A Water Level Sensor Design Using Finite Difference Solution and Its Coding in Matlab

Öz

Water level sensors are commonly used in industry. Some of the sensors are of capacitive nature. It is important to predict water level accurately. That’s why a good sensor model is needed. The finite difference (FD) method is a simple and commonly used numerical method to solve differential equations. In literature, to the best of our knowledge, the finite difference method has not been used to design such a capacitive sensor yet. In this study, the FD method is used to solve Laplace equation in two dimensions. The variation of the sensor capacitance is obtained as a function of water level. The calculation method given here can be used as a starting point for designing such and similar sensors.

Anahtar Kelimeler

• Water level Sensor design
• Finite Difference Method
• Capactive Sensor

Öz

Su seviye sensörleri endüstride yaygın olarak kullanılır. Bazı sensörler kapasitif niteliktedir. Su seviyesini doğru tahmin etmek önemlidir. Bu yüzden iyi bir sensör modeline ihtiyaç vardır. Sonlu farklar (SF) yöntemi, diferansiyel denklemleri çözmek için yaygın olarak kullanılan basit bir sayısal yöntemdir. Literatürde, bildiğimiz kadarıyla, sonlu farklar yöntemi henüz bir kapasitif sensör tasarımında kullanılmamıştır. Bu çalışmada, SF yöntemi Laplace denklemini iki boyutta çözmek için kullanılmıştır. Sensör kapasitansındaki değişim su seviyesinin bir fonksiyonu olarak elde edilmiştir. Burada verilen hesaplama yöntemi, bu ve benzeri sensörleri tasarlamak için bir başlangıç noktası olarak kullanılabilir.

Anahtar Kelimeler

• Su seviyesi Sensörü tasarımı
• Sonlu Farklar Yöntemi
• Kapasitif sensör

Kaynakça

1. Singh, Y., Raghuwanshi, S. K., & Kumar, S. (2019). Review on liquid-level measurement and level transmitter using conventional and optical techniques. IETE Technical Review, 36(4), 329-340.
2. Loizou, K., & Koutroulis, E. (2016). Water level sensing: State of the art review and performance evaluation of a low-cost measurement system. Measurement, 89, 204-214.
3. Popa, G. N., Popa, I., Diniş, C. M., & Iagăr, A. (2008, November). Resistive stepped transducer used for water level measurement. In Proceedings of the 1st WSEAS international conference on Sensors and signals (pp. 66-71). World Scientific and Engineering Academy and Society (WSEAS).
4. Yin, W., Peyton, A. J., Zysko, G., & Denno, R. (2008). Simultaneous noncontact measurement of water level and conductivity. IEEE Transactions on Instrumentation and Measurement, 57(11), 2665-2669.
5. Yoo, J., Jones, N. J., Flynn, K., & Jacobs, R. (2019, March). Performance of a water level sensor using magnetostrictive materials. In Sensors and Smart Structures Technologies for Civil, Mechanical, and Aerospace Systems 2019 (Vol. 10970, p. 109700K). International Society for Optics and Photonics.
6. Sophia S, FLOOD ALERTING SYSTEM THROUGH WATER LEVEL METER, International Research Journal of Engineering and Technology (IRJET), Volume: 05 Issue: 03, Mar-2018, 1123-1128.
7. Rizzolo, S., Périsse, J., Boukenter, A., Ouerdane, Y., Marin, E., Macé, J. R., ... & Girard, S. (2017). Real time monitoring of water level and temperature in storage fuel pools through optical fibre sensors. Scientific reports, 7(1), 8766.
8. A. Thomsen, B. Hansen, K. Schelde, “Application of TDR to water level measurement,” Journal of Hydrology, vol. 236, pp. 252–258, September 2000.

9. X. Yu, X. Yu, “Laboratory Evaluation of Time-Domain Reflectioery for Bidge Scour Measurement Comparison with the Ultrasonic Method,” Advances in Civil Engineering, vol. 2010, Article ID 508172, May 2010.
10. H. Canbolat, "A Novel Level Measurement Technique Using Three Capacitive Sensors for Liquids," in IEEE Transactions on Instrumentation and Measurement, vol. 58, pp. 3762–3768, Oct. 2009.
11. F.R.X. Li, G.C.M. Meijer, “Liquid-level measurement system based on a remote grounded capacitive sensor,” Sensors and Actuators A: Physical, vol. 138, pp. 1–8, July 2007.
12. Reitan, D. K. (1959). Accurate Determination of the Capacitance of Rectangular Parallel‐Plate Capacitors. Journal of Applied Physics, 30(2), 172-176.
13. Li, T. (2010). 3D capacitance extraction with the method of moments.
14. Taflove, A., & Hagness, S. C. (2005). Computational electromagnetics: the finite-difference time-domain method. Artech House, Norwood.
15. Sadiku, M. N. (2000). Numerical techniques in electromagnetics. CRC press.
16. Casulli, V., & Cheng, R. T. (1992). Semi‐implicit finite difference methods for three‐dimensional shallow water flow. International Journal for numerical methods in fluids, 15(6), 629-648.
17. Syed, Z., Choi, G., & Byeon, S. (2018). A numerical approach to predict water levels in ungauged regions—Case study of the meghna river estuary, Bangladesh. Water, 10(2), 110.
18. Dhamodaran, M., & Dhanasekaran, R. (2013, April). Comparison of capacitance computation by different methods. In 2013 International Conference on Communication and Signal Processing (pp. 73-77). IEEE.
19. K.P.S. Jayatilleke, Determination of the capacitance of rectangular parallel-plate capacitor using finite difference method, International Journal of Emerging Technology and Research, Volume 1, Issue 3, Mar-Apr, 2014.