MODELLING OF ORIFICE FLOW RATE AT VERY SMALL OPENINGS

Authors

  • Duqiang Wu Department of Mechanical Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, Saskatchewan, Canada, S7N 5A9
  • Richard Burton Department of Mechanical Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, Saskatchewan, Canada, S7N 5A9
  • Greg Schoenau Department of Mechanical Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, Saskatchewan, Canada, S7N 5A9
  • Doug Bitner Department of Mechanical Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, Saskatchewan, Canada, S7N 5A9

Keywords:

pilot valve, flow control, orifice, flow rate equation, discharge coefficient, Reynolds number

Abstract

Modelling hydraulic control systems that contain flow modulation valves is highly influenced by the accuracy of the equation describing flow through an orifice. Classically, the basic orifice flow equation is expressed as the product of cross-sectional area, the square root of the pressure drop across the orifice and a “flow discharge coefficient”, which is often assumed constant. However, at small Reynolds numbers (such the case of valve pilot stage orifices), the discharge coefficient of the flow equation is not constant. Further, the relationship between the flow cross-sectional area and the orifice opening are extremely complex due to clearances, chamfers, and other factors as a result of machining limita-tions. In this work, a novel modification to the flow cross-sectional area is introduced and the resulting closed form of the flow equation is presented. As a secondary benefit, an analytical form of the orifice flow gain and flow pressure coefficient can be obtained. This closed form equation greatly facilitates the transient and steady state analysis of low flow regions at small or null point operating regions of spool valve.

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Author Biographies

Duqiang Wu, Department of Mechanical Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, Saskatchewan, Canada, S7N 5A9

Duqiang Wu Graduate student for Ph.D. at present, Mechanical Engineering Department, University of Saskatchewan in Canada. Master (1984) at Nanjing University of science and Technology in China. Engi-neer (1986) at Shaanxi Mechanical and Electrical Institute in China. Visiting Scholar (1997) at University of Illinois at Urbana-Champaign.

Richard Burton, Department of Mechanical Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, Saskatchewan, Canada, S7N 5A9

Richard Burton P.Eng, Ph.D, Assistant Dean of the col-lege of Engineering, Professor, Mechani-cal Engineering, University of Saskatch-ewan. Burton is involved in research pertaining to the application of intelligent theories to control and monitoring of hydraulics systems, component design, and system analysis. He is a member of the executive of ASME, FPST Division, a member of the hydraulics' advisory board of SAE and NCFP and a convenor for FPNI.

Greg Schoenau, Department of Mechanical Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, Saskatchewan, Canada, S7N 5A9

Greg Schoenau Professor of Mechanical Engineering at the University of Saskatchewan. He was head of that Department from 1993 to 1999. He obtained B.Sc. and M. Sc. De-grees from the University of Saskatche-wan in mechanical engineering in 1967 and 1969, respectively. In 1974 he ob-tained his Ph.D. from the University of New Hampshire in fluid power control systems. He continues to be active in research in this area and in the thermal systems area as well. He has also held positions in numerous outside engineering and technical organizations.

Doug Bitner, Department of Mechanical Engineering, University of Saskatchewan, 57 Campus Drive, Saskatoon, Saskatchewan, Canada, S7N 5A9

Doug Bitner MSc. Departmental Assistant Mechanical Engineering, University of Saskatchewan. Manager Fluid Power Laboratory and Control Systems Laboratory University of Saskatchewan.

References

Bitner, D. 1986. Analytical and Experimental Analysis of a Load Sensing Pump. M. Sc. thesis, University of Saskatchewan, Canada.

Chaimowitsch, E. M. 1967. Ölhydraulik: Grundlagen und Anwendung. Veb Verlag Technik Berlin.

Krus, P. 1988. On Load Sensing Fluid Power Systems. Dissertation No. 198, Linkoping University, Swe-den.

Lantto, B., Palmberg, J. O. and Krus, P. 1990. Static and Dynamic Performance of Mobile Load-sensing Systems with Two Different Types of Pressure-Compensated Valves. SAE Technical Paper Series. SAE, Sept 10-13, pp. 251.

Lantto, B., Krus, P. and Palmberg, J. O. 1991. Inter-action between Loads in Load-sensing Systems. Proceeding of the 2nd Tampere International Con-ference on Fluid Power. Linkoping, Sweden, pp. 53.

Merritt, H. E. 1967. Hydraulic Control Systems. John Wiley & Sons, Inc.

Palmberg, J. O., Krus, P. and Ding, K. 1985. Dynam-ic Response Characteristics of Pressure-Control Pumps. The 1st International Conference on Fluid Power Transmission and Control, Zhejiang Univer-sity, Hangzhou, China, pp. 110.

Pettersson, H., Krus, P., Jansson, A. and Palmberg, J. O. 1996. The Design of Pressure Compensators for Load Sensing Hydraulic systems. UKACC In-ternational Conference on Control’96, IEE 427, University of Exeter, UK, pp. 1456.

Wu, D. 2002. Analysis and Simulation of LSPC Hy-draulic Systems. Ph.D. thesis, University of Sas-katchewan, work in progress.

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Published

2003-03-01

How to Cite

Wu, D., Burton, R., Schoenau, G., & Bitner, D. (2003). MODELLING OF ORIFICE FLOW RATE AT VERY SMALL OPENINGS. International Journal of Fluid Power, 4(1), 31–39. Retrieved from https://journals.riverpublishers.com/index.php/IJFP/article/view/613

Issue

2003: Vol 04 Iss 1

Section

Original Article