# Application of Fibonacci Sequence and Lucas Sequence on the Design of the Toilet Siphon Pipe Shape

## Authors

• Xiaole Ge College of Mechanical & Electronic Engineering, Huangshan University, Huangshan, Anhui, 245041,
• Hongfeng Wang College of Mechanical & Electronic Engineering, Huangshan University, Huangshan, Anhui, 245041,
• Shengrong Liu College of Mechanical & Electronic Engineering, Huangshan University, Huangshan, Anhui, 245041,
• Zhanfu Li School of Mechanical & Automobile Engineering, Fujian University of Technology, Fuzhou, Fujian, 350118
• Xin Tong School of Mechanical & Automobile Engineering, Fujian University of Technology, Fuzhou, Fujian, 350118
• Jiafei Pu College of Mechanical & Electronic Engineering, Huangshan University, Huangshan, Anhui, 245041

## Keywords:

computational fluid dynamic, Fibonacci sequence, flushing performance, Lucas sequence, siphon pipe shape

## Abstract

The purpose of this study was to explore the method for designing the toilet siphon pipe shape to improve flushing performance. The Fibonacci sequence and the Lucas sequence were used to design the structural parameters of the siphon pipe. The flushing processes of the toilet were simulated using the computational fluid dynamics (CFD) method to analyze the flushing performance under different siphon pipe shapes. Experimental studies were conducted to verify the reliability of the simulation results. The results indicated that when the Lucas numbers and the Fibonacci numbers were utilized to regulate the curvature of the siphon pipe in the Xi direction and the Yj direction respectively, the flushing performance of the toilet was optimal. In order to obtain better flushing performance, the curvature of the siphon pipe should be smooth and have obvious transitions at the connections of different sections. When the overall size of the siphon pipe is kept constant, a short siphon pipe length is helpful for the improvement of toilet flushing performance.

## References

An, I.Y., Lee, Y.L., Jung, E.D. & Cho, W.S., A Study on Performance Optimization of a Toilet by Measuring Accumulated Flow Rate of a Trapway, Journal of Mechanical Science and Technology, 28(4), pp. 1319-1326, 2014.

Cheng, W.S., Lee, R.T., Liu, C.H. & Hsia, C.W., A Study on Evacuation Performance of Siphon-Type Water Closets, The 10th Asian International Conference on Fluid Machinery, 1225, pp. 75-80, 2010.

Zhao, S.Y., Liu, Z.J. & Peng, Z.W., Optimized Design of Toilet Siphon Pipeline Based on Fluent and Its Validated Test, Journal of System Simulation, 20(16), pp. 4412-4416, 2008. (Text in Chinese and Abstract in English).

An, I.Y., Lee, Y.L. & Kim, J.H., A Study of the Characteristics of a Super Water-saving Toilet with Flexible Trapway by Measuring Accumulated Flow Rate, Journal of Mechanical Science and Technology, 28(8), pp. 3067-3074, 2014.

Cheng, W.S. & Jhang, C.Y., Velocity Measurement and Flow Field Simulation of a Sit-Type Water Closet, The 4th International Meeting of Advances in Thermofluids, 1440(1), pp. 1068-1077, 2012.

Wang, Y.H., Xiu, G.J. & Tan, H.S., CAD and CAE Analysis for Siphon Jet Toilet, Physics Procedia, 19(1), pp. 472-476, 2011.

Peng, Z.W., Liu, Z.J. & Huang, D.L., Study of Water Saving and Wastewater Minimization Technology Based on Computational Fluid Dynamics, Technology of Water Treatment, 35(8), pp. 72-75, 2009. (Text in Chinese and Abstract in English)

Pan, X.T., Sun, Y.S., Zhan, J.M. & Li, J., The Determinant Method of Ceramic Sanitary Ware Forming Siphon Phenomenon Based on VOF Model, Acta Scientiarum Naturalium Universitatis Sunyatseni, 46(4), pp. 36-40, 2007. (Text in Chinese and Abstract in English)

Li, Z.F. & Tong, X., Applications of the Discrete Element Method and Fibonacci Sequence on a Banana Screen, Journal of Engineering, Design and Technology, 15(1), pp. 2-12, 2017.

Tashtoush, Y., Darwish, O. & Hayajneh, M., Fibonacci Sequence Based Multipath Load Balancing Approach for Mobile Ad Hoc Networks, Ad Hoc Networks, 16, pp. 237-246, 2014.

Adam, M., Assimakis, N. & Farina, A., Golden Section, Fibonacci Sequence and the Time Invariant Kalman and Lainiotis Filters, Applied Mathematics and Computation, 250, pp. 817-831, 2015.

Livio, M., The Golden Ratio: The Story of Phi, The World's Most Astonishing Number, Broadway Books, 2002.

Liu, F.M. & Pan, X.T., Three-phase Flow Analysis for Siphon Jet Toilet Based on VOF Model, China Ceramics, 47(11), pp. 69-72, 2011. (Text in Chinese and Abstract in English).

Xiu, G.J., Three-dimensional Flow Numerical Simulation and Rapid Manufacturing for Toilet Based on RE, Master Dissertation, School of Mechanical and Automobile Engineering, South China University of Technology, Guangzhou, 2011. (Text in Chinese and Abstract in English)

Zhai, L.X., Wu, J.Q., Zhan, Y. & Zhang, L., Flow Characteristic and Analysis of Closet Pan Outfall, Water & Wastewater Engineering, 40(5), pp. 78-81, 2014. (Text in Chinese and Abstract in English).

2019-08-31

## How to Cite

Ge, X., Wang, H., Liu, S., Li, Z., Tong, X., & Pu, J. (2019). Application of Fibonacci Sequence and Lucas Sequence on the Design of the Toilet Siphon Pipe Shape. Journal of Engineering and Technological Sciences, 51(4), 463-478. https://doi.org/10.5614/j.eng.technol.sci.2019.51.4.2

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