Dimensionless Profiles of Temperature and Steam Mass Fraction in Flows of Steam-Air Mixtures on a Flat Plate

Wall functions are generally used in a turbulent analysis with a computational fluid dynamics (CFD) code and large computation cells. The logarithmic law based on the analogy between momentum, energy, and mass transfer is widely used in wall functions for turbulent flows, but its validity in the turbulent boundary layer has not been confirmed for dimensionless profiles of temperature and steam mass fraction in flows of steam and noncondensable gases. In this article, therefore, we evaluated dimensionless profiles of temperature and steam mass fraction in flows of steam and air on a flat plate by using existing data. From the heat and mass transfer equations at the condensation surface based on the gradient of temperature or steam mass fraction, we showed that the convection heat flux q_conv (which is used for the definition of the dimensionless temperature T⁺) should include the term of condensate mass flux m_s and that the dimensionless steam mass fraction Y_s⁺ should be a function of the dimensionless distance y⁺ (= u_τ y/ν where u_τ is the friction velocity), the Schmidt number Sc and the air mass fraction (1−X_s). Values obtained from the newly defined T⁺ and Y_s⁺ and the existing data agreed relatively well with the linear function near the viscous sublayer (a few data points were there) but were much smaller than the existing logarithmic law due to condensation in the turbulent boundary layer (i.e., mist generation). On the other hand, the T⁺ and Y_s⁺ values obtained by using the local Nusselt number Nu_y and the local Sherwood number Sh_y (which were proposed in our previous study), respectively, agreed well with the logarithmic law.