ON THE INTENSITY OF HEAT TRANSFER DURING FLASHING IN THE DISCHARGE OF BOILING WATER

A. A. GURCHENOK

(Presented by the scientific seminar of the Department of ATPP)

Recently, in thermal power engineering, interest has increased in studying the transient and regulating properties of processes occurring in machines and apparatuses. Among the processes insufficiently studied in this area is the process of discharge of boiling water. Conducting such studies in a moving flow is difficult, and therefore it is of interest to create and study processes analogous in heat-transfer intensity under stationary boiling conditions.

In the present work, on the basis of available data on experimental and theoretical study of the process of discharge of boiling water, a calculation method and numerical values of the intensity of the heat-transfer process have been obtained for one of the regimes investigated by the author.

As is known, the process of discharge of boiling water proceeds with deviation from the equilibrium process of adiabatic expansion. Such a deviation is explained by the incomplete completion of the vaporization process owing to the excessively short residence time of the liquid particles inside the nozzle. In [1] it is shown that the nonequilibrium process of discharge of boiling water can be constructed in a \(P—V\) diagram (Fig. 1). In this case the curve of the process is constructed as a function of the degree of completion of the vaporization process \(i\). The value of \(i\) is defined as the ratio

Fig. 1

\[ i=\frac{t_1-t}{t_1-t_2}, \tag{1} \]

where \(t_1, t_2\) are the boiling temperatures, respectively, at the initial \(P_1\) and final \(P_2\) pressures;

\(t\) is the temperature in the flow at the outlet section. If vapor formation in the flow does not occur, then

\[ t=t_1,\quad \text{whence } \xi=0, \]

if the process is completed, then

\[ t=t_2,\quad \text{whence } \xi=1. \]

Using the graphs on the \(P\)—\(V\) diagram and projecting the points of the beginning and end of the process onto the pressure axis, we obtain the figure \(12_i34\) \((i=0,\ldots=100\%)\), the area of which represents, to scale, the magnitude of the increase in kinetic energy in the discharge process

\[ S_{12_i,34}\cdot M_f=\frac{c_{\mathrm{в}}^2-c_{\mathrm{н}}^2}{2}. \tag{2} \]

From (2) a relation is obtained for determining the discharge velocity

\[ c_{\mathrm{в}}=\sqrt{2S_{12_i,34}\cdot M_f+c_{\mathrm{н}}^2}. \tag{3} \]

For any cross section of the flow, according to the continuity law, the relation

\[ \frac{c_{\mathrm{н}}}{v' f_{\mathrm{н}}}=\frac{c_{\mathrm{в}}}{v f_{\mathrm{в}}}; \tag{4} \]

is satisfied; for the case of discharge from cylindrical nozzles, expression (4) takes the form

\[ \frac{c_{\mathrm{н}}}{v'}=\frac{c_{\mathrm{в}}}{v}. \tag{5} \]

A distance equal to the length of the nozzle will be traversed by the flow in a time interval

\[ \tau=\frac{l}{c_{\mathrm{cp}}}\ \text{sec}. \tag{6} \]

In [1], from a comparison of experimental data on the flow rate of boiling water during discharge through cylindrical nozzles of different lengths with the results of calculations using a \(P\)—\(V\) diagram, a dependence was found of the degree of completion of the vapor-formation process on the length of the nozzles and, consequently, on the residence time of the liquid particles inside the nozzles. Using the indicated dependence, one can determine the time interval during which the vapor-formation process reaches a specified degree of completion.

With some approximation it may be assumed that inside the nozzle the velocity changes according to the law of uniformly accelerated motion; then the mean value of the velocity will be equal to

\[ c_{\mathrm{cp}}=\frac{c_{\mathrm{н}}+c_{\mathrm{в}}}{2}, \tag{7} \]

whence

\[ \tau=\frac{2l}{c_{\mathrm{н}}+c_{\mathrm{в}}}. \tag{8} \]

The procedure for calculating the intensity of vapor formation is indicated below. For each value of the degree of completion of the vapor-formation process, the magnitude of the utilized heat drop \(\Delta i\), expended on the formation of the vapor phase, can be determined. For the case of nonequilibrium expansion, the thermal parameters of the flow will be characterized by the degree of superheating of the flow and by the corresponding saturation pressure of the medium.

flow. From the indicated parameters, the enthalpy value of the liquid phase of the flow is determined. Thus, the magnitude of heat transfer at a degree of completion of the vaporization process \(\xi\) will be equal to

\[ \Delta i = i_{p_1} - i_{p_{\xi,t}} . \tag{9} \]

The ratio

\[ q=\frac{\Delta i}{\tau} \tag{10} \]

characterizes the magnitude of the intensity of heat release occurring inside the packing in the flow of boiling water. Table 1 presents the results of determining the values of \(q\) from the data of [1]. As can be seen from the table, the magnitude of the intensity of vaporization is approximately the same for all outflow regimes. Consequently, the degree of completion of the vaporization process depends strongly on the residence time of the liquid particle inside the packing. The magnitude of the intensity of the vaporization process is very high. The obtained numerical values of the vaporization intensity make it possible, when modeling the boiling process under stationary conditions, to determine the required capacity of the heat-supply sources.

Table 1

Literature

1. A. A. Gurchenok. On the calculation of parameters in the flow during the outflow of boiling water. Izvestiya TPI, vol. 110, 1962.

2. M. P. Vukalovich. Thermodynamic Properties of Water and Steam. Mashgiz, 1958.