An Adaptively-damped Compressible-liquid Model for Non-cavitating Hydraulic Surges

Document Type : Original Article

Authors

Department of Aerospace Engineering, Indian Institute of Space Science and Technology, Thiruvananthapuram, Kerala, India

Abstract

This research presents a compact and computationally-efficient two-equation compressible-liquid model. The model is specifically developed for the numerical computation of hydraulic surges in pipes under high fluid pressure where cavitation is absent. The proposed model aims to simplify the three-equation model of Neuhaus et al. for two-phase cavitational hammers. Compressible effects in liquid during the transients are considered by including a suitable equation of state into the model. A tunable function of the relative local pressure fluctuation called 'Variable Friction Coefficient' (VFC) for the flow transients is also incorporated into the model. For the accurate modeling of wave propagation, the split-coefficient matrix (SCM) method for characteristic-direction based splitting of eigenvalues is used in the study. The results show that the proposed two-equation model can reproduce the results from the three-equation model at a substantially reduced computational cost. The integration of the variable friction coefficient into the two-equation compressible-liquid model further improved the solver capability.  The results computed using this aggregate solver are superior to the original three-equation model and the two-equation model without VFC. The results also suggest that the variable friction coefficient imparts adaptive damping capability to the solver model. This feature of the model is visible in the improved accuracy in the modeling of decaying pressure waves. The aggregate solver model, i.e., `the variable friction coefficient integrated two-equation compressible-liquid model,' offers a greatly simplified mathematical model and an inexpensive computational solver for the simulation of hydraulic surges in non -cavitating flow transients.

