Library Subscription: Guest
International Journal for Uncertainty Quantification

Published 6 issues per year

ISSN Print: 2152-5080

ISSN Online: 2152-5099

The Impact Factor measures the average number of citations received in a particular year by papers published in the journal during the two preceding years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) IF: 1.7 To calculate the five year Impact Factor, citations are counted in 2017 to the previous five years and divided by the source items published in the previous five years. 2017 Journal Citation Reports (Clarivate Analytics, 2018) 5-Year IF: 1.9 The Immediacy Index is the average number of times an article is cited in the year it is published. The journal Immediacy Index indicates how quickly articles in a journal are cited. Immediacy Index: 0.5 The Eigenfactor score, developed by Jevin West and Carl Bergstrom at the University of Washington, is a rating of the total importance of a scientific journal. Journals are rated according to the number of incoming citations, with citations from highly ranked journals weighted to make a larger contribution to the eigenfactor than those from poorly ranked journals. Eigenfactor: 0.0007 The Journal Citation Indicator (JCI) is a single measurement of the field-normalized citation impact of journals in the Web of Science Core Collection across disciplines. The key words here are that the metric is normalized and cross-disciplinary. JCI: 0.5 SJR: 0.584 SNIP: 0.676 CiteScore™:: 3 H-Index: 25

Indexed in

CLOSURE LAW MODEL UNCERTAINTY QUANTIFICATION

Volume 12, Issue 3, 2022, pp. 31-48
DOI: 10.1615/Int.J.UncertaintyQuantification.2021037714
Get accessGet access

ABSTRACT

The prediction uncertainty in simulators for industrial processes is due to uncertainties in the input variables and uncertainties in specification of the models, in particular the closure laws. In this work, the uncertainty in each closure law was modeled as a random variable and the parameters of its distribution were optimized to correctly quantify the uncertainty in predictions. We have developed two methods for optimization, based on the integrated quadratic distance and the energy score. The proposed methods were applied to the commercial multiphase flow simulator LedaFlow with the liquid volume fraction and pressure gradient as output variables. Two datasets were analyzed. Both describe two-phase gas-liquid flow, but are otherwise fundamentally different. One is gas-dominated stratified/annular flow and the other is liquid-dominated slug flow. The closure law for the gas-wall friction factor is decisive for the gas-dominated predictions, and the estimated relative standard deviation is 4.5% or 8.0% depending on method. The liquid-dominated study showed that the liquid-wall friction factor and the slug bubble velocity are the closure laws with the greatest impact. Moreover, the estimated relative standard deviation in the liquid-wall friction factor is 5%, and the deviation in the slug bubble velocity is 4%. We used direct measurements of the slug bubble velocity to validate the estimated uncertainty.

REFERENCES
  1. Ohm, G.S., The Galvanic Circuit Investigated Mathematically, New York: D. VanNostrand Company, 1905.

  2. Drude, P., Zur Elektronentheorie Der Metalle, Ann. Phys, 306(3):566-613,1900.

  3. Clapeyron, E., Memoire Sur La Puissance Motrice De La Chaleur, J. Ec. Polytech., 14:153-190, 1834.

  4. Darcy, H., Les Fontaines Publiques de la Ville de Dijon: Exposition et Application des Principes a Suivre et des Formules a Employer dans les Questions de Distribution d'Eau, Paris: Victor Dalmont, 1856.

  5. Bejan, A., Convection Heat Transfer, New York: John Wiley & Sons, 2013.

  6. Brennen, C.E. and Brennen, C.E., Fundamentals of Multiphase Flow, Cambridge, UK: Cambridge University Press, 2005.

  7. Boyack, B., Catton, I., Duffey, R., Griffith, P., Katsma, K., Lellouche, G., Levy, S., Rohatgi, U., Wilson, G., Wulff, W., and Zuber, N., Quantifying Reactor Safety Margins. Part 1: An Overview of the Code Scaling, Applicability, and Uncertainty Evaluation Methodology, Nucl. Eng. Des, 119(1):1-15,1990.

