JakobCHR.com

Quick Navigation:
 

Personal:

 Go to Home
 MS Research
 PhD Research
 Curriculum Vitae

General:

 Linux

Soon to come:

 Matlab
 On-line Stores
 Cycling
 Medicine & Health
 LaTeX
 OOP & C++
 Sony PCM-R500 DAT

Steam separator assembly,

The mass conservation for the steam separator (and dryer) assembly can be stated with aid of Figure 5.2 which considers the separator as a black box.

The vapor which accompanies the liquid at the liquid outlet of the steam separator is accounted for by defining a carry-under fraction, ${\mbox{CU}}$ [--],

$${\mbox{CU}} \;\hbox{$=$\kern-0.68em\raise1.1ex \hbox{$\scr... ...}$}_{g_2}}{\mbox{$\dot{m}$}_{\ell_2} + \mbox{$\dot{m}$}_{g_2}}$$ (5.7)

where the mass flow rates in [kg/s] are defined in Figure 5.2.

Similarly, the fraction of liquid which accompanies the vapor at the vapor outlet is accounted for by the carry-over fraction, ${\mbox{CO}}$ [--], defined by

$${\mbox{CO}} \;\hbox{$=$\kern-0.68em\raise1.1ex \hbox{$\scr... ..._{\ell_1}}{\mbox{$\dot{m}$}_{\ell_1} + \mbox{$\dot{m}$}_{g_1}}$$ (5.8)

We will assume that ${\mbox{CU}}$ and ${\mbox{CO}}$ are specified by the user.

With ${\mbox{CU}}$, ${\mbox{CO}}$, $\mbox{$\dot{m}$}_\ell$ and $\mbox{$\dot{m}$}_g$ at hand the four mass flow rates at the separator outlets are calculated by the following expressions

$$\mbox{$\dot{m}$}_{\ell_1} = \left[ \frac{1-{\mbox{CO}}}{{\m... ...rac{{\mbox{CU}}}{1-{\mbox{CU}}}\right) \mbox{$\dot{m}$}_\ell )$$ (5.9)

$$\mbox{$\dot{m}$}_{g_2} = \mbox{$\dot{m}$}_g - \frac{1-{\mbox{CO}}}{{\mbox{CO}}} \mbox{$\dot{m}$}_{\ell_1}$$ (5.10)

$$\mbox{$\dot{m}$}_{\ell_2} = \mbox{$\dot{m}$}_\ell - \mbox{$\dot{m}$}_{\ell_1}$$ (5.11)

$$\mbox{$\dot{m}$}_{g_1} = \mbox{$\dot{m}$}_g - \mbox{$\dot{m}$}_{g_2}$$ (5.12)

where we have assumed ${\mbox{CO}}\ne 0$ and ${\mbox{CU}}\ne 1$. For the physical acceptable case of ${\mbox{CO}}=0$ we have

$$\begin{eqnarray*} \mbox{$\dot{m}$}_{\ell_1} &=& 0 \\ \mbox{$\dot{m}$}_{g_2} &... ...dot{m}$}_{g_1} &=& \mbox{$\dot{m}$}_g - \mbox{$\dot{m}$}_{g_2} \end{eqnarray*}$$

$\parbox{1.50cm}{\begin{eqnarray} \end{eqnarray}}$

As stated previously it is very difficult to construct a theoretical model of a steam separator and this is perhaps the reason for the very limited amount of literature which treats the subject.

The most important separator characteristic in regard to natural circulation BWRs is the irreversible pressure drop induced by the separator. It should be noted that two pressure losses are commonly used to describe the performance of the separator. One pressure loss, $\Delta p_v$, is measured from the inlet to the steam outlet while another pressure drop, the liquid pressure drop $\Delta p_\ell$, is measured from the inlet to the pressure at the liquid surface outside the separator. It is often $\Delta p_v$ which is specified but in a pressure calculation of the closed loop we have to use the liquid pressure drop, $\Delta p_\ell$, which may be considerably less than $\Delta p_v$ according to Rouhani [32, p. 294]. Owing to the lack of detailed information on the steam separator performance we were forced to use the approach of the authors of the NATBWR code [41]. They model the irreversible liquid pressure drop, $\Delta p_\ell$ [Pa], by the expression

$$\Delta p_\ell = - \frac{z_{\mbox{\protect\scriptsize sep,to... ....5ex]{\raisebox{-2.2pt}[0pt][0ex]{\scriptsize 3}}}^2}{2\rho_f}$$ (5.13)

where $z_{\mbox{\protect\scriptsize sep,top}}$ and $z_{\mbox{\protect\scriptsize sep}}$ [m] are elevational data (see Figure 5.1), $K_{\framebox[1.5ex]{\raisebox{-2.2pt}[0pt][0ex]{\scriptsize 3}}}$ [--] is the loss coefficient of the separator, D_e [m] is the hydraulic equivalent diameter (see (6.82) p. ), $f_{\ell 0}$ [--] is the single-phase friction factor (see section 6.7.2.2), $\phi_{\ell 0}^2$ [--] is the two-phase friction multiplier (see section 6.7.2.2) and $\rho_f$ and $\rho_g$ [kg/${\mbox{m}}^3$] are the densities of liquid and vapor at saturation.

In addition to the irreversible pressure change we calculate the elevation pressure change, $\Delta p_{\mbox{\protect\scriptsize el}}$ [Pa], in the following manner

$$\Delta p_{\mbox{\protect\scriptsize el}} = -g(z_{\mbox{\pro... ...box{$<\!{\alpha}\!>$}_{\mbox{\protect\scriptsize sep}}\rho_g )$$ (5.14)

where g [m/${\mbox{s}}^2$] is the gravitational acceleration and we have assumed that the void fraction along the steam separator flow path $\mbox{$<\!{\alpha}\!>$}_{\mbox{\protect\scriptsize sep}}$ is constant along the separator and equal to the inlet void fraction which is taken as the value at the outlet of the riser, ie

$$\mbox{$<\!{\alpha}\!>$}_{\mbox{\protect\scriptsize sep}} = ... ...ramebox[1.5ex]{\raisebox{-2.2pt}[0pt][0ex]{\scriptsize 2}}},e}$$ (5.15)

The calculation of the elevation pressure drop is performed in an arbitrary fashion since the void fraction increases along the separator as more and more of the liquid is removed.

The total pressure change associated with the steam separator, $\Delta p_{\framebox[1.5ex]{\raisebox{-2.2pt}[0pt][0ex]{\scriptsize 3}}}$ [Pa], is the sum of the irreversible and elevation pressure changes, ie given by

$$\Delta p_{\framebox[1.5ex]{\raisebox{-2.2pt}[0pt][0ex]{\scr... ...}}} = \Delta p_\ell + \Delta p_{\mbox{\protect\scriptsize el}}$$ (5.16)

where $\Delta p_\ell$ and $\Delta p_{\mbox{\protect\scriptsize el}}$ are given by (5.14) and (5.15) respectively.

  Contents   Index  
 
 
 

Top Quality Developed with Danish Brain Power