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Research Papers: Flows in Complex Systems

A Novel Method to Determine the Discharge Coefficient of Constant Section Nozzles Under Compressible Dynamic Flow Conditions

[+] Author and Article Information
A. Comas

Mem. ASME
Heat Engines Department,
Polytechnic University of Catalonia,
Colon 7-11,
Terrassa 08222, Spain
e-mail: comas@mmt.upc.edu

C. Rio-Cano

Mechanical Engineering Department,
Polytechnic University of Catalonia,
Colon 7-11,
Terrassa 08222, Spain
e-mail: carlos.rio-cano@upc.edu

J. M. Bergada

Fluid Mechanics Department,
Polytechnic University of Catalonia,
Colon 7-11,
Terrassa 08222, Spain
e-mail: josep.m.bergada@upc.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received April 27, 2018; final manuscript received December 17, 2018; published online January 30, 2019. Assoc. Editor: Devesh Ranjan.

J. Fluids Eng 141(7), 071108 (Jan 30, 2019) (13 pages) Paper No: FE-18-1300; doi: 10.1115/1.4042374 History: Received April 27, 2018; Revised December 17, 2018

The present paper introduces a novel transient experimental method employed to determine the discharge coefficient of constant section nozzles of small diameters of 1–3 mm and with a length/diameter ratio of around one. Flow is considered to be real and compressible; the discharge process was analyzed at relatively high pressures, the fluid used was N2. Based on the experimental data, a generalized expression characterizing the discharge coefficient for nozzles of different diameters, lengths, and fluid conditions was developed. In order to check the precision of the analytical equation presented, experimental upstream reservoir pressure decay was compared with the temporal pressure decay obtained using the new analytical equation. Good correlation was achieved for pressure differentials up to 7.6 MPa. Despite the fact that the procedure established can be extended to other gases and nozzle configurations, so far the equation presented to estimate the discharge coefficient, can only be applied to orifices with length to diameter ratios of around one.

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References

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Nakao, S. , 2005, “ Development of Critical Nozzle Flow Meter for High Pressure Hydrogen Gas Flow Measurements,” Proceedings of JSME, Fluid Dynamics Section, Vol. 201, Kanazawa, Japan, p. 2005.
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Lee, B. I. , and Kesler, M. G. , 1975, “ A Generalized Thermodynamic Correlation Based on Three-Parameter Corresponding States,” AIChE J., 21(3), pp. 510–527. [CrossRef]
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Figures

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Fig. 1

Double chamber pneumatic suspension

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Fig. 2

Isentropic flow through a convergent nozzle computation algorithm flow diagram

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Fig. 3

Discharge process between two generic reservoirs

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Fig. 4

(a) Upstream pressure decay for a low pressure discharge process (0.2–0.1 MPa). Fluid used: N2. (b) Upstream pressure decay for a high pressure discharge process (5–0.1 MPa). Fluid used: N2.

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Fig. 5

(a) Upstream gas temperature for a low pressure discharge process (0.2–0.1 MPa). Fluid used: N2. (b) Upstream gas temperature for a high pressure discharge process (5–0.1 MPa). Fluid used: N2.

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Fig. 6

Discharge coefficient experimental unit

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Fig. 7

(a) Upstream reservoir wall temperature for a high pressure discharge (7.3–0.1 MPa). (b) Upstream reservoir wall temperature for a high pressure discharge (5.1–3.7 MPa). (c) Upstream reservoir wall temperature for a high pressure discharge (4.5–0.1 MPa). Fluid used: N2. Experimental results.

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Fig. 8

(a) Downstream gas temperature evolution and (b) upstream gas temperature evolution. For both cases, upstream/downstream pressure was, respectively, of 4.5 and 0.1 MPa. Fluid used N2.

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Fig. 9

Measured upstream/downstream reservoirs temporal pressure variation. Upstream pressure 4.5 MPa, downstream pressure 0.1 MPa. Fluid used: N2. Experimental results.

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Fig. 10

(a) Downstream reservoir heat transfer for a low pressure discharge (0.2–0.1 MPa). Fluid used: N2. (b) Downstream reservoir heat transfer for a high pressure discharge (4.5–0.1 MPa). Fluid used: N2.

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Fig. 11

Mach number evolution at the nozzle critical section. Upstream pressure 4.5 MPa, downstream pressure 0.1 MPa.

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Fig. 12

(a) Downstream mass for a high pressure discharge and (b) upstream mass for a high pressure discharge. For both cases upstream/downstream pressure was, 4.5 and 0.1 MPa, respectively. Fluid used: N2.

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Fig. 13

(a) Reynolds number at throat for a high pressure discharge and (b) viscosity at throat for a high pressure discharge. For both cases, upstream/downstream pressure was, 4.5 and 0.1 MPa, respectively. Fluid used: N2.

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Fig. 14

Density at throat for a high pressure discharge. Upstream/downstream pressure was, 4.5 and 0.1 MPa, respectively. Fluid used: N2.

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Fig. 15

(a) Discharge coefficient for a low pressure discharge (0.2–0.1 MPa). Fluid used: N2. (b) Discharge coefficient for a high pressure discharge (4.5–0.1 MPa). Fluid used: N2.

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Fig. 16

Ideal and real experimentally based mass flow for a high pressure discharge. Upstream/downstream pressure is, 4.5 and 0.1 MPa, respectively. Fluid used: N2.

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Fig. 17

Flow diagram to obtain the discharge coefficient based on the experimental measurements

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Fig. 18

(a) Upstream pressure for a high pressure discharge (4.9–1.4 MPa). Fluid used: N2. Orifice diameter: 1.3 mm. (b) Upstream pressure for a high pressure discharge (7.7–0.1 MPa). Fluid used: N2. Orifice diameter: 3.05 mm.

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