  8. Wilson, G.E., Boyack, B., Catton, I., Duffey, R., Griffith, P., Katsma, K.R., Lellouche, G.S., Levy, S., Rohatgi, U.S., Wulff, W., and Zuber, N., Quantifying Reactor Safety Margins. Part 2: Characterization of Important Contributors to Uncertainty, Nucl. Eng. Des, 119(1):17-31, 1990.

  9. Wulff, W., Boyack, B., Catton, I., Duffey, R., Griffith, P., Katsma, K., Lellouche, G.S., Levy, S., Rohatgi, U.S., Wilson, G.E., and Zuber, N., Quantifying Reactor Safety Margins. Part 3: Assessment and Ranging of Parameters, Nucl. Eng. Des, 119(1):33-65, 1990.

  10. Lellouche, G., Levy, S., Boyack, B.E., Catton, I., Duffy, R., Griffith, P., Katsma, K., May, R., Rohatgi, U., Wilson, G., Wulff, W., and Zuber, N., Quantifying Reactor Safety Margins. Part 4: Uncertainty Evaluation of Lbloca Analysis Based on TRAC-PF1/MOD 1, Nucl. Eng. Des, 119(1):67-95, 1990.

  11. Zuber, N., Wilson, G.E., Boyack, B.E., Catton, I., Duffey, R.B., Griffith, P., Katsma, K.R., Lellouche, G.S., Levy, S., Rohatgi, U.S., and Wulff, W., Quantifying Reactor Safety Margins. Part 5: Evaluation of Scale-Up Capabilities of Best Estimate Codes, Nucl. Eng. Des., 119(1):97-107, 1990.

  12. Catton, I., Duffey, R., Shaw, R., Boyack, B., Griffith, P., Katsma, K., Lellouche, G.S., Levy, S., Rohatgi, U.S., Wilson, G.E., Wulff, W., and Zuber, N., Quantifying Reactor Safety Margins. Part 6: A Physically Based Method of Estimating PWR Large Break Loss of Coolant Accident PCT, Nucl. Eng. Des, 119(1):109-117, 1990.

  13. Shaw, R.A., Larson, T.K., and Dimenna, R.K., Development of a Phenomena Identification and Ranking Table (PIRT) for Thermal-Hydraulic Phenomena during a PWR LBLOCA, Tech. Rep. NUREG/CR-5074, Idaho National Engineering Lab, 1988.

  14. Wulff, W., Uncertainties in Modeling and Scaling in the Prediction of Fuel Stored Energy and Thermal Response, Tech. Rep. BNL-NUREG-40498, Brookhaven National Lab, 1987.

  15. Cremaschi, S., Kouba, G.E., and Subramani, H.J., Characterization of Confidence in Multiphase Flow Predictions, Energy Fuels, 26(7):4034-4045, 2012.

  16. Picchi, D. andPoesio, P., Uncertainty Quantification and Global Sensitivity Analysis of Mechanistic One-Dimensional Models and Flow Pattern Transition Boundaries Predictions for Two-Phase Pipe Flows, Int. J. Multiphase Flow, 90:64-78,2017.

  17. Strand, A., Smith, I.E., Unander, T.E., Steinsland, I., and Hellevik, L.R., Uncertainty Propagation through a Point Model for Steady-State Two-Phase Pipe Flow, Algorithms, 13(3):53, 2020.

  18. Holm, H., Saha, P., Suleymanov, V., Vanvik, T., and Hoyer, N., Shtokman Flow Assurance Challenges-A Systematic Approach to Analyze Uncertainties-Part 1, Proc. of the 15th Int. Conf. on Multiphase Production Technology, Cannes, France, BHR Group, pp. 173-189,2011.

  19. Holm, H., Saha, P., Suleymanov, V., Vanvik, T., and Hoyer, N., Shtokman Flow Assurance Challenges-A Systematic Approach to Analyze Uncertainties-Part 2, Proc. of the 15th Int. Conf. on Multiphase Production Technology, Cannes, France, BHR Group, pp. 191-206, 2011.

