Efficiency of the Stationary Part in Utilizing the Heat of Exhaust Steam from Steam Locomotives

I. N. BUTAKOV

Let us first determine the efficiency of the stationary part when using the heat of the exhaust steam of steam locomotives, in relation to the amount of heat arriving at the depot with the thermal accumulators. We shall proceed from the movement of 48 pairs of trains per day, when in one hour \(4 \cdot 5 \cdot 10^4 = 2 \cdot 10^5\) kg of hot water at \(95^\circ\mathrm{C}\) enters the depot, with the distance between depots being 130 km. Thus, the initial data adopted are those that figured in the author’s article published in No. 7 of Vestnik inzhenerov i tekhnikov for 1947.

One may write:

\[ \frac{860 \cdot \mathcal{E} + W}{\eta'_{cm}} = 95 \cdot 2 \cdot 10^5 \cdot 8760 = 166 \cdot 10^9 \ \text{cal/year} \tag{1} \]

Here \(\mathcal{E}\) is the output in kWh per year by the vacuum turbine of the utilization installation; \(W\) is the number of calories per year supplied to heat consumers, including soil heating in glass-covered market gardens; \(\eta'_{cm}\) is the overall efficiency of the stationary part of the utilization installation.

From expression (1) we have

\[ \eta'_{cm} = \frac{\mathcal{E}\left(1 + W/860\mathcal{E}\right)} {194 \cdot 10^6} \tag{2} \]

Figure 1 gives a nomogram demonstrating the dependence of \(\eta'_{cm}\) on the energy coefficient \(W/860\mathcal{E}\). This dependence is rectilinear: a family of straight lines is obtained for different values of \(\mathcal{E}\).

From the above-mentioned article it is seen that, for the particular example analyzed there,

\[ W = 8.5 \cdot 8760 = 74600 \cdot 10^6 \ \text{cal/year} \]

and

\[ \mathcal{E} = \frac{500 + 110}{2} \cdot 8760 = 2.628 \cdot 10^6 \ \text{kWh/year}. \]

Then \(\eta'_{cm}=0.46\), which is also obtained from Fig. 1, bearing in mind that the energy coefficient is

\[ \frac{W}{860\mathcal{E}} = \frac{74600}{860 \cdot 2.63} \simeq 33. \]

To determine \(\eta''_{cm}\)—the absolute efficiency of the stationary part of the installation with respect to the heat of the fuel burned during the year in the furnaces of steam locomotives—for one depot we have

\[ \eta''_{cm} = \frac{95 \cdot P_0 \cdot n \cdot 8760 \cdot \eta'_{cm} \cdot 10^4} {v_{mk} \cdot L \cdot Q \cdot n \cdot 7000 \cdot 8760}. \tag{3} \]

Here \(P_0\) is the quantity, in kg, of hot water brought to the depot by each steam locomotive; \(n\) is the number of steam locomotives per hour arriving at the depot with tender-accumulators; \(v_{mk}\) is the consumption of standard fuel by the steam locomotives, in kg per measuring—

… \(10^4\) tkm gross; \(L\) is the distance, in km, between depots; \(Q\) is the gross train weight in tons. Then from expression (3) we obtain

\[ \eta''_{cm}=\frac{135\cdot P_0\cdot \eta'_{cm}}{v_{tk}\cdot L\cdot Q} \tag{4} \]

Figure 2 gives a nomogram for determining \(\eta''_{cm}\) as a function of other variable factors.

Fig. 1

For the conditions of the particular example analyzed in the aforementioned article, and for \(\eta'_{cm}=0.46\), we have \(\eta''_{cm}=0.055\), with \(v_{tk}\) taken as \(220\ \text{kg}/10^4\ \text{tkm}\). If up to now a locomotive of the FD series consumed \(250\ \text{kg}/10^4\ \text{tkm}\) in trains, then with the introduction of tender-accumulators, chemical water treatment, feedwater heating,

air heating and increased superheating of steam, fuel consumption should decrease significantly (by 40--60%), for chemical water treatment reduces fuel consumption by 10--20%; feed-water heating, air heating, and increased superheating of steam (Academician Syromyatnikov) by 25--30%; elimination of stops at intermediate stations by 5--10%. Therefore the adopted value

