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A general framework for verification and validation of large eddy simulations

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Abstract

A general framework (methodology and procedures) for verification and validation (V&V) of large eddy simulations in computational fluid dynamics (CFD) is derived based on two hypotheses. The framework allows for quantitative estimations of numerical error, modeling error, their coupling, and the associated uncertainties. To meet different needs of users based on their affordable computational cost, various large eddy simulation (LES) V&V methods are proposed. These methods range from the most sophisticated seven equation estimator to the simplest one-grid estimator, which will be calibrated using factors of safety to achieve the objective reliability and confidence level. Evaluation, calibration and validation of various LES V&V methods in this study will be performed using rigorous statistical analysis based on an extensive database. Identification of the error sources and magnitudes has the potential to improve existing or derive new LES models. Based on extensive parametric studies in the database, it is expected that guidelines for performing large eddy simulations that meet pre-specified quality and credibility criteria can be obtained. Extension of this framework to bubbly flow is also discussed.

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Literatur

  1. JOHNSON F. T., TINOCO E. N. and YU N. J. Thirty years of development and application of CFD at boeing commercial airplanes, seattle[J]. Computers and Fluids, 2005, 34(10): 1115–1151.

    Article  Google Scholar 

  2. STERN F., YANG J. and WANG Z. et al. Computational ship hydrodynamics: Nowadays and way forward[J]. International shipbuilding Progress, 2013, 60(1-4): 3–105.

    Google Scholar 

  3. QUALLEN S., XING T. and CARRICA P. et al. CFD simulation of a floating offshore wind turbine system using a quasi-static crowfoot mooring-line model[J]. Journal of Ocean and Wind Energy, 2014, 1(3): 143–152.

    Google Scholar 

  4. QUALLEN S., XING T. and CARRICA P. et al. DISCUSSION: CFD Simulation of a floating offshore wind turbine system using a quasi-static crowfoot moo-ring-line model[J]. Journal of Ocean and Wind Energy, 2014, 1(3): 185–188.

    Google Scholar 

  5. QUALLEN S., XING T. and CARRICA P. et al. CFD simulation of a floating offshore wind turbine system using a quasi-static crowfoot mooring-line model[C]. 23rd International Ocean and Polar Engineering Conference. Anchorage, USA, 2013.

    Google Scholar 

  6. POPE S. B. Turbulent flows[M]. New York, USA: Cambridge university press, 2000.

    Book  Google Scholar 

  7. MAHESH K., CONSTANTINESCU G. and APTE S. et al. Large-eddy simulation of reacting turbulent flows in complex geometries[J]. ASME Journal of Applied Mechanics, 2006, 73(3): 374–381.

    Article  Google Scholar 

  8. YOU D., WANG M. and MOIN P. et al. Large-eddy simulation analysis of mechanisms for viscous losses in a turbomachinery tip-clearance flow[J]. Journal of Fluid Mechanics, 2007, 586: 177–204.

    Article  Google Scholar 

  9. YOU D., HAM F. and MOIN P. Discrete conservation principles in large-eddy simulation with application to separation control over an airfoil[J]. Physics of Fluids, 2008, 20: 101515.

    Article  Google Scholar 

  10. FUREBY C. Large eddy simulation of ship hydrodyna-mics[C]. 27th Symposium on Naval Hydrodynamics. Seoul, Korea, 2008.

    Google Scholar 

  11. XING T., CARRICA P. and STERN F. Large-scale RUPANS and DDES computations of KVLCC2 at drift angle 0 Degree[C]. A Workshop on CFD in Ship Hydrodynamics Gothenburg. Gothenburg, Sweden, 2010.

    Google Scholar 

  12. LI Y., PAIK K.-J. and XING T. et al. Dynamic overset CFD simulations of wind turbine aerodynamics[J]. Renewable Energy, 2012, 37(1): 285–298.

    Article  Google Scholar 

  13. WANG Z., SUH J. and YANG J. et al. Sharp interface LES of breaking waves by an interface piercing body in orthogonal curvilinear coordinates[C]. 50th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition. Nashville, Tennessee, USA, 2012.

    Google Scholar 

  14. ASME. ASME guide on verification and validation in computational fluid dynamics and heat transfer[R]. Techical Report by ASME Performance Test Code Committee PTC-61, ANSI Standard V&V-20, 2008.

