On the Dependence of Relative Indicated Efficiencies on the Distribution of Power Between the Engine and Turbine of Marine Combined Plants

A. M. Podsushnyi

The magnitude of the relative indicated efficiency of the cylinders of a piston engine, and consequently the magnitude of the relative indicated efficiency of the engine as a whole, is influenced by the following factors: a) the degree of steam expansion, b) the pressure drop, c) the state of the steam, d) the engine speed, and other factors.

With a decrease in the degree of steam expansion, while maintaining a constant initial steam temperature, the mean temperature of the cylinder walls increases, which leads to a decrease in heat exchange between the steam and the cylinder walls, i.e., to an increase in the relative indicated efficiency of the cylinders and, consequently, of the engine. From processing the results of tests of marine combined plants [1; 2; 3], the dependence of relative indicated efficiencies on the degree of steam expansion can be represented in the form of the curves shown in Fig. 1. It is evident from the graphs that the relative indicated efficiency of the LP cylinder of a triple-expansion engine, for example, increased with an engaged exhaust-steam turbine from 0.70 to 0.82, and without an exhaust turbine—

Fig. 1. Dependence of indicated efficiency on the overall degree of steam expansion

of the exhaust steam—respectively from 0.50 to 0.53. Such a comparatively large increase in the relative indicated efficiency of the low-pressure cylinder is explained chiefly by the increase in back pressure behind the engine caused by the connection of the exhaust-steam turbine, which reduced the temperature drop across the engine and the cylinders, and hence the heat-exchange losses. The overall relative indicated efficiency of the plant thereby increases from 0.715 to 0.750.

With a decrease in the pressure drop across a cylinder, the relative indicated efficiency of the cylinder also increases. For example, Danilovskii [1] indicates, on the basis of processing experimental data, that at an unchanged initial steam pressure before the engine of 14.1 ata, an increase in the back pressure behind the engine from 0.20 ata to 1.5 ata causes an increase in the relative indicated efficiency of the engine from 0.675 to 0.890, mainly owing to an increase in the relative indicated efficiency of the low-pressure cylinder. When operating with superheated steam, the relative indicated efficiency of the cylinders increases in comparison with operation on saturated steam chiefly owing to the reduction of heat exchange between the steam and the cylinder walls. With an increase in the back pressure behind the engine, the working process of the steam in the reciprocating engine shifts into the region of higher parameters, without reaching the region of greater saturation. Consequently, the relative indicated efficiency of the engine thereby increases.

On the basis of processing experimental test data for combined marine plants, as well as experimental operating data and literature materials, we arrive at the conclusion that the dependences of the relative indicated efficiencies of the cylinders and of the exhaust-steam turbine on the relative turbine power can be expressed by the graph in Fig. 2, where the following notation is used:

Fig. 2. Dependence of indicated efficiencies on the load of the low-pressure turbine

\(\eta_{ivd}\) — relative indicated efficiency of the HP cylinder;
\(\eta_{icd}\) — relative indicated efficiency of the MP cylinder;
\(\eta_{ind}\) — relative indicated efficiency of the LP cylinder;
\(\eta_{em}\) — relative internal efficiency of the exhaust-steam turbine;
\(\eta_{itm}\) — relative indicated efficiency of the exhaust-steam turbine, introduced in order to reduce the turbine to a single mechanical efficiency and determined, according to Golynskii [5], from the expression:

\[ \eta_{itm}=\eta_{em}\cdot \beta \frac{\eta_{mt}\cdot \eta_{pm}}{\eta_{mm}}, \]

where

\(\beta\) — coefficient allowing for steam leakage through the change-over valve into the main condenser;
\(\eta_{mt}\) — mechanical efficiency of the turbine;
\(\eta_{pm}\) — mechanical efficiency of the transmission from the turbine to the propeller shaft, including the hydraulic coupling;
\(\eta_{mm}\) — mechanical efficiency of the engine, taken as the mechanical efficiency of the entire plant.

In Fig. 2, the region of relative power of the exhaust-steam turbine

\[ \frac{N_{itm}}{N_{ik}} \]

from 0.35 to 0.40 has been constructed by extrapolation.

