Abstract
The theory of boiling shock is developed. A boiling shock is shown to be a rarefaction shock wave. An analysis is carried out of the boiling shock adiabat. The entropy is shown to increase across the shock front. The stability of the boiling shock is investigated. Two possible situations are singled out: a shock formed under transient conditions following a seal failure of high pressure vessels (the U-shock) and a shock formed when the limiting (spinodal) superheats are reached in the flow (the S-shock). The mechanisms of flow choking with formation of an S-shock are examined. The model proposed is shown to adequately describe the experimental data on the discharge from diaphragms and short nozzles. The structure of the S-shock front is studied. The appearance of the S-shock is shown to be always accompanied by the formation of oscillations specific to this class of problems. A conclusion is made that under certain conditions the process of boiling of liquid acquires a self-accelerating character, when the development of the process of phase transitions triggers a growth of liquid superheat. Besides, discharge regimes with radial jet expansion also appear, when the jet of boiling liquid acquires a specific daisy-shaped form. Moreover, in these regimes the reactive force abruptly drops down to zero or to small negative values. The gas dynamics of these discharge regimes is given a detailed treatment. Patterns of shock waves accompanying discharge process are obtained. Mechanisms of propagation of the U-shock in a bulk of superheated liquid are considered. The velocity of its propagation is shown to be well described by the theory developed. The requirement of the stability of the U-shock leads to a well-defined quantity of superheat ahead of its front (the pressure undershot), which is an unambiguous function of the initial liquid temperature and its properties. All the conclusions of the above analysis are well supported by the experimental evidence.
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Notes
- 1.
Physically, this situation corresponds to the degenerate case of a near isobaric transition of stagnant liquid into the equilibrium two-phase mixture.
- 2.
In view of (8.19) it is maximum.
- 3.
In the terminology of L.D. Landau, to perturbation of the entropy propagating in gas 2 and to a displacement of the shock wave itself.
- 4.
By estimates of Skripov et al. (1980), in the majority of experiments on discharge of a boiling liquid from short channels with near-spinodal superheats, the value \(I_{V} = 10^{15} - 10^{21} \, 1 / ( {\text{m}}^{3} {\text{s}})\) is attained.
- 5.
In the theory of isentropic discharge of boiling liquid, which was considered in the previous chapter, this maximal value is known as the critical discharge defined in the framework of the homogeneous equilibrium model (HEM).
- 6.
In the critical discharge of a compressible medium from orifices, the presence of an area of two-dimensional flow implies that the medium flow rate becomes always smaller than the value obtained in the framework of the one-dimensional model. So, for a discharge of air from a sharp-edged orifice this difference may be as high as 15 % (Chaplygin 1976). Judging from the available experimental data, for a critical discharge of an equilibrium two-phase mixture this difference is at most 5–10 %.
- 7.
In the experiments under consideration, there was a substantial inhomogeneity in the temperature distribution over the pipe section. In particular, the temperature at the bottom and top points of the tube cross-section were found to differ by 8.3Â K. For the calculations, the value of the temperature on the lower temperature was used.
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Avdeev, A.A. (2016). Theory of Boiling Shock. In: Bubble Systems. Mathematical Engineering. Springer, Cham. https://doi.org/10.1007/978-3-319-29288-5_8
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