  20. Hoyer, N., Kirkedelen, M., Biberg, D., Johnson, G., Valle, A., Johansson, P., and Nossen, J., A Structured Approach for the Evaluation of Uncertainties in Flow Assurance Systems, Proc. of the 16th Int. Conf. on Multiphase Production Technology, Cannes, France, BHR Group, pp. 77-91, 2013.

  21. Wang, J., Wu, J.L., and Xiao, H., Incorporating Prior Knowledge for Quantifying and Reducing Model-Form Uncertainty in RANS Simulations, Int. J. Uncertainty Quantif, 6(2):109-126, 2016.

  22. Xiao, H. and Cinnella, P., Quantification of Model Uncertainty in RANS Simulations: A Review, Prog. Aerospace Sci., 108:1-31,2019.

  23. Beck, J.L., Bayesian System Identification Based on Probability Logic, Struct. Control Health Monit., 17(7):825-847, 2010.

  24. Beck, J.L. and Taflanidis, A., Prior and Posterior Robust Stochastic Predictions for Dynamical Systems Using Probability Logic, Int. J. Uncertainty Quantif, 3(4):271-288, 2013.

  25. Oliver, T.A., Terejanu, G., Simmons, C.S., and Moser, R.D., Validating Predictions of Unobserved Quantities, Comput. Methods Appl. Mech. Eng., 283:1310-1335,2015.

  26. Thorarinsdottir, T.L., Gneiting, T., and Gissibl, N., Using Proper Divergence Functions to Evaluate Climate Models, SIAM/ASAJ Uncertainty Quantif., 1(1):522-534, 2013.

  27. Gneiting, T., Stanberry, L.I., Grimit, E.P., Held, L., and Johnson, N.A., Assessing Probabilistic Forecasts of Multivariate Quantities, with an Application to Ensemble Predictions of Surface Winds, Test, 17(2):211-235, 2008.

  28. Gneiting, T. and Raftery, A.E., Strictly Proper Scoring Rules, Prediction, and Estimation, J. Am. Stat. Assoc., 102(477):359-378, 2007.

  29. Moller, A., Lenkoski, A., and Thorarinsdottir, T.L., Multivariate Probabilistic Forecasting Using Ensemble Bayesian Model Averaging and Copulas, Q. J. R. Meteorol. Soc., 139(673):982-991, 2013.

  30. Kjelaas, J., De Leebeeck, A., and Johansen, S., Simulation of Hydrodynamic Slug Flow Using the LedaFlow Slug Capturing Model, Proc. of the 16th Int. Conf. on Multiphase Production Technology, Cannes, France, BHR Group, 2013.

  31. Smith, I.E., Nossen, J., Kjelaas, J., and Lund, B., Development of a Steady-State Point Model for Prediction of Gas/Oil and Water/Oil Pipe Flow, J. Dispersion Sci. Technol, 36(10):1394-1406, 2015.

  32. Kjelaas, J., Unander, T.E., Wolden, M., Schumann, H., Leinan, P.R., Smith, I.E., and Shmueli, A., Large Scale Experiments on Slug Length Evolution in Long Pipes, OTC Offshore Technol. Conf, Houston, TX, 2020.

  33. Paudel, D. and Hostikka, S., Propagation of Modeling Uncertainty in Stochastic Heat-Transfer Simulation Using a Chain of Deterministic Models, Int. j. Uncertainty Quantif., 9(1):1-14, 2019.

  34. Farokhpoor, R., Liu, L., Langsholt, M., Hald, K., Amundsen, J., and Lawrence, C., Dimensional Analysis and Scaling in Two-Phase Gas-Liquid Stratified Pipe Flow-Methodology Evaluation, Int. J. Multiphase Flow, 122:103139, 2020.

Begell Digital Portal Begell Digital Library eBooks Journals References & Proceedings Research Collections Prices and Subscription Policies Begell House Contact Us Language English 中文 Русский Português German French Spain