    Google Scholar 

  15. STERN F., WILSON R. V. and COLEMAN H. W. et al. Comprehensive approach to verification and validation of CFD simulations-Part 1: Methodology and procedu-res[J]. Journal of Fluids Engineering, 2001, 123(4): 793–802.

    Article  Google Scholar 

  16. COLEMAN H., STERN F. Uncertainties and CFD code validation[J]. Journal of Fluids Engineering, 1997, 119(4): 795–803.

    Article  Google Scholar 

  17. ROACHE P. J. Verification and validation in computational science and engineering[M]. Socorro, New Mexico, USA: Hermosa Publishers, 1998.

    Google Scholar 

  18. ROACHE P. J. Fundamentals of verification and validation[M]. Socorro, New Mexico, USA: Hermosa Publishers, 2009.

    Google Scholar 

  19. CELIK I. B., GHIA U. and ROACHE P. J. et al. Proce-dure for estimation and reporting of uncertainty due to discretization in CFD applications[J]. Journal of Fluids Engineering, 2008, 130(7): 078001.

    Google Scholar 

  20. COSNER R. R., OBERKAMPF W. L. and RUMSEY C. L. et al. AIAA committee on standards for computational fluid dynamics: Status and plans[C]. 44th AIAA Aerospace Sciences Meeting and Exhibit. Reno, Nevada, USA, 2006, AIAA 2006–889.

    Google Scholar 

  21. OBERKAMPF W. L., ROY C. J. Verification and validation in scientific computing[M]. New York, USA: Cambridge University Press, 2010.

    Book  Google Scholar 

  22. STERN F., WILSON R. and SHAO J. Quantitative V&V of CFD simulations and certification of CFD codes[J]. International Journal for Numerical Methods in Fluids, 2006, 50(11): 1335–1355.

    Article  Google Scholar 

  23. WILSON R., SHAO J. and STERN F. Discussion: Cri-ticisms of the “correction factor” verification method[J]. Journal of Fluids Engineering, 2004, 126(4): 704–706.

    Article  Google Scholar 

  24. XING T., STERN F. Factors of safety for Richardson extrapolation[J]. Journal of Fluids Engineering, 2010, 132(6): 061403.

    Google Scholar 

  25. XING T., STERN F. Closure to Discussion of “Factors of safety for Richardson extrapolation” (2011, Journal of Fluids Engineering, 133: 115501), Journal of Fluids Engineering, 2011, 133(11): 115502.

    Google Scholar 

  26. CELIK I., HU G. Single grid error estimation using error transport equation[J]. Journal of Fluids Engineering, 2004, 126(5): 778–790.

    Article  Google Scholar 

  27. EÇA L., HOEKSTRA M. An evaluation of verification procedures for CFD applications[C]. 24th Symposium on Naval Hydrodynamics. Fukuoka, Japan, 2002.

    Google Scholar 

  28. EÇA L., HOEKSTRA M. and BEJA PEDRO J. F. et al. On the characterization of grid density in grid refinement studies for discretization error estimation[J]. International Journal for Numerical Methods in Fluids, 2013, 72(1): 119–134.

    Article  MathSciNet  Google Scholar 

  29. EÇA L., HOEKSTRA M. Discretization uncertainty estimation based on a least squares version of the grid convergence index[C]. Proceedings of the Second Workshop on CFD Uncertainty Analysis. Lisbon, Portugal, 2006.

    MATH  Google Scholar 

  30. PHILLIPS T. S., ROY C. J. Richardson extrapolation-based discretization uncertainty estimation for computational fluid dynamics[J]. Journal of Fluids Engineering, 2014, 136(12): 121401.

    Google Scholar 

  31. VIOLA I., BOT P. and RIOTTE M. On the uncertainty of CFD in sail aerodynamics[J]. International Journal for Numerical Methods in Fluids, 2013, 72(11): 1146–1164.

    Article  MathSciNet  Google Scholar 

  32. OBERKAMPF W. L., TRUCANO T. G. Validation methodology in computational fluid dynamics[C]. AIAA 2000-2549, Fluids 2000 Conference and Exhibit. Denver, USA, 2000.

    Google Scholar 

  33. GEURTS B. J., FFÇHLICH J. A framework for predicting accuracy limitations in large-eddy simulation[J]. Physics of Fluids, 2002, 14(6): L41–L42.

    Article  Google Scholar 

  34. GEURTS B. J. Balancing errors in LES, direct and large-eddy simulation III[M]. Dordrecht, The Netherlands: Springer, 1999, 1–12.

