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IMPNS Computations of the X-15 Flight Vehicle: A Validation and Verification Case Study

NAFEMS International Journal of CFD Case Studies

Volume 6, January 2007

ISSN 1462-236X


IMPNS Computations of the X-15 Flight Vehicle: A Validation and Verification

S Shaw, M Mifsud, B Wagner, A Moureaux and J Bennett
School of Engineering, Cranfield University, Cranfield, Bedfordshire MK43 0AL

https://doi.org/10.59972/0sjv74yh

Keywords: IMPNS, Validation, Verification, Space-Marching Flow Solver, Hierarchical and X-15 Wind Tunnel

 


Abstract

A verification and validation study of the IMPNS space-marching flow solver has been undertaken for a complete hypersonic air-vehicle configuration. A hierarchical approach was adopted in which the vehicle aerodynamics was decomposed and related flow phenomenon studied. Using this hierarchy benchmark solutions and laboratory experiments were identified that provide the basis of the verification and validation exercises. Detailed comparisons of iterative and grid converged IMPNS computations with benchmark solutions and wind tunnel measurements are presented. Computations of the X-15 wind tunnel and flight experiments are described and comparison is made with measured surface and off-surface pressure measurements and wind tunnel flow visualization observations that demonstrate the reliability and capability of the IMPNS flow solver for complex configurations.

References

[1] Roache, PJ. Verification and Validation in Computational Science and Engineering, Hermosa Publishers, 1998.

[2] Oberkampf, WL and Blottner, FG. Issues in Computational Fluid Dynamics Code Verification and Validation, AIAA Journal, Vol. 36, No. 5, pp. 687-695, 1998.

[3] Oberkampf, WL, Trucano, TG. Verification and validation in computational fluid dynamics, Progress in Aerospace Sciences, Vol. 38 (3), pp. 209-272, 2002.

[4] Qin N and Richards BE. Finite volume 3DNS and PNS solutions of hypersonic viscous flows around a delta wing using Osher’s flux difference splitting, Proc. of a Workshop on Hypersonic Flows for Re-entry Problems, 1990.

[5] Birch TJ, Qin N and Jin X. Computation of supersonic viscous flows around a slender body at incidence, AIAA Paper 94-1938, 1994.

[6] Shaw ST and Qin N. A matrix-free preconditioned Krylov subspace method for the PNS equations, AIAA Paper 98-111, 1998.

[7] Qin N, Ludlow DK, Zhong B, Shaw ST and Birch TJ. Multi-grid acceleration of a preconditioned GMRES implicit PNS solver, AIAA Paper 99-0779, 1999.

[8] Birch TJ, Ludlow DK and Qin N. Towards an efficient, robust and accurate solver for supersonic viscous flows, Proc. of the ICAS 2000 Congress, Harrogate, UK, 2000.

[9] Birch TJ, Prince SA, Ludlow DK and Qin N. ‘The application of a parabolized Navier-Stokes solver to some hypersonic flow problems’, AIAA Paper 2001-1753, 2001.

[10] Qin N and Ludlow DK. A cure for anomalies of Osher and AUSM+ schemes for hypersonic viscous flows around swept cylinders, Proc. of the 22nd International Symposium on Shock Waves, Imperial College, London, UK, July 18-23, (Editors: Ball GJ, Hillier R and Roberts GT), pp. 635-640, 1999.

[11] Osher S and Solomon F. Upwind Difference Schemes for Hyperbolic Systems of Conservative Laws, Math. of Comp. 38, 339–374, 1992.

[12] Saad Y and Schultz MH. GMRES: A generalised minimal residual algorithm for solving non-symmetric linear systems, SIAM J. Sci. Stat. Comput. 7, pp. 856–869, 1986.

[13] Brandt A. Multi-Level Adaptive Solutions to Boundary-Value Problems, Math. of Comp. 31, pp. 333–390, 1977.

[14] Baldwin B and Lomax H. Thin-layer approximation and algebraic model for separated turbulent flows, AIAA 16th Aerospace Sciences Meeting, 1978.

[15] Degani D and Schiff LB. Computation of Turbulent Supersonic Flows around Pointed Bodies Having Crossflow Separation, J. Comp. Phys. 66, pp. 173–196, 1986.

[16] Spalart PR and Allmaras SR. A one-equation turbulence model for aerodynamic flows, AIAA Paper 92-0439, 1992.

[17] Wilcox, DC. Turbulence Modeling for CFD Second Edition, DCW Industries, 1998.

[18] Richtmeyer, RD and Morton, KW. Difference methods for initial-value problems, Wiley-Interscience, 1967.

[19] Roache, PJ. Perspective: A method for uniform reporting of grid refinement studies, ASME J. Fluids Eng., Vol. 116, pp. 405-13, 1994.

[20] Kleb, B and Wood, B. CFD: A Castle in the Sand?, AIAA Paper 2004-2627, 2004.

[21] Kleb, B and Wood B. Computational simulations and the scientific method, AIAA Paper 2005-4873, 2005.

[22] Mifsud, M and Shaw, ST. Credible CFD Simulations of Complex Supersonic Weapon Configurations using the IMPNS Software, CCA Report 2005-02, Cranfield University, 2005.

