ON THE DISTRIBUTION OF COOLING SURFACE ACROSS WATER PASSES IN SURFACE CONDENSERS

V. A. Bragin, Yu. A. Marakulin

(Presented by the Department of Thermal Power Installations)

In designing condensers for steam turbines and in their reconstruction, the cooling surface—or, what is the same thing, the number of tubes—across the water passes is recommended to be distributed approximately equally. This question is determined mainly by layout considerations [3]. As a result, cases are encountered, especially after the reconstruction of old condensers, in which the ratio of the number of tubes across the water passes deviates rather substantially from unity in both directions. Examination of reconstructed condensers shows that the ratio \(N_1/N_2\) varies within the limits from \(0.83 \div 0.87\) to \(1.15 \div 1.20\). Here \(N_1\) is the number of tubes located in the first water pass, and \(N_2\) is the same in the second pass.

An approach to the distribution of the number of tubes across the water passes based only on layout considerations leads to the fact that, in a number of cases, the features of heat exchange in individual parts of the cooling surface are forgotten. As a result, the effect of reconstruction is not fully achieved. It is known that the condenser surfaces by water passes, from the standpoint of heat-transfer intensity, operate under different conditions. Here, first of all, one should distinguish condensers with a series and a parallel arrangement of water passes relative to the steam flow. In both types of condensers, such a low-efficiency surface as the air cooler is usually placed in the first water pass, where the heat-transfer coefficient depends mainly on heat transfer on the steam–air mixture side. In condensers of the first type, the main cooling surface located in the first pass is also fed by a steam–air mixture with an already noticeable content of noncondensable gases, and therefore heat transfer on the steam side also plays a significant role here. In contrast, for the surface located in the second water pass (the zone of bulk condensation), heat transfer on the water side already has the decisive role. In addition, heat exchange in the indicated surfaces is affected by the drop in steam pressure along the path of the steam–air mixture, which determines the temperature difference between the steam and the cooling water. All these factors must be taken into account simultaneously with layout considerations for condensers of the first type.

Analysis of a number of reconstructed condensers shows that, from the standpoint of layout, it is almost always possible to adopt quite definite ratios \(N_1/N_2\) that take into account the above-described features of heat exchange in different sections of the cooling surface.

First of all, it is desirable to have ratios \(N_1/N_2\) somewhat greater than unity or, in the extreme case, close to unity. These recommendations, with respect to condensers with a sequential arrangement of the water passes relative to the steam flow, are not new [1, 2, 6].

The investigations [6], carried out on a two-pass heat exchanger with a horizontal tube bundle during steam condensation, confirm what has been stated above and show a rather interesting pattern in the dependence of the overall heat-transfer coefficient of the heat exchanger on the ratio \(N_1/N_2\). It turns out that the maximum value of the heat-transfer coefficient (Fig. 1) is observed at a ratio \(N_1/N_2 = 1.0 \div 1.4\). Here curve 1 corresponds to an absolute steam pressure of \(0.98\) bar, and curve

Fig. 1

2—to a pressure of \(0.84\) bar. At a pressure of \(0.98\) bar, a transition from the ratio \(N_1/N_2 = 0.8\) to \(1.0\) leads, other conditions being equal, to an increase in the heat-transfer coefficient of the heat exchanger by approximately a factor of \(1.05\). Bringing the ratio of the number of tubes to \(1.2\) increases the heat-transfer coefficient by a factor of \(1.065\). As the pressure in the heat exchanger decreases, the influence of the ratio of the number of tubes in the water passes on the heat-transfer coefficient increases. Within the range of variation of the ratio \(N_1/N_2\) from \(1.1\) to \(1.4\), the heat-transfer coefficient remains almost unchanged.

