Numerical prediction of the influence of uncertain inflow conditions in pipes by polynomial chaos

References

• Bratley, P., and B.L. Fox. 1988. “Algorithm 659 Implementing Sobol's Quasirandom Sequence Generator.” ACM Transactions on Mathematical Software 14: 88–100.
   Web of Science ®Google Scholar
• Cameron, R.H., and W.T. Martin. 1947. “The Orthogonal Development of Nonlinear Functionals in Series of Fourier-Hermite Functionals.” Annals of Mathematics 48: 385–392.
   Web of Science ®Google Scholar
• Congedo, P.M., C. Duprat, G. Balarac, and C. Corre. 2011. “Effects of Inlet Uncertainties on Prediction of Turbulent Flows Using RANS and LES Simulations.” In 20th AIAA Computational Fluid Dynamics Conference, edited by AIAA, AIAA 2011-3869. Honolulu, HI doi: 10.2514/6.2011-3869.
   Google Scholar
• Congedo, P.M., C. Duprat, G. Balarac, and C. Corre. 2013. “Numerical Prediction of Turbulent Flows Using Reynolds-Averaged Navier-Stokes and Large-Eddy Simulation with Uncertain Inflow Conditions.” International Journal for Numerical Methods in Fluids 72: 341–358.
   Web of Science ®Google Scholar
• García-Sánchez, C., D.A. Philips, and C. Gorlé. 2014. “Quantifying Inflow Uncertainties for CFD Simulations of the Flow in Downtown Oklahoma City.” Building and Environment 78: 118–129.
   Web of Science ®Google Scholar
• Gersten, K. 2005. “Fully Developed Turbulent Pipe Flow.” In Fluid Mechanics of Flow Metering, edited by W. Merzkirch, 1–22. Berlin: Springer.
   Google Scholar
• Gersten, K., and G. Herwig. 1992. Strömungsmechanik: Grundlagen der Impuls-, Wärme- und Stoffübertragung aus asymptotischer Sicht [Fluid Mechanics: Fundamentals of Momentum, Heat, and Mass Transfer from an Asymptotic Point of View]. Braunschweig: Vieweg.
   Google Scholar
• Gerstner, T., and M. Griebel. 1998. “Numerical Integration Using Sparse Grids.” Numerical Algorithms 18: 209–232.
   Web of Science ®Google Scholar
• Ghanem, R., and P. Spanos. 1991. Stochastic Finite Elements: A Spectral Approach. New York: Springer.
   Google Scholar
• Gibson, N.L., C. Gifford-Miears, A.S. Leon, and V.S. Vasylkivska. 2014. “Efficient Computation of Unsteady Flow in Complex River Systems with Uncertain Inputs.” International Journal of Computer Mathematics 91: 781–797.
   Web of Science ®Google Scholar
• Han, X., P. Sagaut, and D. Lucor. 2012. “On Sensitivity of RANS Simulations to Uncertain Turbulent Inflow Conditions.” Computers & Fluids 61: 2–5.
   Web of Science ®Google Scholar
• Han, X., P. Sagaut, D. Lucor, and I. Afgan. 2012. “Stochastic Response of the Laminar Flow Past a Flat Plate Under Uncertain Inflow Conditions.” International Journal of Computational Fluid Dynamics 26: 101–117.
   Web of Science ®Google Scholar
• Horner, B., and F. Mesch. 1995. “An Induction Flowmeter Insensitive to Asymmetric Flow Profiles.” In Process Tomography 1995, 6–8 April 1995, Bergen, Norway, edited by M.S. Beck, 321–330. Manchester: UMIST.
   Google Scholar
• Hosder, S., R.W. Walters, and R. Perez. 2006. “A Non-Intrusive Polynomial Chaos Method for Uncertainty Propagation in CFD Simulations.” In 44th AIAA Aerospace Science Meeting and Exhibit, edited by AIAA, AIAA 2006-891. Reno, NV. doi: 10.2514/6.2006-891
   Google Scholar
• Hrenya, C.M., E.J. Bolio, D. Chakrabarti, and J.L. Sinclair. 1995. “Comparison of Low Reynolds Number k-ε Turbulence Models in Predicting Fully Developed Pipe Flow.” Chemical Engineering Science 50: 1923–1941.
   Web of Science ®Google Scholar
• Knio, O.M., and O.P. Le Maître. 2006. “Uncertainty Propagation in CFD Using Polynomial Chaos Decomposition.” Fluid Dynamics Research 38: 616–640.
   Web of Science ®Google Scholar
• Ko, J., D. Lucor, and P. Sagaut. 2008. “Sensitivity of Two-Dimensional Spatially Developing Mixing Layers with Respect to Uncertain Inflow Conditions.” Physics of Fluids 20:1–20.
   Web of Science ®Google Scholar
• Le Maître, O.P., and O.M. Knio. 2010. Spectral Methods for Uncertainty Quantification. Dordrecht: Springer.
   Google Scholar
• Le Maître, O.P., O.M. Knio, H.N. Najm, and R.G. Ghanem. 2001. “A Stochastic Projection Method for Fluid Flow. I. Basic Formulation.” Journal of Computational Physics 173: 481–511.
   Web of Science ®Google Scholar
• Le Maître, O.P., M.T. Reagan, H.N. Najm, R.G. Ghanem, and O.M. Knio. 2002. “A Stochastic Projection Method for Fluid Flow. II. Random Process.” Journal of Computational Physics 181: 9–44.
   Web of Science ®Google Scholar
• Lin, G., X. Wan, C.-H. Su, and G.E. Karniadakis. 2007. “Stochastic Computational Fluid Mechanics.” Computing in Science & Engineering 9: 21–29.