[23] Ludlow, DK, Qin, N, Birch, TJ and Shaw, ST. IMPNS: A flexible and efficient CFD solver for supersonic/hypersonic flows, Part I: Theory, submitted for publication, 2006.

[24] Vigneron YC, Rakich JV and Tannehill JC. Calculation of supersonic viscous flows over delta wings with sharp leading edges, AIAA Paper 78–1137, 1978.

[25] Anonymous, http://www.grc.nasa.gov/WWW/wind/valid/homepage.html, last visited August 14th 2006.

[26] Grove DV and Wang, ZJ. Computational Fluid Dynamics Study of Turbulence Modeling for an Ogive using Cobalt flow solver and a 2n Tree-Based Cartesian Grid Generator, AIAA Paper 2005-1042, 2005.

[27] Hodges, J, Ward, LC and Birch, TJ. Pressure Measurements on Slender Bodies at Supersonic Speeds and Development of Flow Separation Criteria for Euler Codes, RAE TM Aero 2177, 1990.

[28] Ward, LC and Birch, TJ. An Investigation of Reynolds Number Effects on a Tangent-Ogive Cylinder Body, DRA TM Aero/Prop 4, 1992.

[29] Wagner, BH. PNS Computations of Configurations Related to Realistic Space Vehicles, M.Sc. Thesis, Cranfield University, 2005.

[30] Wagner BH, Mifsud M, Bennett JB and Shaw, ST. Verification and Validation of the IMPNS Flow Solver Using the X-15 Flight Experiment, AIAA Paper 2006-3870, 2006.

[31] Wagner, B, Mifsud, M, Bennett, JB and Shaw ST. Numerical computation of the X-15 Wind Tunnel and Flight Experiments, A Validation and Verification Case Study, in Proceedings of the 25th International Congress of the Aerospace Sciences, 2006.

[32] Moureaux, A. Further computations of the X-15 research vehicle, M.Sc. Thesis, Cranfield University, 2006.

[33] Love, ES. A re-examination of the use of simple concepts for predicting the shape and location of detached shock waves, NACA TN 4170, 1957.

[34] Jones JH, Pressure tests on the standard hypervelocity ballistic model HB-2 at Mach 1.5 to 5, Arnold Engineering Development Center, Technical Documentary Report, AEDC-TDR-64-246, 1964.

[35] Stillwell WH. X-15 research results - with a selected bibliography, NASA SP-60. NASA, Washington, D.C., 1965.

[36] Franklin AE and Lust RM. Investigation of the aerodynamic characteristic of a 0.067-scale model of the X-15 airplane (configuration 3) at Mach numbers of 2.29, 2.98 and 4.65, NASA TM X-38, Washington, D.C., 1959.

[37] Palitz M Measured and calculated flow conditions on the forward fuselage of the X-15 airplane and model at mach numbers from 3.0 to 8.0, NASA TN D-3447, Washington, D.C., 1966.

[38] Hodge L and Burbank PB. Pressure distribution of a 0.0667-scale model of the X15 airplane for an angle-of-attack range of 0 to 28 at Mach number of 2.30, 2.88 and 4.65, NASA TM X-275, Washington, D.C., 1960.

[39] Silvers, HN, Lancaster, JA amd Wills, JS. Investigation of the loading characteristics of the lifting surfaces and the speed brakes of a 0.067 scale model of the North American X-15 airplane (configuration 3) at Mach numbers of 2.29, 2.98 and 4.65, NASA TM X-301, 1960

[40] Pyze, JS. Flight-measured wing surface pressures and loads for the X-15 airplane ay Mach numbers from 1.2 to 6, NASA TN D-2602, 1965.

[41] Keener, ER and Pembo, C. Aerodynamics forces on components of the X-15 airplane, NASA TM X-712, 1961.

[42] Maughmer, M, Straussfogel, D, Ozoroski, L and Long, L. Validation of engineering methods for predicting hypersonic vehicle control forces and moments, J. Guidance, Control and Dynamics, Vol. 16(4), pp.762-9, 1993.

[43] Ilif, KW and Shafer, MF. A comparison of hypersonic flight and prediction results, AIAA Paper 93-3111, 1993

[44] Hawkins, R, Dilley, W and Arthur, D. CFD comparisons with wind tunnel and flight data for the X-15, AIAA-Paper 92-5047, 1992.

[45] Baker, ML, Munson, MJ, Alston, KY and Hoppus, GW. Integrated Hypersonic Aeromechanics Tool (IHAT), AIAA Paper 2003-6952, 2003.

[46] Le, A-T, Gray, K and Baker, M. Building the Aerodynamics Module for the Integrated Hypersonic Aeromechanics Tool, AIAA-Paper 2004-215, 2004.

Cite this paper

S Shaw, M Mifsud, B Wagner, A Moureaux, J Bennett, IMPNS Computations of the X-15 Flight Vehicle: A Validation and Verification, NAFEMS International Journal of CFD Case Studies, Volume 6, 2007, Pages 55-91, https://doi.org/10.59972/0sjv74yh

Document Details

ReferenceCFDJ6-5
AuthorsShaw. S Mifsud. M Wagner. B Moureaux. A Bennett. J
LanguageEnglish
TypeJournal Article
Date 3rd January 2007
OrganisationCranfield University

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