Keywords


Bergant, A., Tijsseling, A.S., Vítkovský, J.P., Covas, D.I.C., Simpson, A.R. and Lambert, M.F., "Parameters affecting water-hammer wave attenuation, shape and timing-part 1: Mathematical tools", Journal of Hydraulic Research,  Vol. 46, No. 3, (2008), 373-381. doi: 10.3826/jhr.2008.2848
Khudayarov, B., Turaev, F. “Mathematical simulation of nonlinear oscillations of viscoelastic pipelines conveying fluid”. Applied Mathematical Modelling, Vol. 66, (2019), 662-679. doi: https://doi.org/10.1016/j.apm.2018.10.008
Skulovich, O., Perelman, L., Ostfeld, A. “Modeling and optimizing hydraulic transients in water distribution systems”. Procedia Engineering, Vol. 70, (2014), 1558-1565. doi: https://doi.org/10.1016/j.proeng.2014.02.172
Moghaddam, M. A. "Analysis and design of a simple surge tank." International Journal of Engineering Transactions A, Vol. 17, No. 4, (2004), 339. doi: http://www.ije.ir/article_71544.html
Zamani, J., M. A. Samimi, F. Sardarzadeh, and M. H. Ghezelayagh. "An Optical Measurement System to Measure Velocity and Provide Shock Wave Pressure Diagrams.", International Journal of Engineering, Vol. 33, No. 3, (2020), 505-512. doi: 10.5829/ije.2020.33.03c.15
Yamini, O. A., Kavianpour, M. R., Mousavi, S. H., Movahedi, A., and Bavandpour, M. "Experimental investigation of pressure fluctuation on the bed of compound flip buckets." ISH Journal of Hydraulic Engineering, Vol. 24, No. 1, (2018), 45-52. doi: https://doi.org/10.1080/09715010.2017.1344572
Yamini, O. A., Kavianpour, M. R., and Movahedi, A. “Pressure Distribution on the Bed of the Compound Flip Buckets.” The Journal of Computational Multiphase Flows, Vol. 7, No. 3, (2015), 181–94. doi:10.1260/1757-482X.7.3.181.
Fadaei-Kermani, E., Barani, G. A.,  and Ghaeini-Hessaroeyeh, M. "Numerical Detection of Cavitation Damage on Dam Spillway." Civil Engineering Journal, Vol. 2, No. 9, (2016), 484-490. doi: 10.28991/cej-2016-00000051
Nikitin, E., Shumatbaev, G., Terenzhev, D., Sinyashin, K., and Rastergaev, E. "New Sintanyl Phosphonates for Protection of Oil and Gas Pipelines from Steel Corrosion." Civil Engineering Journal Vol. 5, No. 4 (2019), 789-795. doi: 10.28991/cej-2019-03091288
Sadafi, M., Riasi, A., Nourbakhsh, S.A. “Cavitating flow during water hammer using a generalized interface vaporous cavitation model”. Journal of Fluids and Structures, Vol. 34, (2012), 190-201. doi: https://doi.org/10.1016/j.jfluidstructs.2012.05.014
Pinho, J., Lema, M., Rambaud, P., Steelant, J. “Multiphase investigation of water hammer phenomenon using the full cavitation model”. Journal of Propulsion and Power, Vol. 30, No. 1, (2014), 105-113. doi: https://doi.org/10.2514/1.B34833
Hadj-Taieb, L., Hadj-Taieb, E. “Numerical simulation of transient flows in viscoelastic pipes with vapour cavitation”. International Journal of Modelling and Simulation, Vol. 29, No. 2, (2009), 206-213. doi: https://doi.org/10.1080/02286203.2009.11442526
Neuhaus, T., Dudlik, A. “Experiments and comparing calculations on thermohydraulic pressure surges in pipes”. Kerntechnik, Vol. 71, No. 3, (2006), 87-94. doi: 10.3139/124.100280
Chandran, R. J., Salih, A. “A modified equation of state for water for a wide range of pressure and the concept of water shock tube”. Fluid Phase Equilibria, Vol. 483, (2019), 182-188. doi: https://doi.org/10.1016/j.fluid.201811.032
Neuhaus, T., Dudlik, A., Tijsseling, A.S. “Experiments and corresponding calculations on thermohydraulic pressure surges in pipes”. CASA-report 545. (2005). url: https://research.tue.nl/files/2312420/602216.pdf
Chakravarthy, S., Anderson, D., Salas, M. “The split coefficient matrix method for hyperbolic systems of gasdynamic equations”. In: 18th Aerospace Sciences Meeting. (1980), 268. doi: https://doi.org/10.2514/6.1980-268
Wang, Z., Su, G., Qiu, S., Tian, W. “Preliminary study on split coefficient matrix method for two-phase flow equation solving”. Atomic Energy Science and Technology, Vol. 49, No. 6, (2015), 1045-1050. Retrieved     from: http://inis.iaea.org/search/search.aspx?orig_q=RN:48072547
Zhang, T., Tan, Z., Zhang, H., Fan, J., Yang, Z. “Axial coupled response characteristics of a fluid-conveying pipeline based on split-coefficient matrix finite difference method”. Zhendong yu Chongji/Journal of Vibration and Shock, Vol. 37, (2018), 148-154. doi: 10.13465/j.cnki.jvs.2018.05.022.
Pezzinga, G., Ghidaoui, M.S., Axworthy, D.H., Zhao, M., McInnis, D.A. “Extended thermodynamics derivation of energy dissipation in unsteady pipe flow”. Journal of Hydraulic Engineering, Vol. 127, No. 10, (2001), 888-890. doi: https://doi.org/10.1061/(ASCE)0733-9429(2001)127:10(888)
Ghidaoui, M.S., Mansour, S. “Efficient treatment of the vardy-brown unsteady shear in pipe transients”. Journal of Hydraulic Engineering, Vol. 128, No. 1, (2002), 102-112. doi: https://doi.org/10.1061/(ASCE)0733-9429(2002)128:1(102)
Daily, J., Hankey Jr, W., Olive, R., Jordaan Jr, J. “Resistance coefficients for accelerated and decelerated flows through smooth tubes and orifices”. Tech. Rep.; Massachusetts Inst of Tech Cambridge. (1955). url: https://apps.dtic.mil/dtic/tr/fulltext/u2/a280851.pdf
Ghidaoui, M.S., Zhao, M., McInnis, D.A., Axworthy, D.H. “A Review of Water Hammer Theory and Practice”. Applied Mechanics Reviews, Vol. 58, No. 1, (2005), 49-76. doi: https://doi.org/10.1115/1.1828050
Nosrati, K., Tahershamsi, A., and Taheri, S. H. S. "Numerical Analysis of Energy Loss Coefficient in Pipe Contraction Using ANSYS CFX Software." Civil Engineering Journal Vol. 3, No. 4 (2017): 288-300. doi: 10.28991/cej-2017-00000091
Axworthy, D.H., Ghidaoui, M.S., McInnis, D.A. “Extended thermodynamics derivation of energy dissipation in unsteady pipe flow.” Journal of Hydraulic Engineering, Vol. 126, No. 4, (2000): 276-287. doi: https://doi.org/10.1061/(ASCE)0733-9429(2000)126:4(276)
Ghidaoui, M. S. “On the fundamental equations of water hammer”. Urban Water Journal, Vol. 1, No. 2, (2004), 71-83. doi: https://doi.org/10.1080/15730620412331290001
Wahba, E. “Modelling the attenuation of laminar fluid transients in piping systems”. Applied Mathematical Modelling, Vol. 32, No. 12, (2008), 2863-2871. doi: https://doi.org/10.1016/j.apm.2007.10.004
Toro, E. “Riemann Solvers and Numerical Methods for Fluid Dynamics: A Practical Introduction”. Springer Berlin Heidelberg; (2013). ISBN 9783662039151. doi: 10.1007/b79761
Peng, J., Zhai, C., Ni, G., Yong, H., Shen, Y. “An adaptive characteristic-wise reconstruction weno-z scheme for gas dynamic euler equations”. Computers & Fluids, Vol. 179, (2019), 34-51. doi: https://doi.org/10.1016/j.compfluid.2018.08.008.19