   Web of Science ®Google Scholar
• McKeon, B.J., J.F. Morrison, W. Jiang, J. Li, and A.J. Smits. 2004. “Revised Log-Law Constants for Fully-Developed Turbulent Pipe Flow.” In IUTAM Symposium on Reynolds Number Scaling in Turbulent Flow, Vol. 74 of Fluid Mechanics and its Applications, edited by A.J. Smits, 265–270. Netherlands: Springer.
   Google Scholar
• Menter, F. R. 1993. “Two-Equation Eddy-Viscosity Turbulence Models for Engineering Applications.” AIAA Journal 32: 1598–1605.
   Web of Science ®Google Scholar
• Mickan, B., G. Wendt, R. Kramer, and D. Dopheide. 1996. “Systematic Investigation of Pipe Flows and Installation Effects Using Laser Doppler Anemometry — Part II. The Effect of Disturbed Flow Profiles on Turbine Gas Meters — A Describing Empirical Model.” Flow Measurement and Instrumentation 7: 151–160.
   Web of Science ®Google Scholar
• Myong, H.K., and N. Kasagi. 1990. “A New Approach to the Improvement of k-ε Turbulence Model for Wall-Bounded Shear Flows.” JSME International Journal 33: 63–72.
   Web of Science ®Google Scholar
• Myong, H.K., N. Kasagi, and M. Hirata. 1989. “Numerical Prediction of Turbulent Pipe Flow Heat Transfer for Various Prandtl Number Fluids with the Improved k-ε Turbulence Model.” JSME International Journal 32: 613–622.
   Web of Science ®Google Scholar
• Najm, H.N. 2009. “Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics.” Annual Review of Fluid Mechanics 41: 35–52.
   Web of Science ®Google Scholar
• Smolyak, S.A. 1963. “Quadrature and Interpolation Formulas for Tensor Products of Certain Classes of Functions.” Doklady Akademii Nauk SSSR 148: 1042–1045.
   Google Scholar
• Sobol, I.M. 1967. “On the Distribution of Points in a Cube and the Approximate Evaluation of Integrals.” USSR Computational Mathematics and Mathematical Physics 7: 86–112.
   Google Scholar
• Tartakovsky, D. M., and D. Xiu. 2006. “Stochastic Analysis of Transport in Tubes With Rough Walls.” Journal of Computational Physics 217: 248–259.
   Web of Science ®Google Scholar
• Tawackolian, K. 2013. “Fluiddynamische Auswirkungen auf die Messabweichung von Ultraschall-Durchflussmessgeräten [Fluid Dynamic Influences on the Measurement Deviation of Ultrasonic Flow Meters].” PhD diss., Technische Universität Berlin.
   Google Scholar
• Wan, X., and G.E. Karniadakis. 2006. “Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures.” SIAM Journal on Scientific Computing 28: 901–928.
   Web of Science ®Google Scholar
• Wendt, G. 2014. “Investigation and Characterization of Water Meter Behavior Under Different Flow Conditions.” OIML Bulletin 55: 5–14.
   Google Scholar
• Wendt, G., B. Mickan, R. Kramer, and D. Dopheide. 1996. “Systematic Investigation of Pipe Flows and Installation Effects Using Laser Doppler Anemometry — Part I. Profile Measurements Downstream of Several Pipe Configurations and Flow Conditioners.” Flow Measurement and Instrumentation 7: 141–149.
   Web of Science ®Google Scholar
• Wiener, N. 1938. “The Homogeneous Chaos.” American Journal of Mathematics 60: 897–936.
   Web of Science ®Google Scholar
• Wildemann, C., W. Merzkirch, and K. Gersten. 2002. “A Universal, Nonintrusive Method for Correcting the Reading of a Flow Meter in Pipe Flow Disturbed by Installation Effects.” Journal of Fluids Engineering - Transaction of the ASME 124: 650–656.
   Web of Science ®Google Scholar
• Witteveen, J.A.S., and H. Bijl. 2008. “Efficient Quantification of the Effect of Uncertainties in Advection-Diffusion Problems Using Polynomial Chaos.” Numerical Heat Transfer B 53: 437–465.
   Web of Science ®Google Scholar
• Xiu, D. 2009. “Fast Numerical Methods for Stochastic Computations: A Review.” Communications in Computational Physics 5: 242–272.
   Web of Science ®Google Scholar
• Xiu, D. 2010. Numerical Methods for Stochastic Computations: A Spectral Method Approach. Princeton, NJ: Princeton University Press.
   Google Scholar
• Xiu, D., and G.E. Karniadakis. 2002. “The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations.” SIAM 24: 1118–1139.
   Google Scholar
• Xiu, D., and G.E. Karniadakis. 2003. “Modeling Uncertainty in Flow Simulations Via Generalized Polynomial Chaos.” Journal of Computational Physics 187: 137–167.
   Web of Science ®Google Scholar
• Yeh, T.T., and G.E. Mattingly. 1994. “Pipeflow Downstream of a Reducer and its Effects on Flowmeters.” Flow Measurement and Instrumentation 5: 181–187.
   Web of Science ®Google Scholar
• Yeh, T.T., and G.E. Mattingly. 1995. Laser Doppler Velocimeter Studies of the Pipeflow Produced by a Generic Header. Technical Note 1409. National Institute of Standards and Technology.
   Google Scholar
• Yeh, T.T., and G.E. Mattingly. 1996. Flowmeter Installation Effects Due to A Generic Header. Technical Note 1419. National Institute of Standards and Technology.
   Google Scholar
• Zimmermann, H. 1999. “Examination of Disturbed Pipe Flow and its Effects on Flow Measurement Using Orifice Plates.” Flow Measurement and Instrumentation 10: 223–240.
   Web of Science ®Google Scholar