Shock Waves

, Volume 28, Issue 2, pp 321–333 | Cite as

A reduced theoretical model for estimating condensation effects in combustion-heated hypersonic tunnel

  • L. Lin
  • X. Luo
  • F. Qin
  • J. Yang
Original Article


As one of the combustion products of hydrocarbon fuels in a combustion-heated wind tunnel, water vapor may condense during the rapid expansion process, which will lead to a complex two-phase flow inside the wind tunnel and even change the design flow conditions at the nozzle exit. The coupling of the phase transition and the compressible flow makes the estimation of the condensation effects in such wind tunnels very difficult and time-consuming. In this work, a reduced theoretical model is developed to approximately compute the nozzle-exit conditions of a flow including real-gas and homogeneous condensation effects. Specifically, the conservation equations of the axisymmetric flow are first approximated in the quasi-one-dimensional way. Then, the complex process is split into two steps, i.e., a real-gas nozzle flow but excluding condensation, resulting in supersaturated nozzle-exit conditions, and a discontinuous jump at the end of the nozzle from the supersaturated state to a saturated state. Compared with two-dimensional numerical simulations implemented with a detailed condensation model, the reduced model predicts the flow parameters with good accuracy except for some deviations caused by the two-dimensional effect. Therefore, this reduced theoretical model can provide a fast, simple but also accurate estimation of the condensation effect in combustion-heated hypersonic tunnels.


Homogeneous condensation Combustion-heated hypersonic tunnel Theoretical model 



This work was sponsored by the Natural Science Foundation of China (11172292, 11402218, 21476221).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.School of Environment and ResourceSouthwest University of Science and TechnologyMianyangPeople’s Republic of China
  2. 2.Advanced Propulsion Laboratory, Department of Modern MechanicsUniversity of Science and Technology of ChinaHefeiPeople’s Republic of China

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