On Steam and Heat Consumption in a Shipboard Steam Power Plant and by Auxiliary Consumers

A. M. PODSUSHNYI

The interrelation of individual energy consumers in a modern shipboard steam power plant is fairly complex: the main engine consumes live steam directly from the boilers; auxiliary consumers operate partly with live steam at boiler parameters, partly with steam of reduced parameters cooled in an internal boiler cooler, partly with throttled steam, and partly with extraction steam from the main engine. In this case the total steam consumption for the power plant as a whole proves not to be equal to the sum of the visible steam consumptions of the individual consumers, if by visible steam consumption one means the quantity of steam consumed by an individual consumer. For such a complex case, the balance equation for steam consumption by the plant as a whole cannot be represented in the form of the commonly used equation

\[ D = D'_0 + \sum D_k, \tag{1} \]

where \(D\) is the steam consumption for the power plant,
\(D'_0\) is the steam consumption for the main engine,
\(D_k\) is the steam consumption for an individual auxiliary consumer.

Equation (1) is valid only in the special case when each auxiliary consumer is supplied with live steam from the boilers.

1. Steam Consumption for the Plant

For a thermal scheme of any complexity in the interaction of individual energy consumers, the steam consumption for the power plant should be determined as the sum of:

a) the steam consumption for the main engine operating without extractions or steam admissions into intermediate stages at the same power;

b) the change in steam consumption for the main engine in connection with extractions of steam for feedwater heating;

c) the change in steam consumption for the main engine and the power plant in connection with the operation of auxiliary consumers. Then the increase in steam consumption from the boilers for the power plant caused by the steam consumption of some \(k\)-th consumer should be called the true steam consumption for this consumer.

True energy consumptions determine the economy of the individual consumers in the given concrete steam power plant; they determine the nature of the connection of this consumer with the other elements of the steam power plant, i.e., ultimately, the economy of the thermal scheme.

The steam consumption for the main engine, operating without extractions or admissions of steam into intermediate stages, is determined by the well-known formula

\[ D'_0=\frac{632.3\,N_i}{H_i}. \]

In this case the steam flow \(D'_0\) passes unchanged (neglecting steam leakage) through all stages of the main engine into the condenser and is the main steam flow, understanding by the main steam flow the quantity of it leaving the main engine for the condenser. Within the power plant, additional steam flows for auxiliary consumers are joined to this main steam flow.

When the main engine operates with steam extractions or admissions into its intermediate stages, the steam flow changes both within the main engine and throughout the entire power plant. The main steam flow \(D_{ot}\) in this case will not be equal to the conventional steam flow of the main engine without extractions, \(D'_0\). Here two cases of steam extractions (admissions) may be distinguished: the case when steam extractions are made only for heating feed water according to the regenerative cycle, and the case when steam extractions are made both for heating feed water and for the operation of auxiliary consumers.

Steam consumptions with extractions only for regeneration

With steam extractions only for heating feed water, the steam consumption for the main engine is represented by the equation

\[ D'_{gm}=D_{ot}+\sum D_{op}, \tag{2} \]

where \(D_{ot}\) is the main steam flow in this case,

\(D_{op}\) is the steam extraction from the \(n\)-th extraction stage of the main engine, taking the numbering of the extraction stages in accordance with the numbering of the feed-water heating stages along its path from the condenser to the boilers.

We calculate the relative magnitudes of steam extractions with respect to the main steam flow

\[ \alpha_{op}=\frac{D_{op}}{D_{ot}}. \]

Substituting \(\alpha_{op}\) into (2), we obtain the expression for the steam consumption for the main engine in the form

\[ D'_{gm}=D_{ot}\left(1+\sum \alpha_{op}\right). \tag{3} \]

From the condition of maintaining unchanged power of the main engine with and without steam extractions, we form the equality of internal works in the form

\[ D'_0 H_i = D_{ot} H_i + \sum D_{op} h_{in}, \tag{4} \]

where \(h_{in}\) is the internal heat drop used in the stages of the main engine before the extraction.

In this equality, the first term on the right-hand side represents the work of the main steam flow in the main engine, and the second term the work of the additional steam flows going to extraction.

