Two semi-analytical approaches for solving condensation shocks in supersonic nozzle flows

Bolaños-Acosta, A.F.; Restrepo, Julián C.; Simões-Moreira, José R.

doi:10.1016/j.ijheatmasstransfer.2021.121212

Cited by 15 publications

(7 citation statements)

References 28 publications

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“…The Rankine–Hugoniot relations – are widely known for the treatment of discontinuities on compressible flows (e.g. shock waves, detonations (Thompson 1971 b ) or even evaporation waves (Simões-Moreira & Shepherd 1999) and condensation shocks (Bolaños-Acosta, Restrepo & Simões-Moreira 2021)). The three conservation equations valid for a discontinuity are presented next, where the index 1 denotes the upstream state and 2 denotes the downstream state: …”

Section: Compressible Viscous Real Gas Governing Equationsmentioning

confidence: 99%

Viscous effects on real gases in quasi-one-dimensional supersonic convergent divergent nozzle flows

Restrepo

Simões-Moreira²

2022

J. Fluid Mech.

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Viscous effects on an ideal gas flow in a supersonic convergent–divergent nozzle are a well-studied subject in classical gas dynamics. However, the ideal assumption fails on fluids that exhibit complex behaviours such as near-critical-region and non-ideal dense vapours. Under those conditions, a realistic equation of state (EOS) plays a vital role for a precise and realistic computation. This work examines the problem for solving the quasi-one-dimensional viscous compressible flow using a realistic EOS. The governing equations are discretised and solved using the fourth-order Runge–Kutta method coupled with a state-of-the-art EOS to calculate the thermodynamic properties. The role of the Grüneisen parameter along with viscous and real gas effects and their influence on the sonic point formation are discussed. The study shows that the flow may not achieve the supersonic regime for any pressure ratio depending on the combination of that parameter and the normalised friction factor. In addition, the analysis yields the discharge coefficient and the isentropic nozzle efficiency, which may achieve maximum values as a function of the stagnation conditions. Finally, the study also evaluates the formation and intensity of normal shock waves by using the Rankine–Hugoniot relations, which now depend on the real gas and viscous effects in opposition to the inviscid solution. Moreover, the methodology used captures the sonic point and shock wave position by a space marching algorithm using the Brent method for scalar minimisation. Experimental data available in the open literature corroborate the approach.

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Section: Compressible Viscous Real Gas Governing Equationsmentioning

confidence: 99%

Viscous effects on real gases in quasi-one-dimensional supersonic convergent divergent nozzle flows

Restrepo

Simões-Moreira²

2022

J. Fluid Mech.

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“…Supersonic separation is an emerging technology for natural gas purification [7] . Widespread attention has been quickly gained because of its advantages of strong separation ability [8] , non-chemical properties [1] , simple structure [9] , and low cost [10] . Correspondingly, numerical studies on the flow properties of supersonic separators are also emerging to obtain higher purity natural gas [11][12][13] .…”

Section: Introductionmentioning

confidence: 99%

A modified Euler-Lagrange-Euler approach for modelling homogeneous and heterogeneous condensing droplets and films in supersonic flows

Ding

Yang

Wen

2023

International Journal of Heat and Mass Transfer

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“…If the nozzle exit pressure is higher than the environment discharging pressure, but lower than the critical subsonic solution, a normal shock wave should be formed within the nozzle. The Rankine-Hugoniot relations (4.34 -4.36) are widely known for the treatment of discontinuities on compressible flows (e.g, shock-waves, detonations (Thompson, 1971), or even evaporation waves (Simões-Moreira; Shepherd, 1999) and condensation shocks (Bolaños- Acosta et al, 2021). The three conservation equations valid for a discontinuity are presented next, where the index 1 stand for the upstream state and 2 for downstream one:…”

Section: Rankine-hugoniot Relationsmentioning

confidence: 99%

“…For the single fluid model implementation one must establish the following assumptions (Bolaños- Acosta et al, 2021):…”

Section: Single Fluid Modelmentioning

confidence: 99%

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Avaliação teórica e experimental da remoção de dióxido de carbono de ar seco pela técnica de separação supersônica.

Lozano¹

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Two semi-analytical approaches for solving condensation shocks in supersonic nozzle flows

Cited by 15 publications

References 28 publications

Viscous effects on real gases in quasi-one-dimensional supersonic convergent divergent nozzle flows

Viscous effects on real gases in quasi-one-dimensional supersonic convergent divergent nozzle flows

A modified Euler-Lagrange-Euler approach for modelling homogeneous and heterogeneous condensing droplets and films in supersonic flows

Avaliação teórica e experimental da remoção de dióxido de carbono de ar seco pela técnica de separação supersônica.

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