    Book  Google Scholar 

  35. CELIK I. B., CEHRELI Z. N. and YAVUZ I. Index of resolution quality for large eddy simulations[J]. Journal of Fluids Engineering, 2005, 127(5): 949–958.

    Article  Google Scholar 

  36. CELIK I., KLEIN M. and JANICKA J. Assessment measures for engineering LES applications[J]. Journal of Fluids Engineering, 2009, 131(3): 031102.

    Google Scholar 

  37. KLEIN M. An attempt to assess the quality of large eddy simulations in the context of implicit filtering[J]. Flow, Turbulence and Combustion, 2005, 75(1-4): 131–147.

    Google Scholar 

  38. FREITAG M., KLEIN M. An improved method to assess the quality of large eddy simulations in the context of implicit filtering[J]. Journal of Turbulence, 2006, 7(40): 1–11.

    Google Scholar 

  39. MEYERS J., GEURTS B. J. and BAELMANS M. Da-tabase analysis of errors in large-eddy simulation[J]. Physics of Fluids, 2003, 15(9): 2740–2755.

    Article  Google Scholar 

  40. TRAVIN A., SHUR M. and STRELETS M. et al. De-tached-eddy simulations past a circular cylinder[J]. Flow, Turbulence and Combustion, 2000, 63(1): 293–313.

    Article  Google Scholar 

  41. SAGAUT P., DECK S. Large eddy simulation for aero-dynamics: Status and perspectives[J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2009, 367(1899): 2849–2860.

    Article  Google Scholar 

  42. EÇA L., HOEKSTRA M. Code verification of unsteady flow solvers with the method of the manufactured solutions[C]. 17th International Offshore and Polar Engineering Conference. Lisbon, Portugal, 2007.

    Google Scholar 

  43. XING T., SHAO J. and STERN F. BKW-RS-DES of unsteady vortical flow for KVLCC2 at large drift angles[C]. The 9th international conference on Numerical Ship Hydrodynamics. Ann Arbor, Michigan, USA, 2007.

    Google Scholar 

  44. EÇA L. Private communication to T. Xing[R]. 2014.

    Google Scholar 

  45. EÇA L., VAZ G. and HOEKSTRA M. Code verification, solution verification and validation in RUPANS sol-vers[C]. 29th International Conference on Ocean, Offshore and Arctic Engineering. Shanghai, China, 2010.

    Google Scholar 

  46. SATHIAH P., KOMEN E. and ROEKAERTS D. The role of CFD combustion modeling in hydrogen safety management—Part I: Validation based on small scale experiments[J]. Nuclear Engineering and Design, 2012, 248: 93–107.

    Article  Google Scholar 

  47. STERNEL D. C., SCHÄFER M. and Gauß F. et al. Influence of numerical parameters for large eddy simulations of complex flow fields[J]. European Conference on Compuational Fluid Dynamics, ECCOMAS CFD 2006. Egmond aan Zee, The Netherlands, 2006.

    Google Scholar 

  48. PARK T. Effects of time-integration method in a large-eddy simulation using the PISO algorithm: Part I—Flow field[J]. Numerical Heat Transfer, Part A: Applications, 2006, 50(3): 229–245.

    Article  MathSciNet  Google Scholar 

  49. XING T., KANDASAMY M. and STERN F. Unsteady free-surface wave-induced separation: analysis of turbulent structures using detached eddy simulation and single-phase level set[J]. Journal of Turbulence, 2007, 8(44): 1–35.

    Google Scholar 

  50. XING T., BHUSHAN S. and STERN F. Vortical and turbulent structures for KVLCC2 at Drift Angle 0, 12, and 30 degrees[J]. Ocean Engineering, 2012, 55: 23–43.

    Article  Google Scholar 

  51. HEDGES L. S., TRAVIN A. K. and SPALART P. R. Detached-eddy simulations over a simplified landing gear[J]. Journal of Fluids Engineering, 2002, 124(2): 413–423.

    Article  Google Scholar 

  52. NOLAN K. P., ZAKI T. A. Conditional sampling of transitional boundary layers in pressure gradients[J]. Journal of Fluid Mechanics, 2013, 728: 306–339.

    Article  MathSciNet  Google Scholar 

  53. VREMAN B., GEURTS B. and KUERTEN H. Comparison of numerical schemes in large-eddy simulation of the temporal mixing layer[J]. International Journal for Numerical Methods in Fluids, 1996, 22(4): 297–298.

