A 20,000-kW turbogenerator is supplied
with steam at 300 lb / in2 (abs) (2067.0
kPa) and a temperature of 650-F
(343.3-C). The backpressure is 1 in (2.54 cm) Hg
absolute. At best efficiency, the steam
rate is 10 lb (25.4 kg) per kWh. (a) What is
the combined thermal efficiency (CTE)
of this unit? (b) What is the combined
engine efficiency (CEE)? (c) What is
the ideal steam rate?
Calculation Procedure:
1. Determine the combined thermal
efficiency
(a) Combined thermal efficiency, CTE =
(3413/wr)(1/[h1 - h2]), where wr = combined steam rate, lb/kWh
(kg/kWh); h1 = enthalpy of steam at throttle pressure and
temperature, Btu/ lb (kJ / kg); h2 = enthalpy of steam at the turbine
backpressure, Btu/ lb (kJ / kg). Using the steam tables and Mollier
chart and substituting in this equation, CTE = (3413/10)(1/[1340.6 -
47.06]) = 0.2638, or 26.38 percent.
2. Find the combined engine efficiency
(b) Combined engine efficiency, CEE =
(wi)/(we ) = (weight of steam used by ideal engine, lb /kWh (weight
of steam used by actual engine, lb /kWh). The weights of steam used
may also be expressed as Btu/ lb (kJ / kg). Thus, for the ideal
engine, the value is 3413 Btu/ lb (7952.3 kJ/ kg). For the actual
turbine, h1 – h2x is used, h2x is the enthalpy of the wet steam at
exhaust conditions; h1 is as before.
Since the steam expands isentropically
into the wet region below the dome of the T-S diagram, we must first
determine the quality of the steam at point 2 either from a T-S
diagram or Mollier chart or by calculation.
By calculation using the method of
mixtures and the entropy at each point: S1 = S2 = 0.0914 – (x2
(1.9451). Then x2 = (1.6508 - 0.0914)/1.9451 = 0.80, or 80 percent
quality. Substituting and summing, using steam-table values, h2x =
47.06 - 0.8(1047.8) = 885.3 Btu/ lb (2062.7 kJ/ kg).
(c) To find the CEE we first must
obtain the ideal steam rate, wi = 3413/ (h1 - h2x ) = 3413/(1340.6 -
885.3) = 7.496 lb /kWh (3.4 kg/kWh).
Now, CEE = (7.496/10)(100) = 74.96
percent. This value is excellent for such a plant and is in a range
being achieved today. Related Calculations. Use this approach to
analyze the efficiency of any turbogenerator used in central-station,
industrial, marine, and other plants.
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