fully diffusive with full moment and energy accommodation; • Code validation was established [Riabov, 1998] by comparing numerical results with experimental data [Gusev et al., 1977; Riabov, 1995] related to the simple-shape bodies; • TEST: a single plate in air flow at 0.02 < Kn,L < 3.2, M = 10, tw = 1; • Independence of flow profiles and aerodynamic characteristics from mesh size and number of molecules has been evaluated; • EXAMPLE: 12,700 cells in eight zones, 139,720 molecules; • The G. Bird’s criterion for the time step is used: 1×10-8tm 1×10-6 s; • Ratio of the mean separation between collision partners to the local mean free path and the CTR ratio of the time step to the local mean collision time have been well under unity over flowfield; • Computing time of each variant on Intel IV PC is variable: 4 – 60 hours. Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  47. Drag of a blunt plate Fig. 1 Total drag coefficient of the plate vs. Knudsen number Kn∞,L in air at M∞ = 10, tw = 1, and α = 0 deg.Experimental data is from [V. Gusev, et al., 1977]. Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  48. Number of cells Number of molecules per cell Drag coefficient Time of calculation 12,700 11 0.4524 12 h. 28 min. 12,700 22 0.4523 21 h. 03 min. 49,400 11 0.4525 62 h. 06 min. 203,200 11 0.4526 187 h. 11 min. Table: Drag coefficient of a single plate in airflow at Kn ,L = 0.13, M= 10, γ = 1.4, tw = 1, and different numerical parameters Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  49. Lift-drag ratio Y/X for a wedge (θ = 20 deg) in helium flow at Kn∞,L = 0.3(Re0 = 4) and M∞ = 9.9 and 11.8. Experimental data from [Gusev, et al., 1977]. Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

  50. Drag coefficient Cx for a disk (α = 90 deg) vs Knudsen number Kn∞,Din argon (triangles) and nitrogen (squares). Experimental data from [Gusev, et. al., 1977]. Vladimir V. Riabov: Hypersonic Rarefied Aerothermodynamics

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