    Article  Google Scholar 

  54. MOSER R. D., KIM J. and MANSOUR N. N. Direct numerical simulation of turbulent channel flow up to Re = 590 [J]. Physics of Fluids, 1999, 11(4): 943–945.

    Article  Google Scholar 

  55. VERSTAPPEN R., WISSINK J. G. and CAZEMIER W. et al. Direct numerical simulations of turbulent flow in a driven cavity[J]. Future Generation Computer Systems, 1994, 10(2-3): 345–350.

    Article  Google Scholar 

  56. WISSINK J. G., RODI W. Numerical study of the near wake of a circular cylinder[J]. International Journal of Heat and Fluid Flow, 2008, 29(4): 1060–1070.

    Article  Google Scholar 

  57. HUNG L., MOIN P. and KIM J. Direct numerical simulation of turbulent flow over a backward-facing step[J]. Journal of Fluid Mechanics, 1997, 330: 349–374.

    Article  Google Scholar 

  58. PINTO-HEREDERO A., XING T. and STERN F. URANS and DES analysis for a Wigley hull at extreme drift angles[J]. Journal of Marine Science and Technology, 2010, 15(4): 295–315.

    Article  Google Scholar 

  59. XING T., CARRICA P. and STERN F. Computational towing tank procedures for single run curves of resistance and propulsion[J]. Journal of Fluids Engineering, 2008, 130(10): 101–102.

    Article  Google Scholar 

  60. BHUSHAN S., XING T. and CARRICA P. et al. Model- and full-scale UPRAN simulations of athena aesistance, powering, seakeeping, and 5415 maneuve-ring[J]. Journal of Ship Research, 2009, 53(4): 179–198.

    Google Scholar 

  61. FUREBY C. Iles and LES of complex engineering turbulent flows[J]. Journal of Fluids Engineering, 2007, 129(12): 1514–1523.

    Article  MathSciNet  Google Scholar 

  62. FUREBY C. Towards the use of large eddy simulation in engineering[J]. Progress in Aerospace Sciences, 2008, 44(6): 381–396.

    Article  Google Scholar 

  63. LARSSON L., STERN F. and BERTRAM V. Bench-marking of computational fluid dynamics for ship flows: The Gothenburg 2000 workshop[J]. Journal of Ship Research, 2003, 47(1): 63–81.

    Google Scholar 

  64. LARSSON L., STERN F. and VISONNEAU M. CFD in ship hydrodynamics-results of the Gothenburg 2010 workship[C]. Marine 2011-IPV International Conference on Computational Methods in Marine Engineering. Lisbon, Portugal, 2011.

    Google Scholar 

  65. ISMAIL F., CARRICA P. M. and XING T. et al. Evaluation of linear and nonlinear convection schemes on multidimensional non-orthogonal grids with applications to KVLCC2 tanker[J]. International Journal for Numerical Methods in Fluids, 2010, 64: 850–886.

    MathSciNet  MATH  Google Scholar 

  66. EÇA L., VAZ G. and HOEKSTRA M. Assessing convergence properties of RUPANS solvers with manufactured solutions[C]. European Congress on Computational Methods in Applied Sciences and Engineering (ECOMAS 2012). Vienna, Austria, 2012.

    Google Scholar 

  67. SMAGORINSKY J. General circulation experiments with the primitive equations: I. The basic experiment[J]. Monthly Weather Review, 1963, 91(3): 99–164.

    Article  Google Scholar 

  68. GERMANO M., PIOMELLI U. and MOIN P. et al. A dynamic subgrid-scale eddy viscosity model[J]. Physics of Fluids A: Fluid Dynamics, 1991, 3(7): 1760–1765.

    Article  Google Scholar 

  69. LILLY D. K. Proposed modification of the Germano subgrid-scale closure method[J]. Physics of Fluids A: Fluid Dynamics, 1992, 4(3): 633–635.

    Article  Google Scholar 

  70. RIZZI A., VOS J. Toward establishing credibility in computational fluid dynamics simulations[J]. AIAA Journal, 1998, 36(5): 668–675.

    Article  Google Scholar 

  71. KREYSZIG E. Advanced engineering mathematics[M]. 7th Edition, New York, USA: Wiley, 2007.

    MATH  Google Scholar 

  72. MEYERS J., GEURTS B. and SAGAUT P. A computational error-assessment of central finite-volume discreti-zations in large-eddy simulation using a Smagorinsky model[J]. Journal of Computational Physics, 2007, 227(1): 156–173.

