On the Head of Circulation Pumps of Thermal Power Plants
Abstract Generated abstract
This article examines the reduction of circulating pump head in large thermal power plants, where each meter of head can impose substantial auxiliary power consumption. It argues that, when geometric lift and system resistance are minimized, condenser hydraulic resistance becomes a major component of total head, making the choice between single-pass and two-pass condensers economically significant. Using simplified boundary conditions based on equal cooling surface and equal pumping energy, the paper derives relations for identifying when each condenser type is preferable under given local design conditions. It proposes that design organizations apply these approximate calculations to select condenser configurations more rationally, thereby reducing pump head and in-house energy use.
Full Text
On the Head of Circulating Pumps of Thermal Power Plants
V. A. Bragin
Recently, in the design of stations, much attention has been given to reducing the head of circulating pumps, which helps reduce expenditures for auxiliary needs. This question acquires especially great importance for stations with capacities of 1.2–2.4 million kW. Calculations show that at such stations each meter of pump head causes an expenditure of electric power for auxiliary needs on the order of 600–1180 kW.
It may be considered that, for large condensing stations, the head of the circulating pumps consists of the following two main parts: the geometric height of water lift and the hydraulic resistance of the entire system, except for the condenser, and, finally, the hydraulic resistance of the condenser itself. The magnitude of the first part of the head depends on the degree to which the main building is brought close to the source of water supply, the corresponding lowering of the condenser room, the use of a rational type of water supply to the turbine hall, and, for different stations, ranges within 3–7 m, reaching in individual cases 10–13 m.
The second part of the head—the hydraulic resistance of the condenser—depends mainly on the number of water passes and ranges from 2.7 to 5 m. Thus, for properly designed stations, when the total pump head is relatively small, the main share of it is the hydraulic resistance of the condenser. The ratio of the first part of the head to the second, for different conditions, is
\[ \varphi = \frac{\Delta H}{H_k} \ge 0.3 : 2.8. \]
Therefore, in design it is necessary to pay considerable attention to the correct choice of condenser. Unfortunately, at present a techno-economic choice of the number of water passes is not made because of the complexity of the calculations. Design organizations, when developing the water-supply system, adopt those condensers that are supplied by the plant together with the turbines.
For this reason, at present two-pass condensers have become most widespread, which in a number of cases in the design of stations does not give the correct solution and subsequently leads to excessive expenditures of electric power for auxiliary needs, especially at small \(\varphi\).
It appears most correct that, when developing a water-supply system, design organizations should work out the question of choosing a rational type of condenser as applied to specific local conditions, which the factories cannot do. As a first approximation, the question of the type of condenser can be solved on the basis of the following comparatively simple considerations [1]. If there are no restrictions of any kind for the turbine, a single-pass or two-pass condenser may be used. Condensers may be designed so that there will be observed: a) equality of their cooling surfaces, to which correspond the temperature heads of the single-pass condenser \(\Delta t_{k1}^{n}\) and of the two-pass condenser \(\Delta t_{k2}\); b) equality of the energy expenditures for pumping the cooling water, to which correspond the temperature heads \(\Delta t_{k1}^{v}\) for single-pass and \(\Delta t_{k2}\) for two-pass condensers.
These two conditions make it possible approximately to establish the regions of rational use of single-pass \((z=1)\) and two-pass \((z=2)\) condensers. Indeed, if the inequality
\[ \Delta t_{k1}^{v} > \Delta t_{k1} > \Delta t_{k1}^{n}, \]
is satisfied, then it is more advantageous to use a condenser with \(z=1\); with the reverse inequality, \(z=2\). The indices “\(n\)” and “\(v\)” indicate that the given quantity refers to the condition of the lower or upper boundary. The relation between the temperature heads of single-pass and two-pass condensers for the boundary conditions is readily established. For this purpose it may be assumed that the principal design characteristics of the condensers and the conditions of their operation are identical. Then, using the well-known expression of Doctor of Technical Sciences L. D. Berman for the heat-transfer coefficient,
\[ k = 3500 \cdot a \cdot \varphi_{w} \cdot \varphi_{t} \cdot \varphi_{z} \cdot \varphi_{d}, \]
we obtain the relation for the lower boundary
\[ B_{n}\, \frac{\left(\delta-\Delta t_{k1}^{n}\right)^{1-x}} {\ln \dfrac{\delta}{\Delta t_{k1}^{n}}} = \frac{\left(\delta-\Delta t_{k2}\right)^{1-x}} {\ln \dfrac{\delta}{\Delta t_{k2}}} \]
and for the upper boundary
\[ \frac{B_{v}} {\ln^{\frac{2}{1-x}} \dfrac{\delta}{\Delta t_{k2}}} = \frac{1} {\left[ (1-\psi)\dfrac{\delta-\Delta t_{k1}^{v}}{\delta-\Delta t_{k2}^{v}}-\psi \right]\, \ln^{\frac{2}{1-x}} \dfrac{\delta}{\Delta t_{k1}^{v}}} . \]
Here the notation is:
\[ \delta = t_{k}-t_{1} \]
—the difference between the saturation temperature of the steam corresponding to the pressure in the condenser and the temperature of the cooling water at the inlet;
\[ \psi=\frac{\Delta H_{z}}{H_{k2}} \]
—the ratio of the hydraulic resistance of the entire system, excluding the condenser, to the hydraulic resistance of the condenser in the case \(z=2\);
\[ B_{n}=0.5^{x}\cdot \left(1-0.1\cdot \frac{35-t_{1}}{35}\right), \]
\[ B_{v}=8\cdot \frac{2^{\frac{2x}{1-x}}} {\left(1-0.1\cdot \dfrac{35-t_{1}}{35}\right)^{\frac{2}{1-x}}}, \qquad x=0.096\cdot(1+0.15\cdot t_{1}) \]
—coefficients depending on the initial temperature of the cooling water.
Using the equations obtained, in Fig. 1, for example, for \(p_k = 0.03\) ata and \(t_1 = 10^\circ\mathrm{C}\), we construct a graph by means of which it is possible, for the specific conditions of the plant being designed, to determine the optimal number \(z\) of water passes. For this purpose it is necessary to make an approximate calculation of \(H_{k2}\) and \(\Delta H_2\) for the case of using a two-pass condenser, the type most often supplied by the manufacturer with the turbine. Then, from \(\Delta t_{k2}\) and \(\psi\), the presence or absence of a zone in which it is advantageous to use \(z = 1\) is established.
Fig. 1.
Such approximate calculations can always be carried out by the design organization and make it possible to take the correct approach to selecting the type of condenser and thereby to achieve a reduction in the head of the circulating pumps and, consequently, in the consumption of energy for in-house needs.
It was indicated above that the derivation of the formulas presented was made under the assumption of identical structural forms of the condensers being compared, which, of course, is incorrect in a number of cases. The proposed method can be used in an analogous way for comparing condensers, for example, with different dimensions of condenser tubes, etc.
REFERENCES
- V. I. Bulanin. On single- and two-pass surface condensers of steam-turbine installations. TsKTI, book 7, Condensers of Steam Turbines, 1947.