On Method Of Moments For Condensation Flow And Its Applications

The compressible flow with the condensation of vapor has many important appli-cations in the industrial production and life.The latent heat released by the condensation will influence the structure of the flow field and the change of the flow field will affect the process of the condensation in turn.The coupling of the condensation and the com-pressible flow makes the problem more complex.The study of the vapor condensation has a long history.With the use of computers,numerical studies provide new methods for the problems which are difficult to investigate theoretically or experimentally be-fore.Among various numerical methods concerning the compressible flow with vapor condensation,the Method of Moments is a method taking into account the computa-tional efficiency and the information of the droplet distribution.Compared with the Quadrature Method of Moments and the Direct Quadrature Method of Moments,the conventional Method of Moments,i.e.Hill's Method of Moments,is simpler and easi-er to be integrated to numerical programs.A lot of practice also shows its accuracy.The compressible flow with the condensation of vapor is investigated using the conventional Method of Moments in the present work,which are briefly introduced as follows:Firstly,the conventional Method of Moments is used to study the homogeneous condensation of vapor in a Prandtl-Meyer(PM)expansion flow.Two configurations are taken into account:a bounded corner expansion and an upper unbounded corner expansion.For the former configuration,the numerical results show the condensation shock turns from the steady state to the unsteady state with the increasing of the satura-tion ratio of the incoming flow.For the unbounded PM flow,the wave pattern exhibits a periodic two-dimensional distribution.To be specific,the condensation shock is em-bedded in the bounded PM flow and concave with respect to the incoming flow for the low saturation ratio case.The shock is not connected to the corner of a turning point.The influence of the corner is investigated by employing another configuration with a rounded corner instead of a sharp corner.The result shows the influence is small if the flow near the corner is neglected.With the initial saturation ratio increasing,the self-oscillation shock motion appears.The cause of the oscillation is discussed.The process of the oscillation and the frequency are analyzed.For the unbounded PM flow,the periodic two-dimensional wave pattern is due to the complex interaction between the self-inhibition of the condensation and the expansion flow.Secondly,the conventional Method of Moments is extended to deal with the prob-lem of the heterogeneous condensation.The heterogeneous nucleation model is simpli-fied by introducing an "instantaneous-activating model".With this hypothesis,the process of the liquid film formed on the particle surface is ignored.The particle with radius bigger than the critical radius will grow as a droplet.This hypothesis is adopt-ed for the inert particles with radii less than one hundred nanometers.Integrating the heterogeneous nucleation model to the moment equations,the Method of Moments for the heterogeneous condensation is formed.The Smolders' heterogeneous condensa-tion experiment is simulated using the new method.The numerical results show good agreements with those of the experiment,which indicates the validation of the new method.After that,this method is applied to a shock tube problem with heterogeneous condensation and a parametric study is made.Finally,an extended Method of Moments is formed to deal with the condensation flow considering the mass,momentum and energy exchange between the phases.The moment equations of the conventional Method of Moments are rewritten based on the mean velocity of the liquid phase.The gas phase and the liquid phase are treated sepa-rately.This method is applied to study the vortex flow with homogeneous condensation,including a composite Rankine vortex and a starting vortex shedding from a bevel cut.The generation process of the condensation in the vortex is investigated as well as the liquid phase distribution.The numerical results show the droplets formed by the vapor condensation will leave the core region of the vortex due to the centrifugal forces.This characteristic cannot be obtained by the conventional Method of Moments.But the re-sults of the new method still show some differences from those of the experiments.It needs further improvement.In summary,the works in the present paper deepen the understanding of the flow with vapor condensation.The conventional Method of Moments is extended to deal with the heterogeneous condensation problems and the problems with strong interaction between the phases.These works laid the foundation for the further researches.