Numerical simulation of transonic flow of wet steam in nozzles and turbines

Abstract

The paper presents several modifications of the flow model published in Štastný and Šejna (Proceedings of the 12th international conference of the properties of water and steam, Begel House, pp 711–719, 1995). Modifications related to the droplet growth model and the equation of state and their implementation into numerical code are described. The effect of droplet size spectra of incoming wet steam is also discussed. Numerical results of three-dimensional flow of wet steam in a turbine cascade show the effect of surface tension correction.

Appendix

The system of transport equations for the one-dimensional case with the variable cross-sectional area $A(x)$ reads

$$\begin{aligned}&\displaystyle \dfrac{\partial (A(x)\mathbf{W})}{\partial t} +\dfrac{\partial (A(x)\mathbf{F})}{\partial x}=\mathbf{P}+A(x)\mathbf{Q},&\\&\displaystyle \mathbf{W}=\left[\begin{array}{c} \rho \\ \rho u \\ e \\ \rho \chi \\ \rho Q_2 \\ \rho Q_1 \\ \rho Q_0 \end{array}\right],\quad \mathbf{F}=\left[\begin{array}{c} \rho u \\ \rho u^2+p \\ (e+p)u \\ \rho \chi u \\ \rho Q_2 u \\ \rho Q_1 u \\ \rho Q_0 u \end{array}\right],\quad \mathbf{P}=\left[\begin{array}{c} 0 \\ p A^{\prime }(x) \\ 0 \\ 0 \\ 0 \\ 0 \\ 0 \\ \end{array}\right],&\nonumber \\&\displaystyle \mathbf{Q}=\left[\begin{array}{c}0 \\ 0 \\ 0 \\ \frac{4}{3}\pi r_c^3 J \rho _l +4 \pi \rho \left(\int \nolimits _{0}^{\infty } r^2 N(r) \dot{r}(r) dr\right) \rho _l \\ r_c^2 J + 2 \rho \left(\int \nolimits _{0}^{\infty } r N(r) \dot{r}(r) dr\right) \\ r_c J + \rho \left(\int \nolimits _{0}^{\infty } N(r) \dot{r}(r) dr\right)\\ J \end{array}\right].\nonumber&\end{aligned}$$

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