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Power

Cold water

Distilled water

Power

Figure 4.3 OTEC configurations include the open-cycle type without distilled water production (a), the open-cycle type with distilled water recovery (b), the close-cycle (c), and the hybrid-cycle (d).

hybrid cycles (Figure 4.3d). The open cycle avoids heat exchangers (or, if fresh water is desired, it requires only a single heat exchanger). However, the low pressure of the steam generated demands very large diameter turbines. This difficulty is overcome by using a close (or a hybrid) cycle with ammonia as a working fluid. Most work has been done on the close-cycle configuration, which is regarded as more economical. However, the costs of the two versions may turn out to be comparable.

4.3 Turbines

A turbine (Figure 4.4) generates mechanical energy from a difference in pressure. Usually, the state of the gas at the inlet and the pressure of the gas at the exhaust are specified.

Let pin and Tin be the pressure and the temperature at the inlet of the turbine and pout, Tout the corresponding quantities at the exhaust.

The output of the turbine is the mechanical work, W. The heat, Q, is exchanged with the environment by some means other than the circulating gases. Most practical turbines are sufficiently well insulated to be assumed adiabatic—that is, a condition in which Q = 0.

The inlet gas carries an enthalpy, Hin, into the turbine, while the exhaust removes Hout from the device. Conservation of energy requires that*

Expressing the quantities on a per kilomole basis (quantities per kilomole are represented by lower case letters), we can write

because, under steady-state conditions, iin = iout = i.

Figure 4.4 A turbine.

^Provided there is no appreciable change in kinetic, potential, magnetic, and other forms of energy.

Assuming a constant specific heat, hin hout cp(Tin Tout), (4.4)

Equation 4.6 looks similar to that which describes the behavior of a heat engine. However, the quantity, icpTin, although having the dimensions of energy, is not the heat input to the device; rather, it is the enthalpy input. For a given input state and a given exhaust pressure, the mechanical energy output increases with decreasing exhaust temperature. The lowest possible value of Tout is limited by the second law of thermodynamics that requires that the entropy of the exhaust gases be equal or larger than that of the inlet gases. The lowest exhaust temperature (highest output) is achieved by a turbine operating isentropically, one in which the entropy is not changed. Any deviation from this condition is due to irreversibilities (losses) in the device. These losses will generate heat and thus increase Tout.

Isentropic Processes

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