Modern Engineering Thermodynamics

662 CHAPTER 16: Compressible Fluid Flow
Throat
Increasing pressure
FIGURE 16.9
Diverging subsonic diffuser.
Throat
Decreasing pressure
FIGURE 16.10
Diverging supersonic nozzle.
M < 1
Δp > 0
ΔV < 0
M >1
Δp < 0
ΔV > 0
subsonic, M < 1, and Eq. (16.17a) tells us that ∂p s must be > 0. That is, the
pressure must increase in the direction of a subsonic diverging flow.
■ Equation (16.17b). In the case of diverging subsonic flow, Eq. (16.17b) tells us
that, since ∂A s > 0 and M < 1, ∂V s must be < 0, so the flow velocity must decrease
in the direction of flow. In Chapter 6, we learned that a device that converts
kinetic energy (∂V s < 0) into pressure (∂p s > 0) is called a diffuser.
Consequently, a diverging passage carrying subsonic flow is called a subsonic
diffuser (Figure 16.9).
Diverging supersonic flow: ∂A s > 0 and M > 1
■ Equation (16.17a). Since∂A s > 0andM> 1 here, Eq. (16.17a) tells us
that ∂p s must be < 0 and the pressure must decrease in the direction
of flow.
■ Equation (16.17b). For ∂A s > 0 and M > 1, Eq. (16.17b) tells us that ∂V s must be
> 0 and the flow velocity must increase in the direction of flow. This again
corresponds to the definition of a nozzle as a device that converts pressure into
kinetic energy, so a diverging passage carrying supersonic flow is called a supersonic
nozzle (Figure 16.10). This is the type of nozzle used on the space shuttle rocket
engine, as shown in the schematic of Figure 16.11.
When M = 1.0 in Eq. (16.17b), ð∂A s =AÞ = 0: This corresponds to a point of minimum crosssectional
area. This point is called the throat of the device, characterized by the fact that it
can never have a Mach number greater than 1; that is M throat ≤ 1:0:
When the Mach number at the throat is equal to 1, we say that the throat is at its critical
condition and denote its properties in this state with a superscript asterisk. Then, M throat is
always equal to 1.0, and from Eqs. (16.12), (16.13), and (16.14), the critical condition
properties at the throat are 1
T 2
= T os (16.18)
k + 1
k/ðk–1Þ
p 2
= p os (16.19)
k + 1
Fuel turbines
Throat
Supersonic nozzle
High-altitude
exhaust
Low-altitude
exhaust
High-altitude
exhaust
FIGURE 16.11
Space shuttle rocket engine.
1 These are not the same as the thermodynamic critical state properties. The use of the word critical here refers to a different type of
phenomenon.