CFD modeling of condensation process of water vapor in supersonic flows
Introduction
The condensation phenomenon of vapor plays an important role in various industries, such as the steam flow and water vapor in nozzles [1], turbines [2], ejectors [3], thermos-compressors [4] and supersonic separators [5], [6], [7], [8], [9]. Theoretical and experimental studies have been conducted for the condensation process in supersonic flows, focusing on the nucleation theory, droplet size, latent heat [10], [11], [12]. Numerical simulations have been performed to predict the condensing flow with the development of the computational fluid dynamics (CFD) for several decades.
Hill [13], Noori Rahim Abadi et al. [14] studied the nucleation process of wet steam flows in nozzles at low and high pressure, respectively. White and Young predicted the condensing process using Eulerian-Lagrangian and time-marching methods [15]. Gerber [16] developed the Eulerian-Lagrangian and Eulerian-Eulerian two-phase models for predicting the condensation flow with the classical nucleation theory. The effects of friction factor on the condensation flows in the Laval nozzles were performed using the single fluid model by Mahpeykar and Teymourtash [17], and Jiang et al. [18]. Two-dimensional simulation of the condensing steam was calculated in converging-diverging nozzles using a Jameson-style finite volume method on an unstructured and adaptive triangular mesh [19]. Yang and Sheng [20] described a conservative two-dimensional compressible numerical model for the non-equilibrium condensing of the steam flow based on the classical nucleation theory and the Virial type equation of state. The effect of the expansion rate on the steam condensing flow through a converging-diverging nozzle was studied numerically by Nikkhahi et al. [21]. The steam condensing flow was modeled through the Laval nozzles at low and high inlet pressures by means of the single-fluid model [22]. The Eulerian-Eulerian approach was adopted for modeling the condensing steam flow, and the simulation was conducted on the commercial ANSYS FLUENT 12.1 platform [23].
The condensation phenomenon of water vapor in supersonic flows is still not understood very well as a result of the complex phase change process. Especially, the numerical simulation depends on various nucleation theories and droplet growth models. In this paper, the Euler-Euler two-phase flow model is developed to predict the spontaneous condensing phenomenon in the Laval nozzle. The modified internally consistent classic nucleation theory and Gyarmathy’s droplet growth model are employed to perform the simulation cases. The numerical approach is validated with experimental data. The condensation process of water vapor is numerically analyzed in detail, including the nucleation rate, droplet numbers, droplet radius and droplet fraction.
Section snippets
Governing equations
For the water vapor condensation in a Laval nozzle, the fluid flow is governed by partial differential equations describing the conservation of mass, momentum and energy, as shown in Eqs. ((1), (2), (3)).where ρ, u, p and H are the density, velocity, pressure and total enthalpy, respectively. λeff and T are the effective heat conductivity and temperature. The source terms, Sm, , ,
Results and discussion
The validation, verification and implementation of the numerical studies are conducted using the geometry and experimental data from the available literature by Moses and Stein [12]. In their studies, the Laval nozzle was employed to experimentally study the condensation process of water vapor in supersonic flows. The nozzle throat is located at x = 82.2 mm with the dimension of 10.0 mm (height) × 10.0 mm (depth). A sketch of the geometry of the Laval nozzle used in the experiments is described in
Conclusions
The condensation process of water vapor in the Laval nozzle is simulated numerically with the nucleation and droplet growth theories. The results show that the latent heat is released to heat into the vapor phase during the spontaneous condensation, leading to the jump of the condensing parameters. The degree of supercooling can reach a maximum value of about 33 K and correspondingly the spontaneous condensation occurs in a very short time. The droplet numbers also rapidly rise from 0 to 1.12 × 10
Acknowledgements
This work was supported in part by the Natural Science Foundation of Jiangsu Province, China (No. BK20150270), and the General Program of Natural Science Research Project of Jiangsu Province Universities and Colleges (No. 15KJB440001). C. Wen acknowledges the support of the H.C. Ørsted fellowship co-funded by Marie Curie Actions at the Technical University of Denmark, DTU.
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