Trajectories and singular points in steady-state models of two-phase flows

Bilicki, Z.; Dafermos, Constantine M.; Kestin, J.; Majda, George; Zeng, Dong

doi:10.1016/0301-9322(87)90019-x

Cited by 34 publications

(22 citation statements)

References 5 publications

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“…It can be seen that the quasi onedimensional model compares extremely well with experiemental measurements. In 3 fact, the agreement is even better than the two-dimensional, fully ionized, frozen, axisymmetric model of ref [10]. The transition from electrothermal to electromagnetic m acceleration is evident in the slight change in slope visible in the figure at a current level near 14 kA.…”

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confidence: 53%

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Fundamental Studies on Erosion in MPD Thrusters

Subramaniam¹

1992

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confidence: 53%

“…This is summarized condition. Rather, it must be obeyed in in Table II and is not always intuitive [10]. At addition to the choking condition, equation…”

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confidence: 99%

Fundamental Studies on Erosion in MPD Thrusters

Subramaniam¹

1992

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“…A detailed analysis of difficulties in 'passing' through singular points in non-equilibrium nozzle flows is given by Bilicki et al (1987). We have obtained the regime OB with a singular point S shown by the solid line in figure 10 with the method of 'model expansion' described in the Appendix.…”

Section: Structure Of the Boiling Wavementioning

confidence: 99%

Bubble breakup simulation in nozzle flows

Ivashnyov

Ivashneva

2012

J. Fluid Mech.

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Experiments on high-pressure vessel decompression have shown that vaporization occurs in 'boiling shocks' moving with a velocity of ∼10 m s −1 . To explain this phenomenon, a model accounting for bubble breakup was suggested (Ivashnyov, Ivashneva & Smirnov, J. Fluid. Mech., vol. 413, 2000, pp. 149-180). It was shown that the explosive boiling was caused by chain bubble fragmentation, which led to a sharp increase in the interface area and instantaneous transformation of the mixture into an equilibrium state. In the present study, this model is used to simulate nozzle flows with no change in the free parameters chosen earlier for modelling a tube decompression. It is shown that an advanced model ensures the best correspondence to experiments for flashing flows in comparison with an equilibrium model and with a model of boiling at a constant number of centres. It is also shown that the formation of a boiling shock in a critical nozzle flow leads to autovibrations.

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“…But, considerable time and money has to be spent on performing a high-accuracy multidimensional CFD simula-tion. For a compromise between a fast but incomplete calculation and an accurate but slow multidimensional simulation, a onedimensional method was recommended by many researchers to analyze the performance of the scramjet engine [10][11][12][13]. However, there was a crucial technical difficulty for solving the onedimensional transonic flows: the mathematical singularity problem [2,14,15].…”

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confidence: 99%

“…A method that treats the singular point first as an initial condition was advocated by many researchers [2,11,12,14]. For this method, the location of the sonic point and the conditions at the upstream and downstream of the sonic point were found first.…”

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New Method for Solving One-Dimensional Transonic Reacting Flows of a Scramjet Combustor

Cao

Cui

et al. 2016

Journal of Propulsion and Power

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A new solution method is proposed to solve the one-dimensional transonic reacting flows of a scramjet combustor, which represents a mathematical singularity in the governing equations when the flow velocity approaches the speed of sound. The governing equations of the one-dimensional transonic flows are rewritten by using a variable transformation method and, in this way, the singularity of the governing equations is eliminated. Subsequently, a forward iterative shooting method is introduced to deal with the numerical problem appearing in the flow that includes finite-rate chemistry and high-temperature gas properties. Comparative analysis is performed to evaluate the method presented in this paper and previous methods. The results show that it has a wider applicability and better stability in solving the one-dimensional transonic reacting flows than previous methods. One major advantage of this method is that, as a result of the elimination of the singularity using variable transformation and the introduction of a forward iterative shooting method, a smooth and stable numerical calculation for transonic reacting flows can be ensured.

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Trajectories and singular points in steady-state models of two-phase flows

Cited by 34 publications

References 5 publications

Fundamental Studies on Erosion in MPD Thrusters

Fundamental Studies on Erosion in MPD Thrusters

Bubble breakup simulation in nozzle flows

New Method for Solving One-Dimensional Transonic Reacting Flows of a Scramjet Combustor

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