Ramjets and Afterburners

The ideal ramjet, its thrust and efficiency against Mach number, the afterburning turbojet and where each engine wins

The J58

The Pratt & Whitney J58 powered the Lockheed A-12, the YF-12 and the SR-71, and had to take them from standing still to about 3,200 km/h. It was an afterburning turbojet with one unusual feature: above Mach 2, about 20 % of the air entering the compressor left it after the fourth stage and went through six external tubes straight to the afterburner. At cruise the engine was described as acting like a turboramjet (the J58). The compressor and turbine never stopped. But the faster the aircraft flew, the less there was for them to do — and the more the engine came to depend on the inlet in front of it and the burner behind it. Lesson 3-1 predicted this: near Mach 3 the best compressor ratio falls to 1. This lesson follows that thought to its end — the engine with no compressor at all — and asks what the afterburner buys on the way.

Why speed hurts the turbojet. Ram compression is free, but it heats the air: at Mach 3 in the stratosphere the air reaches the compressor at about 600 K (Lesson 2-1). The turbine sets a limit on

T_{t4}

, so the hotter the compressor exit, the less fuel can be burned. With a fixed compressor ratio there is a Mach number at which the compressor exit reaches

T_{t4}

and the engine can burn nothing at all.

Take the turbomachinery away and the limit moves: a ramjet has no turbine to protect, so its burner can run much hotter — 2000 K and more.

\frac{F}{\dot m_0} = a_0 M_0\left(\sqrt{\frac{\tau_\lambda}{\tau_r}} - 1\right), \qquad \eta_{th} = 1 - \frac{1}{\tau_r}, \qquad f = \frac{c_p T_0(\tau_\lambda - \tau_r)}{h_{PR}}

The ideal ramjet: specific thrust, thermal efficiency and fuel–air ratio. Its only compression is the ram, τr = 1 + (γ − 1)M0²/2.

Derivation

The ideal ramjet

A ramjet is a turbojet with

\tau_c = \tau_t = 1

. The turbojet's jet velocity becomes

\left(\frac{V_9}{a_0}\right)^2 = \frac{2}{\gamma - 1}\,\frac{\tau_\lambda}{\tau_r}(\tau_r - 1) = \frac{2}{\gamma - 1}\,\frac{\tau_\lambda}{\tau_r}\cdot\frac{\gamma - 1}{2}M_0^2 = M_0^2\,\frac{\tau_\lambda}{\tau_r},

V_9/V_0 = \sqrt{\tau_\lambda/\tau_r} = \sqrt{T_{t4}/T_{t0}}

: the jet is faster than the flight speed in proportion to the square root of the temperature rise. Thrust per unit mass flow is

a_0(V_9/a_0 - M_0)

, and the Brayton efficiency with

\tau_c = 1

1 - 1/\tau_r

📐An ideal ramjet across the Mach range

T_{t4} = 2000

K in the stratosphere (Lab 1):

Mach 0.5: 290 N·s/kg at a TSFC of 143 mg/(N·s) — five times a turbojet's.
Mach 2: 746 N·s/kg, TSFC 50, $\eta_{th} = 44\,\%$ .
Peak specific thrust 759 N·s/kg at Mach 2.34.
Mach 4: 570 N·s/kg, $\eta_{th} = 76\,\%$ , TSFC 45.
Thrust falls to zero at Mach 6.4, where ram compression alone heats the air to 2000 K.

The ramjet gives no thrust at rest — something else must get it moving — and its thermal efficiency, set entirely by speed, becomes excellent only when it is fast.

The afterburner. A turbojet's turbine leaves the gas well below

T_{t4}

— but with plenty of unburned oxygen. An afterburner (reheat) sprays more fuel into the gas between the turbine and the nozzle and burns it, raising the nozzle-entry temperature to

T_{t7}

, limited only by the burner and the nozzle walls. More temperature means a faster jet and more thrust; burning fuel at the low pressure behind the turbine means it is converted to work far less efficiently.

