## Theory

A steam turbine develops mechanical work by converting to work the available heat energy in the steam expansion. Heat and mechanical work, being two forms of energy, can be converted from one to the other.

The heat energy is converted in two steps. The steam expands in nozzles and discharges at a high velocity, converting the available heat energy to velocity (kinetic) energy. The high-velocity steam strikes moving blades, converting the velocity energy to work. Because the total heat energy available in the steam is converted to velocity (kinetic) energy, the magnitude of the steam velocity is dependent upon the available energy.

The mechanical work that is developed in the turbine by the high-velocity steam striking the buckets is a function of the speed of the buckets. Maximum work occurs when the bucket velocity is approximately one-half the steam jet velocity for an impulse stage and one-fourth the steam jet velocity for a velocity-compounded impulse stage. Although the steam jet velocity is fixed by the available heat energy, the bucket velocity is fixed by the speed of the turbine and the diameter of the turbine wheel on which the buckets are mounted. The work developed, or the efficiency of the turbine, ignoring losses in the turbine, is therefore determined by the size of the turbine and the turbine (pump) speed for a fixed amount of available heat energy.

The most common single-stage turbine is the velocity-compounded (Curtis) type. The complete expansion from inlet to exhaust pressure occurs in one step. The Curtis stage,

FIGURE 5 Velocity-compounded stages: (a) Curtis stage; steam flows once through moving buckets; (b) re-entry stage; steam flows twice through moving buckets; (c) re-entry stage; steam flows three times through moving buckets (reprinted with permission from Power, June 1962)

FIGURE 5 Velocity-compounded stages: (a) Curtis stage; steam flows once through moving buckets; (b) re-entry stage; steam flows twice through moving buckets; (c) re-entry stage; steam flows three times through moving buckets (reprinted with permission from Power, June 1962)

with two rows of rotating buckets, and two re-entry-type velocity-compounded stages are illustrated in Figure 5.

Single-stage turbines are available with a wide range of efficiencies because they are manufactured with a variety of wheel diameters: 9 to 28 in (22 to 71 cm).

Multistage turbines are manufactured with a more limited variety of wheel sizes. The efficiency of multistage turbines is varied primarily by varying the number of stages. When the total available energy of the steam results in a steam velocity greater than twice the bucket velocity (using convenient wheel sizes), a multistage turbine will be more efficient. In a multistage turbine, the total steam expansion is divided among the various impulse stages to produce the desired steam velocity for each row of buckets.

A steam turbine is normally evaluated using steam rate—the amount of steam required by the turbine to produce the specified power per hour at the specified speed— rather than efficiency. The steam rate is a direct function of the turbine efficiency.

The steam consumption can be expressed either as steam rate, pounds of steam per horsepower-hour (kilograms per kilowatt-hour) or as steam flow, pounds of steam per hour (kilograms per hour). The higher the efficiency, the lower the steam rate or steam flow, and vice versa.

The total available energy of the steam is that available from an isentropic expansion. For given initial steam pressure and temperature and exhaust pressure, the available energy in British thermal units per pound (kilojoules per kilogram) of steam can be obtained from the tables or the Mollier chart in Reference 3.

The available energy can be converted to power units and expressed as the theoretical steam rate—pounds per horsepower-hour or pounds per kilowatt-hour (kilograms per kilowatt-hour). The theoretical steam rate is the steam rate for a 100% efficient turbine and therefore can be used more conveniently than energy in British thermal units per pound (kilojoules per kilogram) for the calculation of turbine steam rates. Theoretical steam rates can be obtained directly from theoretical steam rate tables (ASME) or from the polar Mollier chart (Elliott Company).

The actual steam rate for a turbine is greater than the theoretical steam rate because of the losses that occur in the turbine when the available energy is converted to mechanical work and because of the ratio of the steam velocity to bucket velocity. The energy remaining in the steam exhausting from the turbine is greater than that after an isen-tropic expansion, as illustrated in Mollier diagram shown in Figure 6, where

1 = energy in steam at initial steam pressure and temperature

2 = energy in steam at exhaust pressure for an isentropic expansion

3 = actual energy in steam at exhaust pressure

ENTROPY (s) FIGURE 6 Mollier diagram with energy losses

The efficiency of the turbine is hi — h3

hi — h2 actual steam rate

The governor and trip valve pressure drop losses are a function of the sizes of these two valves and the steam flow. The governor valve pressure drop will vary more than the trip valve pressure drop because of changes in valve position with power required by the driven pump, speed variations, and changes in inlet and exhaust steam conditions.

The nozzle loss is due to friction in the nozzles as the steam expands. The efficiency of the nozzles is a function of the ratio of the actual and ideal exit steam velocities squared. The efficiency is usually between 95 and 99%.

The windage and disk friction losses are due to the friction between the stream and the disks and the blades fanning the steam. This loss varies inversely with the specific volume of the steam, increases with exhaust pressure, and increases with the diameter of the wheel and the length of the blades.

The use of a larger-diameter wheel may increase the efficiency, but the windage and disk friction losses will reduce the improvement and may even cause a net loss in overall efficiency.

The exhaust losses represent the kinetic energy remaining in the steam as a result of the velocity of the steam leaving the bucket and the pressure drop in the steam as it passes out the exhaust connection.

The energy conversion loss is due to the nonideal conversion of the steam velocity energy to mechanical work in the buckets as a function of the steam velocity and bucket velocity, plus nonideal nozzle and bucket angles, friction in the system, and so on.

The performance that can be expected from a single-stage Curtis-type turbine may be obtained from Figures 7,8, and 9, and Table 1 after determining the theoretical steam rate.

superheat correction factor power

To obtain superheat, subtract temperature given in Table 1 from total initial temperature.

FIGURE 7 Base steam rates (Elliott)
FIGURE 8 Power loss (lb/in2 x 6.895 = kPa) (Elliott)

0_20 40_60_80 100 120 1 40 160

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