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Research Papers

A Mathematical Model for Simulation of Flow Rate and Chamber Pressures in Spool Valves

[+] Author and Article Information
Ahmet C. Afatsun

Motion Systems Design Department,
Roketsan, Inc.,
Elmadag 06780, Ankara, Turkey
e-mail: can.afatsun@roketsan.com.tr

R. Tuna Balkan

Professor
Mechanical Engineering,
Middle East Technical University,
Çankaya 06800, Ankara, Turkey
e-mail: balkan@metu.edu.tr

1Type 30 Nozzle-Flapper Flow Control Valves, Moog Inc., East Aurora, NY.

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT,AND CONTROL. Manuscript received February 16, 2018; final manuscript received August 21, 2018; published online October 5, 2018. Assoc. Editor: Youngsu Cha.

J. Dyn. Sys., Meas., Control 141(2), 021004 (Oct 05, 2018) (9 pages) Paper No: DS-18-1077; doi: 10.1115/1.4041300 History: Received February 16, 2018; Revised August 21, 2018

In this paper, a mathematical model to simulate the pressure and flow rate characteristics of a spool valve is derived. To improve the simulation accuracy, the discharge coefficient through the spool valve ports is assumed to be a function of both the Reynolds number and the orifice geometry rather than treating it as a constant. Parameters of the model are determined using the data obtained by computational fluid dynamics (CFD) analyses conducted on two-dimensional axisymmetric domains using ANSYS Fluent 15® commercial software. For turbulence modeling, shear stress transport (SST) k–ω model is preferred after a comparison of performance with the other available turbulence model options. The resulting model provides consistent pressure and flow rate estimations with CFD analyses and a smooth transition between different geometrical conditions. The ultimate aim of this study is to fulfill the need for a model to precisely determine the geometrical tolerances of spool valve components for optimum performance. Estimations of the developed model is compared with the experimental data of a spool valve, and the model is proved to be able to accurately estimate the maximum leakage flow rate, the pressure sensitivity, and the shapes of leakage flow/load pressure curves.

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References

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Figures

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Fig. 1

Port configurations of a spool valve

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Fig. 2

Overlap condition in a spool valve

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Fig. 3

Orifice opening for underlap condition in a spool valve

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Fig. 4

Comparison of flow rate estimations of aforementioned formulae to CFD data

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Fig. 5

The truncated conical area between the spool and sleeve

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Fig. 6

Details of analysis domain

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Fig. 7

Details around the radial clearance in a sample grid

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Fig. 8

Comparison of discharge coefficient versus Reynolds number estimation curves obtained using different turbulence model and wall function combinations

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Fig. 9

Comparison of discharge coefficient data in the paper of Posa et al. to the ones obtained by SST kω turbulence model. Different discharge coefficients for same port openings are obtained by using different flow rates.

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Fig. 10

Comparison of discharge coefficient data obtained by SST kω turbulence model and output of the fitted function

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Fig. 11

Parameters which are used to define the underlap condition

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Fig. 12

Cθ curves obtained from CFD analyses

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Fig. 13

Change in Cθ with respect to θ for Re* < 10

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Fig. 14

Comparison of developed Cθ function to CFD data

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Fig. 15

The valve geometry which is used to test final model

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Fig. 16

Flow rate estimations of developed model and CFD analysis

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Fig. 17

Error map of the model's output for the test case

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Fig. 18

A picture of the spool and the sleeve used in the tests

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Fig. 19

Cross-sectional view of tested spool valve's computer-aided design model

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Fig. 20

Hydraulic scheme of test configuration

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Fig. 21

Error map of the model's output for the test case

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Fig. 22

Error map of the model's output for the test case

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