Fig. 2

\(\varepsilon_{tk} = 220\ \mathrm{kg}/10^4\ \mathrm{tkm}\) should be regarded as a figure more likely exaggerated for the near future than understated. After what has been said,

\[ \eta''_{st}=\frac{135\cdot 50000\cdot 0.46}{220\cdot 130\cdot 2000}=0.055. \]

In the preceding, as also in the above-mentioned article by the author in Vestnik inzhenerov i tekhnikov [Bulletin of Engineers and Technicians], it was assumed that

\[ W=(7/2+5)8760=74600\ \mathrm{mkg/year} \]

and

\[ E=\frac{500+110}{2}\cdot 8760=2.63\cdot 10^6\ \mathrm{kWh/year}. \]

These figures approximately correspond to the climatic conditions of the middle belt of Siberia. In fact, the hourly heat loss of buildings may be determined by the generally known formula

\[ Q=x\cdot V(t_{in}-t_{out}), \]

where \(x\) is the thermal characteristic of the buildings \((\mathrm{kcal}/\mathrm{m}^3\ ^\circ\mathrm{C}\ \mathrm{hour})\); \(V\) is their volume in \(\mathrm{m}^3\); \(t_{in}\) is the indoor temperature, and \(t_{out}\) the outdoor temperature. For buildings of any given depot area, \(x\cdot V=\mathrm{const}\). If, further, for the sake of simplicity, we take \(t_{in}=18^\circ\mathrm{C}\) for all rooms, then, knowing the meteorological conditions of the given locality, we can construct Rosander's graph, plotting along the ordinate axis \((t_{in}-t_{out})\), and along the abscissa axis the number of days per year corresponding to the persistence of one or another temperature.

of the outside air, as indicated in Fig. 3, which schematizes the conditions for Tomsk on the basis of observations by G. K. Tyumentsev over 37 years [1]. The number of heating days is 218; the beginning of the heating period is at an average temperature of \(+5^\circ\mathrm{C}\) [2].

Since the initial temperature of the hot water in the case under consideration is constant, \(90\text{–}95^\circ\mathrm{C}\), the regulation must be quantitative, with a permissible fivefold change in the water velocities. This is attainable, as is seen from Fig. 3, if the lowest outside-air temperature at which the use of hot water from the accumulators is still permissible does not fall below \(20\text{–}25^\circ\mathrm{C}\). With a further decrease in temperature, the water must be heated in peak boilers from the boiler house of the depot. If this condition is fulfilled, the utilization factor of the utilization installation will be greater, and, moreover, it will be possible to increase its efficiency. Let the ordinate in Fig. 3 corresponding to a temperature of \(-22^\circ\mathrm{C}\), on the adopted scale, be 28 mm; in this case the maximum amount of water will be supplied at a temperature of \(90\text{–}95^\circ\mathrm{C}\), i.e., in the particular example under consideration, \(2 \cdot 10^5\) kg/hour. Since the mean ordinate from Rossander’s graph (Fig. 3) is equal to 20.3 mm, and \(28/20.3 = 1.38\), the amount of heat released from the underground reservoir at a temperature of \(90\text{–}95^\circ\mathrm{C}\) over the heating period will be determined as

Fig. 3

\[ W=\frac{35 \cdot 2 \cdot 10^5 \cdot 218 \cdot 24}{1.38}=26600 \text{ Mcal/year}. \]

Introducing the coefficient 1.1, which takes into account the influence of natural ventilation [3], we obtain

\[ 1.1 \cdot 26600 = 29400 \text{ Mcal/year}. \]

The amount of hot water that is supplied to the heating network during the heating period and that, consequently, enters the evaporator of the utilization turbine at a temperature of \(60^\circ\mathrm{C}\) will be

\[ \frac{2 \cdot 10^5 \cdot 24 \cdot 218}{1.38}=76 \cdot 10^7 \text{ kg/year}. \]

This amount of water corresponds to the generation of electrical energy during the heating season

\[ \frac{76 \cdot 10^7 \cdot 15}{571}\cdot \frac{0.6 \cdot 30}{860} =0.42 \cdot 10^6 \text{ kWh/year}. \]

