A general framework for verification and validation of large eddy simulations

Journal of Hydrodynamics, Ser. B - Tập 27 - Trang 163-175 - 2015
Tao Xing1
1Department of Mechanical Engineering, College of Engineering, University of Idaho, Moscow, USA

Tóm tắt

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.

Tài liệu tham khảo

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. 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. 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. 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. 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. POPE S. B. Turbulent flows[M]. New York, USA: Cambridge university press, 2000. 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. 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. 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. FUREBY C. Large eddy simulation of ship hydrodyna-mics[C]. 27th Symposium on Naval Hydrodynamics. Seoul, Korea, 2008. 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. 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. 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. 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. 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. COLEMAN H., STERN F. Uncertainties and CFD code validation[J]. Journal of Fluids Engineering, 1997, 119(4): 795–803. ROACHE P. J. Verification and validation in computational science and engineering[M]. Socorro, New Mexico, USA: Hermosa Publishers, 1998. ROACHE P. J. Fundamentals of verification and validation[M]. Socorro, New Mexico, USA: Hermosa Publishers, 2009. 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. 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. OBERKAMPF W. L., ROY C. J. Verification and validation in scientific computing[M]. New York, USA: Cambridge University Press, 2010. 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. 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. XING T., STERN F. Factors of safety for Richardson extrapolation[J]. Journal of Fluids Engineering, 2010, 132(6): 061403. 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. CELIK I., HU G. Single grid error estimation using error transport equation[J]. Journal of Fluids Engineering, 2004, 126(5): 778–790. EÇA L., HOEKSTRA M. An evaluation of verification procedures for CFD applications[C]. 24th Symposium on Naval Hydrodynamics. Fukuoka, Japan, 2002. 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. 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. 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. 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. OBERKAMPF W. L., TRUCANO T. G. Validation methodology in computational fluid dynamics[C]. AIAA 2000-2549, Fluids 2000 Conference and Exhibit. Denver, USA, 2000. GEURTS B. J., FFÇHLICH J. A framework for predicting accuracy limitations in large-eddy simulation[J]. Physics of Fluids, 2002, 14(6): L41–L42. GEURTS B. J. Balancing errors in LES, direct and large-eddy simulation III[M]. Dordrecht, The Netherlands: Springer, 1999, 1–12. 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. CELIK I., KLEIN M. and JANICKA J. Assessment measures for engineering LES applications[J]. Journal of Fluids Engineering, 2009, 131(3): 031102. 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. 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. 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. 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. 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. 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. 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. EÇA L. Private communication to T. Xing[R]. 2014. 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. 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. 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. 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. 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. 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. 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. NOLAN K. P., ZAKI T. A. Conditional sampling of transitional boundary layers in pressure gradients[J]. Journal of Fluid Mechanics, 2013, 728: 306–339. 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. 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. 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. 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. 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. 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. 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. 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. FUREBY C. Iles and LES of complex engineering turbulent flows[J]. Journal of Fluids Engineering, 2007, 129(12): 1514–1523. FUREBY C. Towards the use of large eddy simulation in engineering[J]. Progress in Aerospace Sciences, 2008, 44(6): 381–396. 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. 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. 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. 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. SMAGORINSKY J. General circulation experiments with the primitive equations: I. The basic experiment[J]. Monthly Weather Review, 1963, 91(3): 99–164. 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. LILLY D. K. Proposed modification of the Germano subgrid-scale closure method[J]. Physics of Fluids A: Fluid Dynamics, 1992, 4(3): 633–635. RIZZI A., VOS J. Toward establishing credibility in computational fluid dynamics simulations[J]. AIAA Journal, 1998, 36(5): 668–675. KREYSZIG E. Advanced engineering mathematics[M]. 7th Edition, New York, USA: Wiley, 2007. 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. MEYERS J. Error-landscape assessment of largeeddy simulations: A review of the methodology[M]. New York, USA: Springer, 65-77. 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. GHOSAL S. An analysis of numerical errors in largeeddy simulations of turbulence[J]. Journal of Computational Physics, 1996, 125(1): 187–206. 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. 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. MEYERS J., SAGAUT P. and GEURTS B. J. Optimal model parameters for multi-objective largeeddy simulations[J]. Physics of Fluids, 2006, 18(9): 095103. 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. 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. XING T. Numerical modeling and simulation of laminar and transitional submerged cavitating jets[D]. Doctoral Thesis, West Lafayette, USA: Purdue University, 2002. 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. 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. XING T., FRANKEL S. H. Effect of cavitation on vortex dynamics in a submerged laminar jet[J]. AIAA Journal, 2002, 40(11): 2266–2276. 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. 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. 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. 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. 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.