On the Distribution of Heat Drops Across the Cylinders of a Reciprocating Machine in a Marine Combined Plant with Steam Extractions for Feedwater Heating
Abstract Generated abstract
The paper examines how indicated heat drops and power should be distributed among the cylinders of a triple-expansion reciprocating steam engine in a marine combined plant with an exhaust-steam turbine and regenerative feedwater heating. It argues that the usual proportional relation between cylinder power and heat drop is insufficient when steam is extracted from receivers, because the steam flow varies through the engine stages. The author derives corrected relations incorporating relative extraction flows, proposes practical power and heat-drop distributions for a 2000 h.p. combined plant, and generalizes the formula to engines with any number of expansion stages and steam extractions.
Full Text
ON THE DISTRIBUTION OF HEAT DROPS AMONG THE CYLINDERS OF THE RECIPROCATING ENGINE OF A MARINE COMBINED PLANT WITH STEAM EXTRACTIONS FOR FEEDWATER HEATING
A. M. PODSUSHNYI
Recently, compounding reciprocating steam engines with exhaust-steam turbines, as a means of increasing the economy of steam-power plants of seagoing vessels, has become fairly widespread. The most common combined plants, possessing the best economy, are plants with a triple-expansion reciprocating engine and an exhaust-steam turbine, operating on one shaft with the engine through a double gear transmission with a hydraulic coupling (the Bauer-Wach system). However, the question of the distribution of heat drops among the cylinders of the engine, and of the distribution of power both between the engine and the turbine and among the cylinders, has not, up to the present time, received complete and finished treatment in the literature. The question is solved in the particular simplest case, when the engine operates without steam extractions. In the absence of steam extractions from the engine receivers, the steam flow in all cylinders of the engine will be the same, if leakage of steam through the rod packings is neglected. In this case the indicated powers of the cylinders will be proportional to the indicated heat drops of the cylinders,
\[ \frac{N_{iв}}{N_{iм}}:\frac{N_{iс}}{N_{iм}}:\frac{N_{iн}}{N_{iм}} = \frac{h_{iв}}{H_{iм}}:\frac{h_{iс}}{H_{iм}}:\frac{h_{iн}}{H_{iм}} . \tag{1} \]
In the presence of steam extractions from the receivers or the admission of steam into the receivers of the engine, this equation will not be valid because of the variability of the amount of working steam in the individual cylinders of the engine. Let, in a particular case, a marine combined plant with a triple-expansion engine and an exhaust-steam turbine have three-stage feedwater heating. Steam extractions are made from all receivers; moreover, from the receiver of the exhaust-steam turbine \(D_{01}\) kg/hour is extracted, from the HP-cylinder receiver \(D_{02}\) kg/hour, and from the IP-cylinder receiver \(D_{03}\) kg/hour of steam. The main steam flow—the amount of steam leaving the turbine for the condenser—will be \(D_{om}\) kg/hour. We calculate the relative steam extractions with respect to the main steam flow:
\[ a_{01}=\frac{D_{01}}{D_{om}};\quad a_{02}=\frac{D_{02}}{D_{om}};\quad a_{03}=\frac{D_{03}}{D_{om}} . \tag{2} \]
Then the ratio of the indicated powers of the cylinders of a triple-expansion steam engine should be determined by the relation...
\[ \frac{N_{i b}}{N_{i m}}:\frac{N_{i c}}{N_{i m}}:\frac{N_{i h}}{N_{i m}} = \]
\[ = \frac{1+\sum^{3}\alpha_{o n}}{L_{i m}}\,h_{i b}: \frac{1+\sum^{2}\alpha_{o n}}{L_{i m}}\,h_{i c}: \frac{1+\sum^{1}\alpha_{o n}}{L_{i m}}\,h_{i h}, \tag{3} \]
where
\[ L_{i m}=\left(1+\sum^{3}\alpha_{o n}\right)h_{i b} +\left(1+\sum^{2}\alpha_{o n}\right)h_{i c} +\left(1+\sum^{1}\alpha_{o n}\right)h_{i h}, \]
where \(L_{i m}\) is the indicated work of the engine, performed by the entire quantity of steam that has passed through the cylinders and referred to 1 kg of steam of the main flow,
\[ 1+\sum^{3}\alpha_{o n}=1+\alpha_{01}+\alpha_{02}+\alpha_{03} \]
is the relative steam flow in the HPC,
\[ 1+\sum^{2}\alpha_{o n}=1+\alpha_{01}+\alpha_{02} \]
is the relative steam flow in the IPC,
\[ 1+\sum^{1}\alpha_{o n}=1+\alpha_{01} \]
is the relative steam flow in the LPC.