Introducing the coefficient of relative loading of the stages of the main engine before extraction as the ratio of the internal heat drop up to the extraction point to the total heat drop in the main engine,

\[ y_n=\frac{h_{in}}{H_i}; \]

we obtain from (4) the value of the main steam flow in this case

\[ D_{om}=D'_0-\sum D_{on}\psi_n . \tag{5} \]

From expression (5) it is evident that, when the main engine operates with steam extractions, the magnitude of the main steam flow decreases, in comparison with operation of the main engine without extractions, by the amount \(\sum D_{on}\psi_n\), which is less than the apparent steam consumption for heating the feed water. As a result of the decrease in the main steam flow, the heat rejected to the condenser decreases; consequently, the economy of the installation increases.

Using formula (5), we rewrite equation (2) in the form

\[ D'_{zm}=D'_0+\sum D_{on}(1-\psi_n), \tag{6} \]

which shows that steam extractions for heating the feed water, with an apparent total steam consumption \(\sum D_{on}\), increase the steam consumption by the main engine only by \(\sum D_{on}(1-\psi_n)\), i.e., this quantity should be regarded as the true steam consumption from the boilers for heating the feed water.

Introducing into (6) the relative steam extractions \(\alpha_{on}\), we obtain the expression

\[ D_{zm}=D'_0+D_{om}\sum\alpha_{on}(1-\psi_n). \tag{7} \]

From equations (3) and (7) we obtain an expression for the relative magnitude of the main steam flow in the form

\[ \chi_{om}=\frac{D_{om}}{D'_0}=\frac{1}{1+\sum\alpha_{on}\psi_n}. \tag{8} \]

The relative increase in steam consumption by the main engine in connection with regeneration is found from equations (7) and (8)

\[ \chi_0=\frac{D'_{zm}}{D'_0} =1+\frac{\sum\alpha_{on}(1-\psi_n)}{1+\sum\alpha_{on}\psi_n} =\frac{1+\sum\alpha_{on}}{1+\sum\alpha_{on}\psi_n}. \tag{9} \]

Since, in the case under consideration, the auxiliary consumers operate on fresh boiler steam, the equation for steam consumption by the power installation will take the form

\[ D=D'_0+\sum D_{on}(1-\psi_n)+\sum D_k . \]

The conclusions of the formulas presented have been made under the assumption that the internal efficiency of the main engine and of its individual stages, selected with allowance for steam extractions, remains unchanged also when the engine operates without steam extractions.

Steam Consumption with Extractions for Regeneration and for Auxiliary Consumers

In modern steam-power installations, steam of elevated parameters is finding ever wider application, since this increases the economy of power installations. At the same time, certain auxiliary steam consumers require steam of low initial parameters for operation (for example, domestic consumers, evaporator plants, etc.). In this case it will be more advantageous for them to operate not on throttled boiler steam, but on steam extracted from the main engine. In the heat-flow diagrams of steam-power installations for turbine ships with elevated steam parameters, developed at TsNIIMF, provision is made, in particular, for steam extraction from the main engine for the operation of domestic consumers. It is also possible for a number of other consumers to operate on steam extracted from the main engine. Consequently, in the general case, with steam extractions for regeneration and for

auxiliary consumers from the main engine, the equality of the work of the machine with bleeds and without bleeds will take the form

\[ D'_0 H_i = D_{om} H_i + \sum D_{on} h_{in} + \sum D_k h_{in}, \]

whence it is easy to obtain the magnitude of the main steam flow

\[ D_{om} = D'_0 - \left(\sum D_{on}\psi_n + \sum D_k\psi_n\right). \tag{10} \]

The steam consumption for the main engine should be considered as the sum of the main steam flow and the additional steam flows for regeneration and for auxiliary consumers:

\[ D_{g.m} = D_{om} + \sum D_{on} + \sum D_k, \]

which, taking (10) into account, gives

\[ D'_{g.m} = D'_0 + \sum D_{on}(1-\psi_n) + \sum D_k(1-\psi_n). \tag{11} \]

Here, on the right-hand side of the equation, the second term represents the true steam consumption for heating the feed water, and the third term is the true steam consumption for auxiliary consumers operating from the bleed of the main engine. As can be seen, any steam consumer operating from the main engine increases the steam consumption for the main engine by \(D_k(1-\psi_n)\), i.e., by less than the apparent steam consumption \(D_k\). The magnitude of the true steam consumption for an individual consumer \(D_k(1-\psi_n)\), when it operates with bleed steam from the main engine, depends on the value of \(\psi_n\), which is determined by the quality of the connection of this consumer with the main engine.

