Drag reduction in a gravity-driven flow system using polyethylene oxide solutions

Modeling Earth Systems and Environment - Tập 9 - Trang 957-966 - 2022
Yennam Rajesh1, Lakshmana Rao Jeeru2
1Department of Chemical Engineering, K. K. Wagh I. E. E. and R Nasik (MS), Affiliated to S. P. Pune University, Pune, India
2School of Petroleum Technology, Pandit Deendayal Energy University, Gandhinagar, India

Tóm tắt

The current study describes the use of a mathematical formula based on macro-scale balances to calculate the efflux time for gravity draining a Newtonian liquid from a large conical tank through an exit pipe at the bottom of the tank when the flow in the pipe line is turbulent. The least amount of time required to drain the tank will be calculated using the efflux time equation, which has been modified using experimental data. When the flow is mixed, that is, partially laminar and partially turbulent, gravity-driven, and once through the system, the percentage reduction in efflux time that the addition of water-soluble polyethylene oxide polymer has on drag reduction is displayed. Therefore, the efflux time equation provides the shortest amount of time needed to acquire the liquid draining from the tank.

Tài liệu tham khảo

Agulilar G, Gaslijevic K, Mathys EF (2006) Reduction of friction in fluid transport: experimental investigation. Revista Mexiciana De Fisca 52:444. https://www.redalyc.org/pdf/570/57065310.pdf Choi KS, Yang X, Calyton BR, Glover EJ, Alatar M, Semenov BN, Kulik VM (1997) Turbulent drag reduction using complaint surfaces. Proc R Soc Lond 453:2229. https://doi.org/10.1098/rspa.1997.0119 David BV, Roche ECJ (1999) Efflux time from tanks with exit pipes and fittings. Int J Eng Ed 5(3): 206–212. https://www.ijee.ie/articles/Vol15-3/ijee1051.pdf Joye DD, Barret BC (2003) The tank draining problem revisited: do these equations actually work. Can J Chem Eng 81:1052–1057. https://doi.org/10.1002/cjce.5450810516 Drappie J, Divoux T, Amarouchene Y, Yertrand F, Rodts S, Cadot O (2006) Turbulent drag reduction by surfactants. Europhys Lett J 74(2):362–368. https://doi.org/10.1209/epl/i2005-10519-x Fortuna G, Hanratty TJ (1972) The influence of drag-reducing polymers on turbulence in the viscous sublayer. J Fluid Mech 53:575–586. https://doi.org/10.1017/S0022112072000321 Hart PW, Sommerfeld JT (1995) Expressions for gravity drainage of annular and Toroidal containers. Process Saf Prog 14(4):238–243. https://doi.org/10.1002/prs.680140406 Henoch C, Krupenkin TN, Olonder PK, Taylor JA, Hodes MS, Lyons AM, Peguero C, Breuer K (2006) Turbulent drag reduction using super hydrophobic surfaces. In: 3rd AIAA Flow Conference. San Francisco, pp 1–5. https://doi.org/10.2514/6.2006-3192 Jones WM, Moddock JL (1969) Relaxation effects in the flow of dilute polymer solutions through tubes of granular beds. Br J App Phys (J. PhyD) 2(2):797–808. https://iopscience.iop.org/article/10.1088/0022-3727/2/6/304/pdf Jurban BA, Zurigat YH, Al-shukri MS, Al-Busaidim HH (2006) The use of drag reduction agent and a detergent for drag reduction in a circulatory vertical flow. Poly Plast Tech Eng 45:533. https://doi.org/10.1080/03602550600554083 Kostic M (1994) The ultimate asymptote and possible causes of friction drag and heat transfer reduction phenomena. J Energy HMT. 16:1–14. https://www.researchgate.net/publication/251516715_The_Ultimate_Asymptotes_and_Possible_Causes_of_Friction_Drag_and_Heat_Transfer_Reduction_Phenomena Li FC, Kawaguchi Y, Yu B, Wei JJ, Hishida K (2008) Experimental study of drag reduction mechanism for a dilute surfactant solution flow. Int J Heat Mass Transf 51:835–843. https://doi.org/10.1016/j.ijheatmasstransfer.2007.04.048 MohamedAS BAD, Konstantin M (2021) Particle subgrid scale modeling in hybrid RANS/LES of turbulent channel flow at low to moderate Reynolds number. Powder Techno. https://doi.org/10.1016/j.powtec.2021.11.057 Paschkewitz JS, Dubief YVES, Dimitropoulos CD, Shaqfeh ESG, Moin P (2004) Numerical simulation of turbulent drag reduction using rigid fibers. J Fluid Mech 518:281–317. https://doi.org/10.1017/S0022112004001144 Peet Y, Sagaut P (2008) Turbulent drag reduction using sinusoidal riblets with triangular cross section. In: 38th AIAA Fluid Dynamics Conference and Exhibit, June 23–26 Seattle, WA. https://doi.org/10.2514/6.2008-3745 Reischman MM, Tiederman WG (1975) Laser doppler anemometer measurement in drag-reducing channel flows. J Fluid Mech 70:369–392 Snelling D (2006) Surfactant drag reduction using mixed counter ions, thesis submitted to Department of Chemical Engineering. The Ohio State University. Sommerfeld JT, Stallybrass MP (1992) Elliptical Integral solutions for drainage of horizontal cylindrical vessels with piping friction. Ind Eng Chem Res 31:743–746. https://doi.org/10.1021/ie00003a015 Subbarao ChV (2011) Comparison of efflux time between cylindrical and conical tanks through an exit pipe. Int J Appl Sci Eng 9: 33. https://gigvvy.com/journals/ijase/articles/ijase-201104-9-1-033.pdf Subbarao ChV, Divya P, Naidu DA, King P (2013) Drag reduction by anionic surfactant solutions in gravity driven flow system. Iran J Chem Chem Eng 32(1): 95–101. https://doi.org/10.30492/ijcce.2013.5909 Toonder JMJ (1995) Drag reduction by polymer additives in turbulent pipe flow, Ph.D Thesis, submitted to Delft University of Technology Viachogiannis M, Hanratty TJ (2003) Influence of wavy structure and large scale polymer structures on drag reduction. Experim Fluids 36: 685–700. https://ui.adsabs.harvard.edu/link_gateway/2004ExFl36685V/doi:10.1007/s00348-003-0745-3 Virk PS (1975) Drag reduction fundamentals. AIChE J 21:625–653. https://doi.org/10.1002/aic.690210402 Vov LVS, Pomyalov A, Procaccia I, Tiberkevich V (2005) Drag reduction by micro-bubbles-the limit of minute bubbles. Phys Rev Lett 94:174502-1–174502-5. https://doi.org/10.1103/PhysRevLett.94.174502 Wang Y, Yu B, Zakin LJ, Shi H (2011) Review on Drag Reduction and Its Heat. Add Adv Mech Eng. https://doi.org/10.1155/2011/478749 Xi L (2019) Turbulent drag reduction by polymer additives: Fundamentals and recent advances. Phys Fluids 31:121302. https://doi.org/10.1063/1.5129619