Development of a benchmark solution in compressible liquid flows: analytical solution to the water shock tube problem

Autor: A. Salih, Jishnu Chandran R
Rok vydání: 2021
Předmět:
Zdroj: Journal of Thermal Analysis and Calorimetry. 147:5279-5292
ISSN: 1588-2926
1388-6150
DOI: 10.1007/s10973-021-10871-7
Popis: This paper discusses the development of an analytical solution to a pure liquid shock tube problem with water as the working fluid. The solution procedure associated with classical gas shock tube problem has been extended for the case of a compressible liquid. The analytical model employed accounts for the compressibility effects in liquid water using the high-accuracy Modified NASG equation of state. The solution methodology presented in this work is unique in that it provides comprehensive modeling of the complete physics of the water shock tube problem. The work also demonstrates the applicability of analytical solution over a wide range of pressures and temperatures. The solution profiles of the water shock tube problem and the air shock tube problem for the same thermodynamic conditions and shock tube geometry were compared and salient features were discussed. The water shock tube problem is also solved numerically in this study, with a more elaborate PDE-based mathematical model, using the AUSM $$^+$$ -up numerical algorithm. The in-depth comparative analysis shows the close agreement of the numerical results with the analytical solution developed. The analytical solution to the liquid shock tube offers multiple flow features, such as shock wave, expansion fan, and contact discontinuity in the solution. These features make the proposed analytical solution a powerful benchmarking tool that could test the various computational capabilities of codes developed for simulation of compressible liquid flow transients. The solution procedure presented in this work is also flexible enough for application to any liquids provided that the relevant equations of state are available.
Databáze: OpenAIRE
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