Having adopted this dependence of efficiency on the distribution of power between the engine and turbine of a marine combined plant, from heat-balance calculations for the particular case of initial steam parameters of 25 ata and \(380^\circ\mathrm{C}\) we obtain the dependence of the relative indicated efficiency of the triple-expansion engine on back pressure, shown in Fig. 3. The calculation was made at an engine speed of 120 rpm. The calculated points obtained are described quite well by the equation of a hyperbola:

Fig. 3. Dependence of the indicated efficiency of the engine on back pressure

\[ \eta_{im}=0.865-\frac{0.11}{P_{2m}+0.46}. \tag{1} \]

According to heat-balance calculations of combined plants made for various initial steam parameters, with different distributions of power between the engine and the turbine and with the adopted dependence of cylinder efficiency on the distribution of power, a dependence of the relative-

relative indicated efficiency of the combined plant on the relative load of the reciprocating engine, presented in Fig. 4. This dependence, within the load limits of the reciprocating engine under consideration, is described with sufficient accuracy by the equation of a hyperbola

Fig. 4. Dependence of the indicated efficiency of the plant on the relative load of the reciprocating engine

\[ \eta_{ik}=0.80-\frac{1}{31(1.16-\psi_1)}. \tag{2} \]

Here the argument is taken to be the ratio of the indicated heat drop of the reciprocating engine to the indicated heat drop of the entire combined plant,

\[ \psi_1=\frac{H_{i.m}}{H_{ik}}, \]

which is a characteristic of the distribution of power between the engine and the turbine without allowance for the difference in the quantity of steam working in the individual cylinders of the engine and in the turbine. If in the present case one passes from the relative load of the engine \(\psi_1\) to the relative power of the engine

\[ \frac{N_{i.m}}{N_{ik}}, \]

then the dependence of \(\eta_{ik}\) on \(\frac{N_{i.m}}{N_{ik}}\) will take the form:

\[ \eta_{ik}=0.80-\frac{1}{31(1.2-N_{i.m}/N_{ik})}. \tag{3} \]

From a comparison of (2) and (3) it is evident that these dependences are very close. An important feature of equation (2) is the circumstance that it does not depend on the initial steam parameters, since the thermal calculations for constructing Fig. 4 were carried out for various initial steam parameters, from 15 ata and \(300^\circ\text{C}\) to 50 ata and \(420^\circ\text{C}\).

For an approximate consideration of a number of questions not requiring high accuracy, in the interval \(\psi_1=0.50\text{–}0.80\) dependence (2) may be represented as rectilinear:

\[ \eta_{ik}=0.685+0.148(1-\psi_1). \tag{4} \]

Analyzing equation (4), we arrive at the conclusion that, with the exhaust-steam turbine disconnected \((\psi_1=1)\), the relative indicated efficiency of the reciprocating engine, at a vacuum in the main condenser of 95%, remains the same as with the 85% vacuum customary for triple-expansion engines. This circumstance, on the one hand, confirms the established view—

that deepening the vacuum of triple-expansion reciprocating engines above 85% is useless; on the other hand, at $\psi_i = 1$ the relative indicated efficiency of the combined plant becomes equal to that of the triple-expansion engine during its normal operation, and its value in this case

\[ \eta_{ik} = \eta_{iM} = 0.685 \]

corresponds to the value of $\eta_{iM}$ obtained in the works of TsNIIMF [4]. The dependences obtained may significantly facilitate investigations of marine combined plants.

REFERENCES

1. Danilovsky G. I. Increasing the efficiency of marine steam-power plants. VNITOT, 1935.

2. “Werft-Reederei-Häfen.” No. 3, 1928; No. 13, 1933; Nos. 23–24, 1935.

3. Semeka V. A. and Kutyn L. N. Selection of the type of steam-power plants for sea-going vessels to be built with installations of 1500 indicated h.p. and less. TsNIIMF, Leningrad, 1950.

4. Golynsky A. V. Theory and thermal calculation of marine steam engines. Morskoi Transport, 1951.