    Article  MathSciNet  Google Scholar 

  73. MEYERS J. Error-landscape assessment of largeeddy simulations: A review of the methodology[M]. New York, USA: Springer, 65-77.

  74. GEURTS B. J. Analysis of errors occurring in large eddy simulation[J]. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2009, 367(1899): 2873–2883.

    Article  MathSciNet  Google Scholar 

  75. GHOSAL S. An analysis of numerical errors in largeeddy simulations of turbulence[J]. Journal of Computational Physics, 1996, 125(1): 187–206.

    Article  MathSciNet  Google Scholar 

  76. KRAVCHENKO A., MOIN P. On the effect of numerical errors in large eddy simulations of turbulent flows[J]. Journal of Computational Physics, 1997, 131(2): 310–322.

    Article  Google Scholar 

  77. RADHAKRISHNAN S., BELLAN J. Explicit filtering to obtain grid-spacing-independent and discretization-order-independent large-eddy simulation of two-phase volumetrically dilute flow with evaporation[J]. Journal of Fluid Mechanics, 2013, 719: 230–267.

    Article  MathSciNet  Google Scholar 

  78. MEYERS J., SAGAUT P. and GEURTS B. J. Optimal model parameters for multi-objective largeeddy simulations[J]. Physics of Fluids, 2006, 18(9): 095103.

    Google Scholar 

  79. NIERHAUS T., VANDEN ABEELE D. and DECONI-NCK H. Direct numerical simulation of bubbly flow in the turbulent boundary layer of a horizontal parallel plate electrochemical reactor[J]. International Journal of Heat and Fluid Flow, 2007, 28(4): 542–551.

    Article  Google Scholar 

  80. BOLOTNOV I. A., JANSEN K. E. and DREW D. A. et al. Detached direct numerical simulations of turbulent two-phase bubbly channel flow[J]. International Journal of Multiphase Flow, 2011, 37(6): 647–659.

    Article  Google Scholar 

  81. XING T. Numerical modeling and simulation of laminar and transitional submerged cavitating jets[D]. Doctoral Thesis, West Lafayette, USA: Purdue University, 2002.

    Google Scholar 

  82. KUBOTA A., KATO H. and YAMAGUCHI H. A new modelling of cavitating flows: A numerical study of unsteady cavitation on a hydrofoil section[J]. Journal of Fluid Mechanics, 1992, 240: 59–96.

    Article  Google Scholar 

  83. SHI Su-guo, WANG Guo-yu. A modified kubota cavi-tation model for computations of cryogenic cavitating flows[J]. Chinese Journal of Theoretical and Applied Mechanics, 2012, 44(2): 269–277.

    Google Scholar 

  84. XING T., FRANKEL S. H. Effect of cavitation on vortex dynamics in a submerged laminar jet[J]. AIAA Journal, 2002, 40(11): 2266–2276.

    Article  Google Scholar 

  85. XING T., LI Z. and FRANKEL S. H. Numerical simulation of vortex cavitation in a three-dimensional submerged transitional jet[J]. Journal of Fluids Engineering, 2005, 127(4): 714–725.

    Article  Google Scholar 

  86. WANG G., OSTOJA-STARZEWSKI M. Large eddy simulation of a sheet/cloud cavitation on a NACA0015 hydrofoil[J]. Applied Mathematical Modelling, 2007, 31(3): 417–447.

    Article  Google Scholar 

  87. DHOTRE M. T., DEEN N. G. and NICENO B. et al. Large eddy simulation for dispersed bubbly flows: A re-view[J]. International Journal of Chemical Engineering, 2013.

    Google Scholar 

  88. BESTION D. Applicability of two-phase CFD to nuclear reactor thermalhydraulics and elaboration of best practice guidelines[J]. Nuclear Engineering and Design, 2012, 253: 311–321.

    Article  Google Scholar 

  89. NIČENO B., DHOTRE M. T. and DEEN N G. One-equation sub-grid scale (SGS) modelling for Euler-Euler large eddy simulation (EELES) of dispersed bubbly flow[J]. Chemical Engineering Science, 2008, 63(15): 3923–3931.

    Article  Google Scholar 

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Correspondence to Tao Xing.

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Biography: XING Tao (1973-), Male, Ph. D., P. E., Assistant Professor

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Xing, T. A general framework for verification and validation of large eddy simulations. J Hydrodyn 27, 163–175 (2015). https://doi.org/10.1016/S1001-6058(15)60469-3

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