The relative magnitude of the main steam flow is found from equation (10)

\[ \gamma_{om}=\frac{D_{om}}{D'_0} =\frac{1-\sum \zeta_k\psi_n}{1+\sum \alpha_{on}\psi_n} \]

or

\[ \gamma_{om}=\frac{\gamma_0-\sum \zeta_k\psi_n}{1+\sum \alpha_{on}}, \tag{12} \]

where \(\zeta_k\) is the relative apparent steam consumption for the \(k\)-th consumer,

\[ \zeta_k=\frac{D_k}{D'_0}. \]

Comparing (6) and (11), we obtain

\[ D_{g.m}=D'_{g.m}+\sum D_k(1-\psi_n), \tag{13} \]

i.e., the steam consumption for the main engine may be considered as the sum of the steam consumption for the main engine with bleeds for heating the feed water and the true steam consumption for the \(k\)-th consumers. From equation (13) it is easy to determine the relative steam consumption for the main engine in this case:

\[ \gamma_{g.m}=\frac{D_{g.m}}{D'_0} =\gamma_0+\sum \zeta_k(1-\psi_n). \tag{14} \]

The steam consumption for the power plant as a whole has the same form as equation (11), if the consumers of live steam from the boilers are considered as operating from the “zero” bleed of the main engine, for which \(\psi_n=0\):

\[ D=D'_0+\sum D_{on}(1-\psi_n)+\sum D_k(1-\psi_n) \tag{15} \]

and in relative form:

\[ z=\frac{D}{D'_0}=z_0+\sum z_k(1-\psi_n). \tag{16} \]

If the visible steam consumptions for regeneration and for auxiliary consumers are combined under a single designation \(D_k\), we arrive at a simpler expression for the steam consumption of the power plant as a whole, in the most general form:

\[ D=D'_0+\sum D_k(1-\psi_n) \tag{17} \]

and in relative form:

\[ z=1+\sum z_k(1-\psi_n). \tag{18} \]

Equation (17) should be used instead of equation (1).

It is not difficult to see that this equation is suitable for any heat-flow diagrams of steam power plants and for any inclusion of auxiliary consumers in the common cycle of the steam power plant. This equation is also convenient for investigations, since it establishes a quantitative and qualitative relationship among the individual consumers. For example, if hotel-service consumers expend \(D_\delta\) kg/hour of steam throttled in a desuperheater, then transferring the hotel-service consumers to supply from extraction steam from the corresponding stage of the main engine will reduce the steam consumption of the power plant by the amount

\[ D_\delta-D_\delta(1-\psi_n)=D_\delta\psi_n. \]

As we see, the saving in steam consumption for the power plant depends on the magnitude of \(\psi_n\), i.e., on the quality of the connection of the hotel-service consumers with the main engine. It is clear that the greater the value of \(\psi_n\), the more work the additional steam flow \(D_\delta\) will have performed in the main engine, and the greater the saving obtained in the steam consumption from the boilers for the power plant as a result of transferring the hotel-service consumers to supply by extraction steam from the main engine.

2. Heat Consumption for the Power Plant

It is convenient to consider the total heat consumption for the steam power plant as a whole as consisting of the heat consumption for producing \(D\) kg/hour of steam with heat content \(i_1\) and the heat consumption for various kinds of losses. Since some auxiliary consumers operate with steam of reduced parameters and, under the operating conditions, it is inexpedient to transfer these consumers to supply from extractions of the main engine (for example, air steam-jet ejectors), it is more advantageous to deliver to them, in an internal-boiler cooler, cooled steam with initial heat content \(i_{1k}\), which will reduce the heat consumption for the power plant owing to the return to the boiler of \((i_1-i_{1k})\) kilocalories of heat with each kg of steam passed through the internal-boiler cooler. We shall consider the heat losses as consisting of two kinds: heat losses through the main steam line from the boiler to the main engine, \(\Delta Q_0\), and heat losses associated with the operation of evaporators, \(\Delta Q_u\). It is more convenient to take the remaining losses into account by increasing the steam consumption for the corresponding consumer. Then the equation for heat consumption for the power plant may be written in the form

