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Research Papers

Modeling and Experimental Validation of the Effective Bulk Modulus of a Mixture of Hydraulic Oil and Air

[+] Author and Article Information
Hossein Gholizadeh

Department of Mechanical Engineering,
University of Saskatchewan,
57 Campus Drive,
Saskatoon, SK S7N 5A9, Canada
e-mail: h.gholizadeh@usask.ca

Doug Bitner

Department of Mechanical Engineering,
University of Saskatchewan,
57 Campus Drive,
Saskatoon, SK S7N 5A9, Canada
e-mail: doug.bitner@usask.ca

Richard Burton

Department of Mechanical Engineering,
University of Saskatchewan,
57 Campus Drive,
Saskatoon, SK S7N 5A9, Canada
e-mail: richard.burton@usask.ca

Greg Schoenau

Department of Mechanical Engineering,
University of Saskatchewan,
57 Campus Drive,
Saskatoon, SK S7N 5A9, Canada
e-mail: greg.schoenau@usask.ca

1Corresponding author.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received December 10, 2013; final manuscript received March 7, 2014; published online June 12, 2014. Assoc. Editor: Gregory Shaver.

J. Dyn. Sys., Meas., Control 136(5), 051013 (Jun 12, 2014) (14 pages) Paper No: DS-13-1499; doi: 10.1115/1.4027173 History: Received December 10, 2013; Revised March 07, 2014

It is well known that the presence of entrained air bubbles in hydraulic oil can significantly reduce the effective bulk modulus of hydraulic oil. The effective bulk modulus of a mixture of oil and air as pressure changes is considerably different than when the oil and air are not mixed. Theoretical models have been proposed in the literature to simulate the pressure sensitivity of the effective bulk modulus of this mixture. However, limited amounts of experimental data are available to prove the validity of the models under various operating conditions. The major factors that affect pressure sensitivity of the effective bulk modulus of the mixture are the amount of air bubbles, their size and the distribution, and rate of compression of the mixture. An experimental apparatus was designed to investigate the effect of these variables on the effective bulk modulus of the mixture. The experimental results were compared with existing theoretical models, and it was found that the theoretical models only matched the experimental data under specific conditions. The purpose of this paper is to specify the conditions in which the current theoretical models can be used to represent the real behavior of the pressure sensitivity of the effective bulk modulus of the mixture. Additionally, a new theoretical model is proposed for situations where the current models fail to truly represent the experimental data.

Copyright © 2014 by ASME
Topics: Pressure , Compression
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References

Figures

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Fig. 1

Schematic diagrams (a) baseline and lumped air cases and (b) distributed air case of the bulk modulus tester. (1) Pressure compensated variable displacement pump, (2) pressure control servo valve, (3) double acting double rod end hydraulic cylinder, (4) double acting double rod end hydraulic cylinder, (5) displacement sensor (MicroTrak II-SA), (6) testing vessel, (7) needle valve, (8) transparent tube, (9) variable throttle valve, (10) vacuum pump, (11) needle valve, (12) pycnometer, (13) pressure transducer, (14) needle valve, (15) venturi orifice, (16) pressure compensated variable displacement pump, (17) compressed air source, and (18) pneumatic pressure regulator.

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Fig. 3

A typical example of bulk modulus measurement in the baseline case (−0.0044%/s)

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Fig. 2

Calculating X0 from the experimental results

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Fig. 5

Nonlinear least squares curve fit of the experimental data in the baseline case when the volume change rate was −0.216%/s

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Fig. 6

An example of a change in the pressure when air is added to the oil and compressed

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Fig. 4

Nonlinear least square curve fit of the experimental data in the baseline case when the volume change rate was −0.0006%/s

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Fig. 7

(a) and (b) Nonlinear least squares curve fit of the experimental data with 1% of lumped air: (a) Kl(P0,T) = 1972 MPa, n = 1.068, and E = 50 MPa; (b) Kl(P0,T) = 1898 MPa, n = 1, and E = 27 MPa.

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Fig. 8

(a) and (b) Nonlinear least squares curve fit of the experimental data with 3% of lumped air: (a) Kl(P0,T) = 1972 MPa, n =1.206, and E = 34 MPa; (b) Kl(P0,T) = 1920 MPa, n = 1.079, and E = 45 MPa

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Fig. 9

(a) and (b) Nonlinear least squares curve fit of the experimental data with 5% of lumped air: (a) Kl(P0,T) = 1972 MPa, n = 1.331, and E = 30 MPa; (b) Kl(P0,T) = 1930 MPa, n = 1.083, and E = 39 MPa

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Fig. 10

(a)–(c) Nonlinear least squares curve fit of the experimental data for different amounts of distributed air for a rapid volume change rate: (a) Kl(P0,T) = 1972 MPa, X0 = 1.5%, PC = 6.5 MPa, (X0)C = 0.97%, and E = 20 MPa; (b) Kl(P0,T) = 1970 MPa, X0 = 3.35%, PC = 6.5 MPa, (X0)C = 2.49%, and E = 20 MPa; (c) Kl(P0,T) = 1970 MPa, X0 = 4.5%, PC = 6.5 MPa, (X0)C = 3%, and E = 31 MPa

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Fig. 11

(a)–(c) Nonlinear least squares curve fit of the experimental data for different amounts of distributed air for an intermediate volume change rate: (a) Kl(P0,T) =1972 MPa, X0 = 1.9%, PC = 6.4 MPa, (X0)C = 0.1%, and E = 36 MPa; (b) Kl(P0,T) = 1970 MPa, X0 = 3.45%, PC = 2.2 MPa, (X0)C = 2.14%, and E = 16 MPa; (c) Kl(P0,T) = 1972 MPa, X0 = 4.4%, PC = 2.1 MPa, (X0)C = 2.24%, and E = 9 MPa

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Fig. 12

(a)–(c) Nonlinear least squares curve fit of the experimental data for different amounts of distributed air for a slow volume change rate: (a) Kl(P0,T) = 1900 MPa, X0 = 1.9%, PC = 6.1 MPa, (X0)C = 1.09%, and E = 37 MPa; (b) Kl(P0,T) = 1890 MPa, X0 = 3.42%, PC =1 MPa, (X0)C = 2.22%, and E =18 MPa; (c) Kl(P0,T) = 1932 MPa, X0 = 4.4%, PC = 0.8 MPa, (X0)C = 2.12%, and E = 18 MPa

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Fig. 15

A new critical pressure definition is introduced based on the saturation limit of oil

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Fig. 13

Graphical representation showing how to use “compression only” bulk modulus curves in order to find “compression and dissolve” model

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Fig. 18

Isothermal and adiabatic tangent bulk modulus variation of Esso Nuto H68 oil with pressure at a temperature of 24 °C

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Fig. 16

Mass fraction of entrained air due to dissolving which is based on the new definition for the critical pressure

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Fig. 14

Comparison of the experimental results with a series of “compression only” bulk modulus curves for isothermal process

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Fig. 17

Viscosity variation of Esso Nuto H68 with temperature

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