In addition, during the heating season electric power will be generated at the expense of water at a temperature of 95°C in the amount

\[ \frac{2\cdot 10^5\cdot 24\cdot 218\cdot 35}{\frac{28}{7.7}\cdot 561}\cdot \frac{0.6\cdot 45}{860} =0.56\cdot 10^6\ \text{kWh/year}. \]

The ratio \(\frac{28}{7.7}=3.66\) is taken from Fig. 3, where 7.7 mm is the mean ordinate,

characterizing, on the adopted scale, the quantity of water at \(t\)-re 95°C entering the evaporator of the utilization turbine. The greater part of this water from the evaporator of the first turbine enters, at \(t\)-re 60°C, the evaporator of the second utilization turbine, where it provides additional generation of electric power in the amount

\[ \frac{2\cdot 10^5\cdot 24\cdot 218\left(1-\frac{35}{561}\right)\cdot 15}{571\cdot \frac{28}{7.7}}\cdot \frac{0.6\cdot 30}{860} =0.156\cdot 10^6\ \text{kWh/year}. \]

During the period without heating, over \(365-218=147\) days, the generation of electric power at the expense of water at \(t\)-re 95°C will be, for the first turbine,

\[ \frac{147\cdot 2\cdot 10^5\cdot 24\cdot 35}{561}\cdot \frac{0.6\cdot 45}{860} =1.27\cdot 10^6\ \text{kWh/year}. \]

Moreover, water from the evaporator of this turbine at \(t\)-re 60°C will ensure the production of electric power in the second turbine

\[ \frac{147\cdot 2\cdot 10^5\cdot 24\left(1-35/561\right)\cdot 15}{571}\cdot \frac{0.6\cdot 30}{860} =0.363\cdot 10^6\ \text{kWh/year}. \]

Thus, in all, there will be generated

\[ E=(0.42+0.56+0.16+1.27+0.36)\cdot 10^6 =2.77\cdot 10^6\ \text{kWh/year}. \]

The energy coefficient will be

\[ \frac{29400+40000}{860\cdot 2.77} =\frac{69400}{2380} =29.2, \]

where 40000 Gcal/year is the heat consumption for glass-covered market gardens:

\[ 8760\cdot 25\cdot 0.91\cdot 2\cdot 10^5 =40000\ \text{Gcal/year}.^{1)} \]

As can be seen, the energy coefficient has turned out to be somewhat smaller, namely by

\[ \frac{33-29.2}{33}\cdot 100=11.5\%, \]

than was determined from the data of the article mentioned. In accordance with this, the efficiencies will also decrease: \(\eta'_{st}=0.42\) (Fig. 1) and \(\eta''_{st}=0.05\) (Fig. 2). These efficiencies were obtained on the basis of the annual graph (Fig. 3) on the assumption that the peak heat load during 22 days of the year will be cut off by an independent boiler house. In district-heating installations, such a direction in solving the question of heat supply has in recent years come to be recognized as the most expedient. It is clear that if we transfer to independent boiler houses a larger peak heat load, beginning to switch on the independent boiler houses not at an outdoor temperature \(t_n=-22^\circ\text{C}\), but, for example, at—

\(^{1)}\) In winter, part of this heat may be used to combat snow by means of ground heating of traction and station tracks.

—18°C, which corresponds to the average temperature of the three winter months in Tomsk, then by the same token we shall raise the utilization coefficient of the recovery installation and, at the same time, increase the efficiencies \(\eta'_{st}\) and \(\eta''_{st}\). At the same time, the circle of heat subscribers will also expand. Thus, the values of the efficiencies \(\eta'_{st}\) and \(\eta''_{st}\) depend to a certain extent on the distribution of the heat load between the independent boiler plant and the recovery installation. It is also clear that both of these efficiencies will depend on the climatic conditions of the location of the recovery installation, since these conditions affect the outlines of the annual load-duration curve.

LITERATURE

1. The City of Tomsk, p. 198, 1912.
2. Tables of Climatological Data and Temperatures for Heat-Engineering Calculations. Inors, p. 15.
3. Kop’ev — District Heating, Heat Consumption, Heat Networks, p. 25, 1940.