The distribution of power between the engine and the turbine of a combined installation is characterized to a certain extent by the relative loading of the engine
\[ \psi_1=\frac{H_{i m}}{H_{i k}}. \tag{4} \]
To obtain greater economy of a steam engine with regenerative steam extractions, a number of authors [1; 2; 3] recommend providing uniform heating of the feed water in each heating stage. In the case where the pressure in the 1st heating stage is specified (in the present case \(\psi_1\) is specified), these authors recommend adopting the relation between the relative loadings of the cylinders in the form
\[ \psi_2=\frac{h_{i b}+h_{i c}}{H_{i k}}\simeq \frac{1}{3}\psi_1 \quad\text{and}\quad \psi_3=\frac{h_{i c}}{H_{i k}}=\frac{2}{3}\psi_1. \tag{5} \]
However, in marine engines using superheated steam, and especially in the engines of combined installations with regenerative steam extractions, it is necessary to overload the HPC and underload the LPC in order to ensure normal degrees of filling of the medium- and low-pressure cylinders (more than 50%). In combined installations this is also dictated by the fact that, during maneuvering and astern running, the reciprocating engine operates on a condenser, in which the vacuum decreases very little compared with the design ahead-running condition. In this case the LPC is overloaded as a result of the reduction of the back pressure behind the engine. Proceeding from these considerations, it is necessary to abandon uniform distribution of power among the cylinders of the reciprocating engine. A. V. Golynskii, for example, recommends [4; 5] that in triple-expansion engines with steam extractions from the receivers and operating on superheated steam the HPC be loaded to 36–40% of the engine power, and the IPC to 33–35%. Taking into account the statements and work of TsNIIMF [6], in the case considered by us, for the triple-expansion engine of a combined installation operating with steam of normal and elevated parameters, the distribution of power among the cylinders may be taken as
\[ \frac{N_{i b}}{N_{i m}}:\frac{N_{i c}}{N_{i m}}:\frac{N_{i h}}{N_{i m}} =0.38:0.34:0.28. \tag{6} \]
On the basis of a study of experimental material and the author’s calculations it has been established that the values of the multipliers at \(h_{iс}\) in equation (3) lie within the limits
\[ \frac{1+\sum^{3}\alpha_{on}}{L_{iм}}=1.11\text{--}1.08,\quad \text{accepted }1.095, \]
\[ \frac{1+\sum^{2}\alpha_{on}}{L_{iм}}=1.02\text{--}0.96,\quad \text{accepted }1.0, \tag{7} \]
\[ \frac{1+\sum^{1}\alpha_{on}}{L_{iм}}=0.930\text{--}0.875,\quad \text{accepted }0.90. \]
These values have been established for combined plants with a triple-expansion engine at a plant power of 2000 h.p. For plants of another type the indicated multipliers should be established separately.
From equation (3) we have the relations between the indicated heat drops of the cylinders in the form:
\[ h_{iв}:h_{iс}:h_{iн} = \frac{\dfrac{N_{iв}}{N_{iм}}}{\dfrac{1+\sum^{3}\alpha_{on}}{L_{iм}}} : \frac{\dfrac{N_{iс}}{N_{iм}}}{\dfrac{1+\sum^{2}\alpha_{on}}{L_{iм}}} : \frac{\dfrac{N_{iн}}{N_{iм}}}{\dfrac{1+\sum^{1}\alpha_{on}}{L_{iм}}}. \tag{8} \]
Substituting here the accepted values of the relative powers of the cylinders according to (6) and the values of the denominators according to (7), we obtain
\[ h_{iв}:h_{iс}:h_{iн}=0.35:0.34:0.31. \tag{9} \]
In this case the relative loads of the cylinders will become equal to
\[ \psi_3=0.35\psi_1, \]
\[ \psi_2=0.69\psi_1 \tag{10} \]
instead of (5).
