Thermodynamics and Propulsion

11.3 Implications of propulsive efficiency for engine design

If we consider our expressions for thrust and propulsive efficiency together,

$$F = \dot{m}(u_e - u_0) \qquad \textrm{and}\qquad \eta_{\textrm{prop}}=\cfrac{2}{1+\cfrac{u_e}{u_0}}$$

we see that

$$\textrm{as}\quad\frac{u_e}{u_0}\uparrow \quad \frac{F}{\dot{m}u_0} \uparrow \quad \textrm{but} \quad \eta_{\textrm{prop}} \downarrow$$

$$\textrm{and as}\quad \frac{u_e}{u_0}\rightarrow 1 \quad \frac{F}{\dot{m}u_0} \downarrow \quad \textrm{and} \quad \eta_{\textrm{prop}} \uparrow.$$

Also note that for

$$\frac{F}{\dot{m}u_0} \uparrow \quad A_{\textrm{inlet}} \downarrow \quad \textrm{Drag} \downarrow,$$

where $A_{\textrm{inlet}}$ is the inlet area of an engine, shown in Figure 11.1.

Figure 11.1: Schematic of the inlet area of an engine

The balance between propulsive efficiency and specific thrust ($\propto$ thrust per unit mass flow) is shown in Figure 11.2.

Figure 11.2: Propulsive efficiency and specific thrust as a function of exhaust velocity (Kerrebrock, 1991).

For fighter aircraft that need high thrust/weight and fly at high speed, it is typical to employ engines with smaller inlet areas and higher thrust per unit mass flow,

$$\therefore \frac{u_e}{u_0} \uparrow \quad \textrm{and} \quad \eta_{\textrm{prop}} \downarrow.$$

The small inlet of one of the F-22 Raptor's two engines is visible just below the cockpit in Figure 11.3.

Figure 11.3: The F-22 Raptor (Copyright 1999 by Lockheed Martin).

However, transport aircraft that require higher efficiency and fly at lower speeds usually employ engines with relatively larger inlet areas and lower thrust per unit mass flow,

$$\therefore \frac{u_e}{u_0} \rightarrow 1 \quad \textrm{and} \quad \eta_{\textrm{prop}} \uparrow.$$

The large inlets of a Boeing 777-200's engines are shown in Figure 11.4.

Figure 11.4: The Boeing 777-200 (Jane's, 1998-9).

At low flight velocities, the highest propulsive efficiency is typically obtained with a propeller or an unducted fan. Figure 11.5 shows a propeller craft, and Figure 11.6 shows a sketch of a jet engine with an unducted fan. Figure 11.7 shows propulsive efficiency as a function of airspeed for different engine bypass ratios.

Figure 11.5: A propeller gives a relatively small impulse ($\Delta u$ ) to a relatively large mass flow (Boeing, 2000)

Figure 11.6: An advanced, contour-rotating, unducted fan concept (Rolls-Royce, 1992)

Figure 11.7: Propulsive efficiency comparison for various gas turbine engine configurations (Rolls-Royce, 1992)