\frac{V_9}{a_0} = \sqrt{\frac{2}{\gamma - 1}\,\frac{T_{t7}}{T_0}\left(1 - \frac{1}{\tau_r\tau_c\tau_t}\right)}, \qquad f_{total} = \frac{c_p T_0\,(T_{t7}/T_0 - \tau_r)}{h_{PR}}

Ideal afterburning turbojet: jet velocity with the nozzle fed at Tt7, and the total fuel–air ratio of both burners.

Derivation

The afterburning turbojet

The ideal afterburner adds heat with no pressure loss, so the nozzle sees the same stagnation pressure ratio as the dry engine,

\tau_r\tau_c\tau_t

in temperature terms, but a higher stagnation temperature

T_{t7}

T_9 = \frac{T_{t7}}{\tau_r\tau_c\tau_t}, \qquad V_9^2 = 2c_p(T_{t7} - T_9) = 2c_p T_{t7}\left(1 - \frac{1}{\tau_r\tau_c\tau_t}\right).

Both burners together raise the air from

T_0\tau_r

(inlet) to

T_{t7}

, less the compressor work, which the turbine returns to the same stream; the net heat is

c_p(T_{t7} - T_0\tau_r)

, which gives

f_{total}

📐What the afterburner buys

A turbojet with

\pi_c = 12

T_{t4} = 1600

K and an afterburner at

T_{t7} = 2200

K (Lab 2):

At rest: thrust ×1.26, TSFC ×1.35.
At Mach 0.9: thrust ×1.37, TSFC ×1.31.
At Mach 2: thrust ×1.68, TSFC ×1.33.

The afterburner is worth most at high speed, where the dry engine's thrust has fallen furthest, and it always costs about a third more fuel per newton. That is why fighters light it for take-off, combat and acceleration — and Concorde only through the transonic range.

💡Which engine for which speed

With the same maximum temperature of 2000 K, an ideal turbojet with

\pi_c = 12

gives more thrust per kilogram of air below Mach 2.38, and the ramjet above it (Lab 3). Its compressor exit would reach 2000 K at Mach 4.2, and above that it could burn no fuel at all.

Turbojet and turbofan: take-off to about Mach 2, the only choice at low speed.
Afterburning turbojet: short bursts of thrust, especially around Mach 1–2.
Ramjet: about Mach 2.5–5, once something else has brought it up to speed.
Scramjet (supersonic combustion, Lesson 2-3's warning): above about Mach 5.

As I have already said, the machine does not isolate man from the great problems of nature but plunges him more deeply into them.

– Antoine de Saint-Exupéry, Wind, Sand and Stars (1939) (Wikiquote)

⚠Afterburner economics

The afterburner's thrust gain is large and its TSFC penalty is permanent. An engine designed to cruise on afterburner would be a poor engine; supersonic-cruise designs such as Concorde's Olympus and the F-22's F119 were built to cruise dry, using reheat only to get there. Lesson 10-1 follows the adaptive-cycle engines that try to be efficient both ways.

💡Where you will use this

Lesson 4-2 adds burner and nozzle losses to the afterburning turbojet. Lesson 7-3 designs afterburner flameholders. Unit 5 designs the inlets that make high-Mach engines possible — at Mach 3 the inlet does most of the compression.

📚Further reading

Jack D. Mattingly and Keith M. Boyer, Elements of Propulsion: Gas Turbines and Rockets (2nd ed., AIAA, 2016), the ideal ramjet and the ideal afterburning turbojet.
William H. Heiser and David T. Pratt, Hypersonic Airbreathing Propulsion (AIAA, 1994), for ramjets and scramjets.
NASA Glenn Research Center, Ramjet and scramjet thrust.

↓But there is a problem

At high speed the winning engine is the one with nothing inside. At low speed it is the opposite: the best engine moves an enormous mass of air very gently — a propeller, or a fan with no core stream at all. To hover, the F-35B takes power off its engine through a shaft and a clutch and turns a 50-inch fan buried in its fuselage.