Research Papers: Multiphase Flows

Modeling of Cavitation-Induced Air Release Phenomena in Micro-Orifice Flows

[+] Author and Article Information
Hans-Arndt Freudigmann

Robert Bosch GmbH,
Corporate Research,
Renningen 71272, Germany
e-mail: hans-arndt.freudigmann@de.bosch.com

Aaron Dörr

Robert Bosch GmbH,
Corporate Research,
Renningen 71272, Germany
e-mail: aaron.doerr@de.bosch.com

Uwe Iben

Robert Bosch GmbH,
Corporate Research,
St. Petersburg 198095, Russia
e-mail: uwe.iben@de.bosch.com

Peter F. Pelz

Chair of Fluid Systems,
Technische Universität Darmstadt,
Darmstadt 64289, Germany
e-mail: peter.pelz@fst.tu-darmstadt.de

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received July 27, 2016; final manuscript received May 15, 2017; published online August 10, 2017. Assoc. Editor: Elias Balaras.

J. Fluids Eng 139(11), 111301 (Aug 10, 2017) (11 pages) Paper No: FE-16-1482; doi: 10.1115/1.4037048 History: Received July 27, 2016; Revised May 15, 2017

Impurities like air bubbles in hydraulic liquids can significantly affect the performance and reliability of hydraulic systems. The aim of this study was to develop a model suited for hydraulic system simulation to determine the rate of degassing of dissolved air in a micro-orifice flow at cavitating conditions. An existing model for the flow through a micro-orifice was extended to account for the generation of vapor which is suggested to play the key-role for the degassing mechanism. In comparison with measurements, the results of the modeling approach imply that diffusive mass transfer of dissolved air into generated vapor cavities is the dominating mechanism for the observed air release phenomena.

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Fig. 1

Scheme of the experimental setup

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Fig. 2

Scheme of the flow through a sharp-edged orifice

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Fig. 3

Exemplary recordings of the flow regime at different distances downstream the orifice exit for an absolute inlet pressure of 50 bar: (a) p3 = 4.2 bar, 1/K1 = 0.916; (b) p3 = 3.4 bar, 1/K1 = 0.932; and (c) p3 = 2.5 bar, 1/K1 = 0.950

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Fig. 4

Results for the degassing ratio obtained in Ref. [13] 100 mm downstream of the orifice exit against the reciprocal of the cavitation number given by Eq. (2). The inlet pressure is kept constant at p1 = 50 bar (○) and 75 bar (×), respectively. For each operation point, 100 images are recorded and evaluated.

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Fig. 5

Scanning electron microscope image of the orifice inlet

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Fig. 6

Mass flow rate m˙ (a) and CD/K1 (b) versus the reciprocal of the cavitation number 1/K1 for the used orifice with p1 = ○ 50 bar; × 60 bar; 75 bar; and ▿ 85 bar

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Fig. 7

Comparison of the loss coefficient ζW (—–) obtained using an empirical correlation of CD according to Ref. [25] andEq. (16) with the friction factor for laminar pipe flow ζlaminar=(64/Re)(l/DD) (– – –) and turbulent pipe flow ζturbulent=(0.316/Re4)(l/DD) (−⋅−⋅) with l = 10.1DD

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Fig. 8

Reference mixture cell with liquid, gas, and vapor

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Fig. 9

Schematic change of state from 1 → 3 in the temperature–entropy diagram in case of cavitation

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Fig. 10

Visualization of the concept of the degassing coefficient αdeg

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Fig. 13

Comparison of experimental results (○) obtained in Ref. [13] 100 mm downstream the orifice for an inlet pressure of 50 bar (a) and 75 bar (b) with the calculated mass fraction μgu,2 of free air. (—–) μgu,2⋅106 according to Eq. (37), (– – –) μgu,2 according to Eq. (42) with αdeg = 0.8, and (……) μgu,2 according to Eq. (42) with a linear relation for αdeg according Eq.(43).

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Fig. 12

Comparison of the calculated discharge coefficient CD (– – –) and the relative effective area Ca (—–) for Shell V-1404 with measurements of CD (×) and Ca (○) obtained by Payri et al. [31] with CC = 0.715, DD = 132 μm, p1 = 300 bar, and l = 5DD. The relative effective area Ca can be interpreted as the relative density ρ2/ρ1 [30].

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Fig. 11

Calculated mass flow rate (a) and the resulting discharge coefficient CD (b) (—–) in comparison with measurements () for p1 = 50 bar and T1 = 23 °C. Figure (c) represents the relative density and Fig. (d) the static pressure for section e(– – –), 2 (−⋅−⋅), and section 3 (—–). Figures (e) and (f) provide the volume fraction αv and mass fraction μv of vapor in section 2.



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