In the general case, the steam engine may be of \(k\)-fold expansion, and steam extractions may be made not only from receivers, but also from the intermediate stages of the exhaust-steam turbine. Considering in this case as an engine stage the part of the engine between adjacent steam extractions, we may express the ratio of the powers of the engine stages through the ratio of the heat drops of the stages in the general form by the equation:
\[ \frac{N_{i(n+1)}}{N_{ik}} : \frac{N_{in}}{N_{ik}} : \frac{N_{i(n-1)}}{N_{ik}} : \ldots : \frac{N_{i1}}{N_{ik}} = \]
\[ = \frac{1+\sum^{n}\alpha_{on}}{L_{ik}}\,h_{i(n+1)} : \frac{1+\sum^{n-1}\alpha_{on}}{L_{ik}}\,h_{in} : \frac{1+\sum^{n-2}\alpha_{on}}{L_{ik}}\,h_{i(n-1)} : \ldots : \frac{h_{i1}}{L_{ik}}, \tag{11} \]
where \(N_{i(n+1)},\,N_{in},\,N_{i(n-1)},\ldots,\,N_{i1}\) is the indicated power of the corresponding stage of the main engine;
\(N_{ik}\) is the indicated power of the main engine;
\(h_{i(n+1)},\,h_{in},\,h_{i(n-1)},\ldots,\,h_{i1}\) is the indicated heat drop of the corresponding expansion stage of the main engine;
\[ 1+\sum_{i=1}^{n} a_{0n} =1+a_{01}+a_{02}+a_{03}+\ldots+a_{0(n-1)}+a_{0n}, \]
\[ 1+\sum_{i=1}^{n-1} a_{0n} =1+a_{01}+a_{02}+a_{03}+\ldots+a_{0(n-1)} \quad \text{etc.}— \]
— the relative steam flow in the corresponding stage of the main engine;
\[ L_{ik}= \left(1+\sum a_{0n}\right) h_{i(n+1)} +\left(1+\sum^{n-1} a_{0n}\right) h_{in} +\left(1+\sum^{n-2} a_{0n}\right) h_{i(n-1)} +\ldots+h_{i1}. \]
\(L_{ik}\)—the total indicated work of the main engine;
\(n\)—the ordinal number of the steam extraction from the main engine, numbering in the direction of feedwater flow from the condenser to the boilers.
Equation (11) may be applied to a steam engine of any type with any number of steam extractions. From this equation it is easy to determine the ratio of heat drops for any specified ratio of the powers of the engine stages, given known values of the relative magnitudes of the steam extractions from the main engine. Equation (3) is a special case of equation (11) as applied to a triple-expansion engine of a combined plant with steam extracted only from the receivers. Equation (1) may also be regarded as a special case of equation (11) when the engine operates without steam extractions. These equations can also be used to find the ratio of the powers of the engine stages from known values of the steam extractions from the main engine and specified values of the heat drops.
Thus, equation (11) is the most general equation relating the magnitudes of the heat drops and the powers of the engine stages to the magnitudes of the steam extractions from the main engine.
REFERENCES
- Rubinshtein Ya. M. Investigation of the regenerative process in steam-turbine installations. Izv. VTI, No. 1 (44), No. 9 (52), 1929.
- Petelin G. I. Regenerative Heating of Feedwater. ONTI, 1932.
- Fuks G. I. Efficiency and pressures of extractions in the regenerative cycle. Izv. TPI, vol. 63, 1945.
- Golynskii A. V. Thermal calculation of steam reciprocating engines. L.K.I., part 1, 1938, part 2, 1939.
- Golynskii A. V. Theory and Thermal Calculation of Marine Steam Engines. “Morskoi transport,” 1951.
- Semeka V. A., Kut’in L. N. Selection of the type of steam-power installations for seagoing vessels under construction, with installations of 1500 h.p. and less. TsNIIMF, Leningrad, 1950.