The heat-transfer features indicated above in different parts of the cooling surface are somewhat smoothed out in condensers with a parallel arrangement of the water passes relative to the steam flow, where the main cooling surfaces located in the first and second passes operate under approximately identical conditions. To determine the influence of the ratio \(N_1/N_2\) on the heat-transfer coefficient in condensers of the second type, various variants of a condenser of the 50-KTsS-4 type, differing in the ratio \(N_1/N_2\), were calculated. In this case the total cooling surface remained unchanged, and the principle of arranging the tube bundle was also preserved. The calculations were performed according to the method set forth in [3, 4, 5]. Initial data: cooling surface—3028 m\(^2\); the air-cooler surface constitutes \(10.5\%\) of the total surface; cooling-water flow rate—\(2.22\) m\(^3\)/s; design ratio \(N_1/N_2 = 1.15\); cooling-water temperature—\(15^\circ\)C; tube diameter—\(25/23\) mm; tube pitch—32 mm; active tube length—6650 mm; air inleakage into the system—0.005 kg/s. The ratio \(N_1/N_2\) was varied within the limits from \(0.8\) to \(1.5\). The results of the calculations are presented

in the form of the curve in Fig. 2, showing the dependence of \(\kappa_i/\kappa_0\) on \(N_1/N_2\). Here, as in Fig. 1*), \(\kappa_i\) is the mean heat-transfer coefficient of the condenser for an arbitrary ratio \(N_1/N_2\), and \(\kappa_0\) is the same for the design ratio \(N_1/N_2\). The curve in Fig. 2 shows a weak dependence of the heat-transfer coefficient on the ratio \(N_1/N_2\), although its character is approximately analogous to that of the curves in Fig. 1. Thus, when the ratio of the number of tubes in the water passes is changed within the range from 0.8 to

Fig. 2

1.3, the heat-transfer coefficient of the condenser increases by only 3–4%. The heat-transfer coefficient reaches its maximum value at the ratio \(N_1/N_2 = 1.2 \div 1.3\). At ratios \(N_1/N_2\) greater than 1.3, the heat-transfer coefficient begins to decrease, which is caused by an increase in the share in heat exchange of the cooling surface located in the first water pass, where the heat-transfer coefficient decreases as this surface increases and the cooling-water flow rate remains constant.

The weak dependence of \(\kappa_i/\kappa_0\) on \(N_1/N_2\) is explained by the fact that the heat-transfer coefficients of the main cooling surfaces of the first and second passes in condensers of the second type differ comparatively little from one another. In both surfaces, heat transfer on the water side plays approximately the same role. Therefore, a change in \(N_1/N_2\) affects the heat-transfer coefficients of these surfaces with almost the same intensity, but only in different directions. If the mean heat-transfer coefficient, for example, for the surface of the second pass increases, then for the surface of the first pass it decreases. The overall heat-transfer coefficient of the condenser, within certain limits of variation of \(N_1/N_2\), changes little, as is reflected in Fig. 2. The influence of \(N_1/N_2\) will be the smaller, the better the operation of the main tube bundles is organized, and the more effective the heat-exchange process in the air cooler is.

Taking this into account, for modern condensers with a parallel arrangement of the water passes relative to the steam flow, it may be recommended that the ratios \(N_1/N_2\) be chosen mainly on the basis of layout considerations. At the same time, the hydraulic resistance of the condenser should be taken into account, although the latter changes only insignificantly within small limits of variation of the ratio \(N_1/N_2\).

*) In Fig. 1, curve 2 for the dependence \(\kappa_i/\kappa_0\) is constructed relative to the design value \(\kappa_0\) at a steam pressure of 0.98 bar.

References

1. M. I. Alyamovskii, A. A. Promyslov. Shipboard condensing installations, Sudpromgiz, 1962.

2. L. D. Berman, I. K. Grishuk. Guidelines for the reconstruction of steam-turbine condensers, GEI, 1954.

3. I. N. Kirsanov. Condensing installations. Energiya, 1965.

4. L. D. Berman. Problems of the thermal calculation of steam-turbine condensers. Energomashinostroenie, No. 1, 1961.

5. L. D. Berman, S. N. Fuks. Calculation of surface heat-exchange apparatuses for condensing steam from a steam–air mixture. Teploenergetika, No. 7, 1959.

6. E. N. Shadrin, V. A. Bragin, B. F. Kalugin, Yu. A. Makaruk. On the influence of the distribution of the cooling surface among water passes on the heat-transfer coefficient during steam condensation in a horizontal tube bundle. Scientific Transactions of OMIIT, vol. 70 (Problems of Thermal Power Engineering), 1967.