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Discussion on the paper: Analysis of EXCOBULLE two-phase expansion tests
Nuclear Engineering and Design 72 (1982) 271 North-Holland Publishing Company
271
LETrER TO THE EDITOR Discussion on the paper: Analysis of E X C O B U L L E two-phase e x p a n s i o n tests, A.B. Reynolds and G. Berthoud, which appeared in: Nucl. Engrg. Des. 67 (1981) 83-100.
The authors are to be congratulated for taking up an analysis of a complex physical problem and the close agreement they achieved with observations. However, the following points need to be clarified. First of all the authors assume that during the initial phases of expansion, the Tayior's instability sets in due to the acceleration of lighter fluid against the more dense cold water. Eventhough this is true for a plane problem considered by Taylor and Lewis, it is not applicable for the spherically symmetric problem as shown by Plesset [1,2]. (Even the work of Chandrasekhar quoted by the authors agrees with Plesset's analysis since the acceleration considered is - r inward). In view of this, the analysis of the unstable phase needs considerable modification which will definitely influence the final results. The second point concerns the adiabatic computations. It would be most helpful to the readers if the authors elaborate on the initial conditions, etc. used for these calculations. Also when the authors refer to "bubble" (for example in fig. 1), do they mean that superheated liquid or vapor is contained in the bubble?
References [1] M.S. Plesset and T.P. Mitchell, On the stability of a spherical shape of a vapor cavity in a liquid, Quart. Appl. Math. 13 (1956) 419-430. [2] M.S. Plesset, Bubble dynamics, in: Cavitation in Real Fluids, Ed. Robert Davis (Elsevier, Amsterdam, 1964) p. 1-18. K.C. Karki and V.H. Arakeri Department of Mechanical Engineering Indian Institute of Science Bangalore- 560012, India R E S P O N S E BY T H E A U T H O R S Messrs. Karki and Arakeri correctly point out that Plesset and Mitchell showed that the classical Taylor instability theory for plane surfaces must be altered for
a spherical surface and that perturbations other than narrow spikes are limited in their growth. Plesset and Mitchell solved the problem for constant internal cavity pressure. In the expanding EXCOBULLE bubbles the pressure dropped off rapidly so that the outward acceleration became negative early; hence, the perturbations should not grow even as much as predicted by the Plesset-Mitchell analysis. For the large perturbations in the EXCOBULLE tests, n was estimated to be of the order of 10. Plesset and Mitchell show substantial growth with expanding radius for perturbations of this high order although we cannot compare the experimental growth rate of the EXCOBULLE perturbations with their model predictions since we do not know the initial amplitudes and do not have enough movie frames during the growth period. In addition to these relatively wide perturbations, we observed many narrow spikes on the spherical surface which we expect grew in a manner more similar to the classical Taylor instabihty theory during the short period of positive acceleration. Plesset and Mitchell noted that, when surface tension is unimportant (as is the case here), "needlelike irregularities" in the spherical surface may grow to significant amplitudes and that their linearized theory is inadequate for these high order distortions. Regarding the initial conditions for the calculations, the zone in fig. 1 of the paper labeled "bubble" refers to two-phase (liquid-vapor) water. Thermodynamic equilibrium between liquid and vapor was assumed throughout the expansion; neither superheated liquid nor superheated vapor was ever present in the model The initial condition of the bubble contents in the calculational model was always saturated liquid at the initial average water temperature. Details of the actual early metastable state and the early nucleation and growth of embryonic bubbles were not included in the analysis. A.B. Reynolds G. Berthoud
271
LETrER TO THE EDITOR Discussion on the paper: Analysis of E X C O B U L L E two-phase e x p a n s i o n tests, A.B. Reynolds and G. Berthoud, which appeared in: Nucl. Engrg. Des. 67 (1981) 83-100.
The authors are to be congratulated for taking up an analysis of a complex physical problem and the close agreement they achieved with observations. However, the following points need to be clarified. First of all the authors assume that during the initial phases of expansion, the Tayior's instability sets in due to the acceleration of lighter fluid against the more dense cold water. Eventhough this is true for a plane problem considered by Taylor and Lewis, it is not applicable for the spherically symmetric problem as shown by Plesset [1,2]. (Even the work of Chandrasekhar quoted by the authors agrees with Plesset's analysis since the acceleration considered is - r inward). In view of this, the analysis of the unstable phase needs considerable modification which will definitely influence the final results. The second point concerns the adiabatic computations. It would be most helpful to the readers if the authors elaborate on the initial conditions, etc. used for these calculations. Also when the authors refer to "bubble" (for example in fig. 1), do they mean that superheated liquid or vapor is contained in the bubble?
References [1] M.S. Plesset and T.P. Mitchell, On the stability of a spherical shape of a vapor cavity in a liquid, Quart. Appl. Math. 13 (1956) 419-430. [2] M.S. Plesset, Bubble dynamics, in: Cavitation in Real Fluids, Ed. Robert Davis (Elsevier, Amsterdam, 1964) p. 1-18. K.C. Karki and V.H. Arakeri Department of Mechanical Engineering Indian Institute of Science Bangalore- 560012, India R E S P O N S E BY T H E A U T H O R S Messrs. Karki and Arakeri correctly point out that Plesset and Mitchell showed that the classical Taylor instability theory for plane surfaces must be altered for
a spherical surface and that perturbations other than narrow spikes are limited in their growth. Plesset and Mitchell solved the problem for constant internal cavity pressure. In the expanding EXCOBULLE bubbles the pressure dropped off rapidly so that the outward acceleration became negative early; hence, the perturbations should not grow even as much as predicted by the Plesset-Mitchell analysis. For the large perturbations in the EXCOBULLE tests, n was estimated to be of the order of 10. Plesset and Mitchell show substantial growth with expanding radius for perturbations of this high order although we cannot compare the experimental growth rate of the EXCOBULLE perturbations with their model predictions since we do not know the initial amplitudes and do not have enough movie frames during the growth period. In addition to these relatively wide perturbations, we observed many narrow spikes on the spherical surface which we expect grew in a manner more similar to the classical Taylor instabihty theory during the short period of positive acceleration. Plesset and Mitchell noted that, when surface tension is unimportant (as is the case here), "needlelike irregularities" in the spherical surface may grow to significant amplitudes and that their linearized theory is inadequate for these high order distortions. Regarding the initial conditions for the calculations, the zone in fig. 1 of the paper labeled "bubble" refers to two-phase (liquid-vapor) water. Thermodynamic equilibrium between liquid and vapor was assumed throughout the expansion; neither superheated liquid nor superheated vapor was ever present in the model The initial condition of the bubble contents in the calculational model was always saturated liquid at the initial average water temperature. Details of the actual early metastable state and the early nucleation and growth of embryonic bubbles were not included in the analysis. A.B. Reynolds G. Berthoud