\[ Q=D(i_1-i'''_{\text{fw}})-\sum D_k(i_1-i_{1k})+\Delta Q_0+\Delta Q_u . \tag{19} \]

Here \(i'''_{\text{fw}}\) is the heat content of the feed water.

It should be borne in mind that, for auxiliary consumers operating on extraction steam from the main engine, the equality \(i_1=i_{1k}\) will hold; i.e., the second term on the right-hand side of the equation covers consume—

cooled in the internal-boiler cooler by steam. The heat consumption for the main engine without steam extraction is determined by the equality

\[ Q'_0=D'_0(i_1-i'''_x)=D'_0\omega . \tag{20} \]

Let us denote

\[ \Delta z_0=\frac{\Delta Q_0}{Q'_0}\quad \text{and}\quad \Delta z_u=\frac{\Delta Q_u}{Q'_0}. \]

Then from formulas (19) and (20), taking expression (16) into account, we obtain the equation for the relative heat consumption of the power plant:

\[ z=\frac{Q}{Q'_0}=\frac{1}{\omega}\left[z(i_1-i'''_{nv})-\sum \xi_k(i_1-i_{1k})\right]+\Delta z_0+\Delta z_u . \tag{21} \]

The relative magnitude of the heat losses associated with operation of the evaporator is taken, according to experimental data, from the formula

\[ \Delta z_u=\xi_u\cdot\frac{q_u}{\omega}, \tag{22} \]

where \(\xi_u\) is the relative quantity of secondary steam from the evaporator,

\[ \xi_u=\frac{D_u}{D'_0}. \]

The capacity of the evaporator in modern installations is taken as equal to about 1% of the boiler capacity, i.e.,

\[ D_u=0.01D. \]

Then the relative quantity of secondary steam from the evaporator is determined by the relation

\[ \xi_u=0.01\cdot\frac{D}{D'_0}=0.01z. \]

According to experimental data, the heat consumption for obtaining 1 kg of secondary steam from the evaporator may be taken on average as \(q_u=50\ \text{kcal/kg}\). Substituting \(\xi_u\) and \(q_u\) in (22), we obtain an expression for determining the relative magnitude of the heat losses associated with operation of the evaporator in the form

\[ \Delta z_u=0.01z\cdot\frac{50}{\omega}=0.5\cdot\frac{z}{\omega}. \]

Substituting into (21), we obtain the equation of relative heat consumption for the steam-power plant in final form as

\[ z=\frac{1}{\omega}\left[z(i_1-i'''_{nv}+0.5)-\sum \xi_k(i_1-i_{1k})\right]+\Delta z_0 . \tag{23} \]

The relative magnitude of heat losses in the main steam pipeline in power installations may, according to experimental data, be taken as \(\Delta z_0=0.005\). Having determined the relative heat consumption from equation (23), it is easy to find also the absolute heat consumption for the steam-power plant as a whole:

\[ Q=zQ'_0. \]

It is then not difficult to compute also the specific fuel consumption for the installation from the expression:

\[ b_i=k_0\frac{Q}{N_i\cdot Q^p_n\cdot \eta_{ik}}\ \text{kg/hp-hr}, \]

where \(k_0\) is the coefficient of increase in fuel consumption under average operating conditions due to wear, corrosion, etc.,
\(N_i\) is the power of the main engine in indicated horsepower,
\(Q_{н}^{p}\) is the calorific value of the fuel,
\(\eta_k\) is the efficiency of the boilers.

The equations obtained are more general and are suitable for any heat-flow arrangements of steam power plants, while the equations used up to now should be regarded as special cases of these equations. In addition, these equations make it easy to carry out calculations of power plants in relative form, which is more convenient.