Steam Turbine Power Cycle Operation and Performance

Ideal Rankine Cycle

The energy available per unit mass (e.g., lbm or kg) of steam flowing through a steam turbine is a function of the turbine pressure ratio (ratio of absolute inlet pressure to absolute exhaust pressure) and the inlet temperature. The maximum ideal thermal efficiency achievable with a steam turbine cycle is, therefore, the difference between the inlet and exhaust energies (or enthalpies). This efficiency is based on the

Evaporative Steam Condenser Turbines
Fig. 11-27 Large Capacity, Central Power-Plant Type Surface Condenser. Source: Babcock & Wilcox

Fig. 11-28 Shell-and-Tube Surface Condenser

Serving 4,500 kW Condensing Unit.

Source: Tuthill Corp., Murray Turbomachinery Div.

Vapor

Vapor Generator (Boiler)

Turbine

Liquid

^Work Out d

Work In

Liquid

Work In

Cooling iCondense^(HWaaOut)

Fig. 11-29 Elements of the Simple Rankine Cycle.

3. Process C-D: Reversible adiabatic expansion of the steam in the turbine from a saturated vapor state to the condenser pressure. For this process:

Fig. 11-28 Shell-and-Tube Surface Condenser

Serving 4,500 kW Condensing Unit.

Source: Tuthill Corp., Murray Turbomachinery Div.

cyclic process being reversible and adiabatic (isentropic).

As shown in Figure 11-29, the simple ideal Rankine cycle can be reduced to four processes:

1. Process A-B: Reversible adiabatic pumping of return condensate into the pressurized boiler. For this process:

2. Process B-C: Constant-pressure heat transfer, resulting in steam generation from return condensate. For this process:

4. Process D-A: Constant-pressure heat transfer resulting in condensation of steam in the condenser. For this process:

Figure 11-30 shows schematic representations of pressure-volume (p-v), temperature-entropy (T-s), and a Mollier diagram for the ideal Rankine cycle.

In the pressure-volume (p-v) diagram, the two constant-pressure phases of admission (4-1) and exhaust (2-3) are connected by an isentropic-expansion phase (1-2). The shaded area 4-1-2-3 represents the work of the cycle.

The temperature-entropy (T-s) diagram shows the properties for liquid, wet vapor, and superheat, as taken from the

Fig. 11-30 Pressure-Volume, Mollier and Temperature-Entropy Diagrams for Ideal Rankine Cycle. Source: Babcock & Wilcox c b a

Fig. 11-30 Pressure-Volume, Mollier and Temperature-Entropy Diagrams for Ideal Rankine Cycle. Source: Babcock & Wilcox steam tables. The Rankine cycle can be superimposed, as shown. Underneath the curve lies the vapor dome in which a liquid vapor mixture exists. The upper of the parallel lines (cd) represents the path of heat addition at constant temperature as high-pressure liquid is vaporized to steam. The line (d-1) leading from the vapor dome to point 1 represents superheating of steam. The isentropic expansion in the steam turbine is the vertical line 1-2. The bottom line (2-a) represents the condensing path in which heat is rejected as low-pressure steam is condensed to a liquid. The isentropic compression in the feed pump is the vertical line a-b. Compression phase is usually negligible and points a and b can, therefore, be considered as a single point, saturated liquid at the exhaust pressure. All of the necessary values for calculating power output and efficiency can be taken from standard steam tables.

Another way to identify the values required for calculating power output and efficiency from a given set of conditions is to use a Mollier (or h-s) diagram to represent the thermodynamic properties of steam. The ordinate (h) is enthalpy and the abscissa (s) is entropy. The available energy that can be converted into work is shown on the Mollier diagram as a vertical line hc — hd.

Ideal simple Rankine cycle thermal efficiency is represented by:

Turbine work out — Pump work (hc — hd) — (hb — ha)

Heat i

Pump work is often left out of this equation*, and thus: Turbine work out (hc — hd)

Heat in

Where TWR is in lbm/hp-h and (hc - hd) is in Btu/lbm. This equation, expressed in kWh output, is:

3,413

Where, TWR (or TSR) is in lbm/kWh and (hc - hd) is in Btu/lbm. c d

Ideal heat rate for a condensing turbine is the product of TWR and boiler heat input. For a back-pressure turbine, where the steam evaporation process is debited to process, heat rate is simply the TWR times the heat drop. Thus:

Ideal heat rate (condensing turbine) = TWR(hc — hb)

Ideal heat rate (back-pressure turbine) = TWR(hc — hd)

Ideal cycle power output is determined by the steam flow rate times the heat drop. It is expressed in terms of hp as:

2,545

Where:

m = steam flow rate, in lbm/h hc - hd = heat drop, in Btu/lbm

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