## “Modeling and Analysis of Fluid Flow through A Non-Prismatic Open Channel with Application to Drilling”Authors: Asanthi Jinasena, Ali Ghaderi and Roshan Sharma,
Affiliation: University of South-Eastern Norway
Reference: 2018, Vol 39, No 4, pp. 261-272. |

**Keywords:**model reduction, shallow water equation, return flow estimation, Bayesian sensitivity analysis, open channel

**Abstract:**This paper presents the development and validation of a simplified dynamic model of a Venturi channel. The existing dynamic models on open channels are based on the open channel flow principles, which are the shallow water equations. Although there are analytical solutions available for steady state analysis, the numerical solution of these partial differential equations is challenging for dynamic flow conditions. There are many complete and detailed models and numerical methods available for open channel flows, however, these are usually computationally heavy. Hence they are not suitable for online monitoring and control applications, where fast estimations are needed. The orthogonal collocation method could be used to reduce the order of the model and could lead to simple solutions. The orthogonal collocation method has been used in many chemical engineering applications. Further, this has been used in prismatic open channel flow problems for control purposes, but no literature is published about its use for non-prismatic channels as per the author's knowledge. The models for non-prismatic channels have more non-linearity which is interesting to study. Therefore, the possibility of using the collocation method for determining the dynamic flow rate of a non-prismatic open channel using the fluid level measurements is investigated in this paper. The reduced order model is validated by comparing the simulated test case results with a well-developed numerical scheme. Further, a Bayesian sensitivity analysis is discussed to see the effect of parameters on the output flow rate.

PDF (5573 Kb) DOI: 10.4173/mic.2018.4.3

**DOI forward links to this article:**

[1] Niels C. Bender, Torben Ole Andersen and Henrik C. Pedersen (2019), doi:10.4173/mic.2019.2.1 | |

[2] Asanthi Jinasena, Glenn-Ole Kaasa and Roshan Sharma (2019), doi:10.1109/JSEN.2019.2923854 | |

[3] Kenneth Olsvik, Morten Hansen Jondahl, Kjell Rune Toftevåg, Remi Kippersund, Geir Elseth and Ivar Kjøsnes (2019), doi:10.2118/195624-MS |

**References:**

[1] Bernstein, A., Chertock, A., and Kurganov, A. (2016). Bernstein, A, , Chertock, A., and Kurganov, A. Central-upwind scheme for shallow water equations with discontinuous bottom topography. Bulletin of the Brazilian Mathematical Society. 47(1):91--103. doi:10.1007/s00574-016-0124-3

[2] Bollermann, A., Chen, G., Kurganov, A., and Noelle, S. (2013). Bollermann, A, , Chen, G., Kurganov, A., and Noelle, S. A Well-Balanced Reconstruction of Wet/Dry Fronts for the Shallow Water Equations. Journal of Scientific Computing. 56(2):267--290. doi:10.1007/s10915-012-9677-5

[3] Chanson, H. (2004). Chanson, H, The Hydraulics of Open Channel Flow: An Introduction. Elsevier Butterworth-Heinemann, Burlington, 2nd edition. .

[4] Chaudhry, M.H. (2008). Chaudhry, M, H. Open-Channel Flow. Springer, New York, 2nd edition. .

[5] Chhantyal, K., Viumdal, H., Mylvaganam, S., and Elseth, G. (2016). Chhantyal, K, , Viumdal, H., Mylvaganam, S., and Elseth, G. Ultrasonic Level Sensors for Flowmetering of non- Newtonian Fluids in Open Venturi Channels: Using Data Fusion based on Artificial Neural Network and Support Vector Machines. In 2016 IEEE Sensors Applications Symposium (SAS). Catania, pages 1--6. doi:10.1109/SAS.2016.7479829

[6] Chow, V.T. (1959). Chow, V, T. Open-Channel Hydraulics. McGraw-Hill, New York. .

[7] Dulhoste, J.-F., Georges, D., and Besancon, G. (2004). Dulhoste, J, -F., Georges, D., and Besancon, G. Nonlinear Control of Open-Channel Water Flow Based on Collocation Control Model. Journal of Hydraulic Engineering. 130(3):254--266. doi:10.1061/(ASCE)0733-9429(2004)130:3(254)

[8] Georges, D., Dulhoste, J.-f., and Besancon, G. (2000). Georges, D, , Dulhoste, J.-f., and Besancon, G. Modelling and Control of Water Flow Dynamics via a Collocation Method. In Math. Theory of Networks and Systems. 2000. .

[9] Isaacson, E. and Keller, H.B. (1966). Isaacson, E, and Keller, H.B. Analysis of Numerical Methods. John Wiley & Sons, New York, 2nd edition. .

[10] Jinasena, A., Kaasa, G.-O., and Sharma, R. (2017). Jinasena, A, , Kaasa, G.-O., and Sharma, R. Use of Orthogonal Collocation Method for a Dynamic Model of the Flow in a Prismatic Open Channel : For Estimation Purposes. In Proceedings of the 58th Conference on Simulation and Modelling (SIMS 58), 138. Linkoping University Electronic Press, Linkopings universitet, Reykjavik, Iceland, pages 90--96. doi:10.3384/ecp1713890

[11] Kurganov, A. (2018). Kurganov, A, Finite-volume schemes for shallow-water equations. Acta Numerica. 27:289--351. doi:10.1017/S0962492918000028

[12] Kurganov, A. and Petrova, G. (2007). Kurganov, A, and Petrova, G. A second-order well-balanced positivity preserving central-upwind scheme for the Saint-Venant system. Communications in Mathematical Sciences. 5(1):133--160. doi:10.4310/CMS.2007.v5.n1.a6

[13] Layton, A.T. (2003). Layton, A, T. A Semi-Lagrangian Collocation Method for the Shallow Water Equations on the Sphere. SIAM Journal on Scientific Computing. 24(4):1433--1449. doi:10.1137/S1064827501395021

[14] Litrico, X. and Fromion, V. (2009). Litrico, X, and Fromion, V. Modeling and Control of Hydrosystems. Springer. .

[15] Pirir, I., Jinasena, A., and Sharma, R. (2017). Pirir, I, , Jinasena, A., and Sharma, R. Model based flow measurement using venturi flumes for return flow during drilling. Modeling, Identification and Control: A Norwegian Research Bulletin. 38(3):135--142. doi:10.4173/mic.2017.3.3

[16] Sivia, D. and Skilling, J. (2006). Sivia, D, and Skilling, J. Data Analysis: A Bayesian Tutorial. Data Analysis: A Bayesian Tutorial. OUP Oxford. .

[17] Tullis, B.P. (2012). Tullis, B, P. Hydraulic Loss Coefficients for Culverts: NCHRP REPORT 734. Technical report, National Cooperative Highway Research Program, Utah. .

**BibTeX:**

@article{MIC-2018-4-3,

title={{Modeling and Analysis of Fluid Flow through A Non-Prismatic Open Channel with Application to Drilling}},

author={Jinasena, Asanthi and Ghaderi, Ali and Sharma, Roshan},

journal={Modeling, Identification and Control},

volume={39},

number={4},

pages={261--272},

year={2018},

doi={10.4173/mic.2018.4.3},

publisher={Norwegian Society of Automatic Control}

};