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Research Papers: Fundamental Issues and Canonical Flows

Correlations for the Choked Mass and Momentum Flux Density Considering Real-Gas Thermodynamics

[+] Author and Article Information
Matthias Banholzer

Institute for Thermodynamics,
Bundeswehr University Munich,
Werner-Heisenberg-Weg 39,
Neubiberg 85577, Germany
e-mail: matthias.banholzer@unibw.de

Michael Pfitzner

Institute for Thermodynamics,
Bundeswehr University Munich,
Werner-Heisenberg-Weg 39,
Neubiberg 85577, Germany
e-mail: michael.pfitzner@unibw.de

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 13, 2018; final manuscript received December 20, 2018; published online January 30, 2019. Assoc. Editor: Sergio Pirozzoli.

J. Fluids Eng 141(8), 081202 (Jan 30, 2019) (10 pages) Paper No: FE-18-1617; doi: 10.1115/1.4042376 History: Received September 13, 2018; Revised December 20, 2018

The choked mass flux density and the choked momentum flux density for the nonideal fluids methane and nitrogen have been calculated using the Soave–Redlich–Kwong equation of state (EoS). For the computation a steady, one-dimensional (1D), isenthalpic and isentropic flow is assumed. The developed algorithm for the calculation of the choked flow properties includes a bounded multidimensional Newton method. A possible second phase emerging in the critical nozzle area is excluded using the saturation properties of the considered fluids. The critical ratios of pressure, density, temperature, and speed of sound are discussed and compared to other publications. Formulations of the choked mass flux density and the choked momentum flux density explicit in Tr, pr, and Zr are given valid for different reduced pressures and temperatures depending on the fluid. Additional computational fluid dynamics (CFD) simulations are carried out in order to validate the findings of the algorithm and the proposed correlations.

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Figures

Grahic Jump Location
Fig. 1

Reduced density ρr (left) and compressibility factor Z (right) of methane for two different isotherms Tr,1 = 1.2 and Tr,2 = 2.6

Grahic Jump Location
Fig. 2

Left: global maximum present → choked state. Right: no global maximum present → liquid phase.

Grahic Jump Location
Fig. 3

Dependency of the reduced plenum pressure on the critical ratios p*/p0 (top left), ρ*/ρ0 (top right), as∗/as,0 (bottom left), and T*/T0 (bottom right) for methane and different reduced temperatures Tr,0. Additional values are given for the ideal-gas assumption showing great discrepancies (same line-style for each temperature in gray).

Grahic Jump Location
Fig. 4

Dependency of the reduced plenum pressure on the critical ratios p*/p0 (top left), ρ*/ρ0 (top right), as∗/as,0 (bottom left), and T*/T0 (bottom right) for a plenum temperature of Tr,0 = 1.3

Grahic Jump Location
Fig. 5

Relative choked mass flux (left) and momentum flux (right) of methane for different reduced temperatures Tr,0

Grahic Jump Location
Fig. 6

Relative choked mass flux (left) and momentum flux (right) for a reduced plenum temperature of Tr,0 = 1.3 and different considered fluids

Grahic Jump Location
Fig. 7

Γ (left) and Ψ (right) for methane and different isothermals Tr,0

Grahic Jump Location
Fig. 8

Schematic of the computational domain

Grahic Jump Location
Fig. 9

Deviations of the critical ratios analyzed within a CFD framework

Grahic Jump Location
Fig. 10

Dependency of the reduced plenum pressure on the critical ratios p*/p0 (top left), ρ*/ρ0 (top right), as∗/as,0 (bottom left), and T*/T0 (bottom right) for nitrogen and different reduced temperatures Tr,0. Additional values are given for the ideal-gas assumption showing great discrepancies (same line-style for each temperature in gray).

Grahic Jump Location
Fig. 11

Dependency of the reduced plenum pressure on the critical ratios p*/p0 (top left), ρ*/ρ0 (top right), as∗/as,0 (bottom left), and T*/T0 (bottom right) for a plenum temperature of Tr,0 = 2.6

Grahic Jump Location
Fig. 12

Relative choked mass flux (left) and momentum flux (right) of nitrogen for different reduced temperatures Tr,0

Grahic Jump Location
Fig. 13

Relative choked mass flux (left) and momentum flux (right) for a reduced plenum temperature of Tr,0 = 2.6

Grahic Jump Location
Fig. 14

Γ (left) and Ψ (right) for nitrogen and different isothermals Tr,0

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