Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

ordinarily one would expect the steam to start condensing when it strikes

the saturation line. However, this is not always the case. Owing to the high

speeds, the residence time of the steam in the nozzle is small, and there may

not be sufficient time for the necessary heat transfer and the formation of

liquid droplets. Consequently, the condensation of the steam may be

delayed for a little while. This phenomenon is known as supersaturation,

and the steam that exists in the wet region without containing any liquid is

called supersaturated steam.Supersaturation states are nonequilibrium (or

metastable) states.

During the expansion process, the steam reaches a temperature lower than

that normally required for the condensation process to begin. Once the tem-

perature drops a sufficient amount below the saturation temperature corre-

sponding to the local pressure, groups of steam moisture droplets of

sufficient size are formed, and condensation occurs rapidly. The locus of

points where condensation takes place regardless of the initial temperature

and pressure at the nozzle entrance is called the Wilson line.The Wilson

line lies between the 4 and 5 percent moisture curves in the saturation

region on the h-sdiagram for steam, and it is often approximated by the

4 percent moisture line. Therefore, steam flowing through a high-velocity

nozzle is assumed to begin condensation when the 4 percent moisture line is

crossed.

The critical-pressure ratio P*/P 0 for steam depends on the nozzle inlet state

as well as on whether the steam is superheated or saturated at the nozzle inlet.

However, the ideal-gas relation for the critical-pressure ratio, Eq. 17–22, gives

reasonably good results over a wide range of inlet states. As indicated in

Table 17–2, the specific heat ratio of superheated steam is approximated as

k
1.3. Then the critical-pressure ratio becomes

When steam enters the nozzle as a saturated vapor instead of superheated

vapor (a common occurrence in the lower stages of a steam turbine), the

critical-pressure ratio is taken to be 0.576, which corresponds to a specific

heat ratio of k
1.14.

P*

P 0

a

2

k 1

b

k>1k 12


0.546

870 | Thermodynamics

s

h

P^1

1

P^2

Saturation

line

2

Wilson line (x = 0.96)

FIGURE 17–59

The h-sdiagram for the isentropic

expansion of steam in a nozzle.

EXAMPLE 17–16 Steam Flow through a

Converging–Diverging Nozzle

Steam enters a converging–diverging nozzle at 2 MPa and 400°C with a neg-

ligible velocity and a mass flow rate of 2.5 kg/s, and it exits at a pressure of

300 kPa. The flow is isentropic between the nozzle entrance and throat, and

the overall nozzle efficiency is 93 percent. Determine (a) the throat and exit

areas and (b) the Mach number at the throat and the nozzle exit.

Solution Steam enters a converging–diverging nozzle with a low velocity.

The throat and exit areas and the Mach number are to be determined.

Assumptions 1 Flow through the nozzle is one-dimensional. 2 The flow is

isentropic between the inlet and the throat, and is adiabatic and irreversible

between the throat and the exit. 3 The inlet velocity is negligible.

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