A STUDY ON THE SCIENCE OF RAMJETS

A Boeing F/A-18 with afterburners on. Note shock/expansion patterns in the supersonic nozzle exhaust.

Image Courtesy: www.boeing.com

Abstract: This paper attempts to study, understand and learn the concepts behind the science of

Ramjets. Starting from their evolution, right after the first flight by the right brothers to the present-day

applications such as Advanced Ramjet Technology using Ultra-Intense Laser Derived In-Situ Antimatter is

briefly explained by illustrating graphs, equations and plots wherever necessary.

A few note-worthy journals, articles and papers have been reviewed to prepare this research paper. This

made it possible to come up with various applications, technologies, methods and limitations that drive

the science of ramjets. An advanced take on supersonic ramjets (Scramjets) have also been incorporated

in this paper making it a good source of study on the subject of Ramjets.

INTRODUCTION

Man had always fantasized about the possibility of flying. Watching birds scale heights with their wings

would have made man wonder if he’d ever do the same. Probably that drove him to discover methods

that could indeed fulfill his long-cherished dream of flying high!

The history of man’s desire to fly find reference even in the mythological Greek legends where flying

humans and super-humans were note-worthy aspects. Of course, the story has evolved far beyond

those mythological tales through the ideas, thoughts, calculations, designs, data and experiences all of

which led to the first flight of the Wright Brothers in the year 1903. In one way, we’d assume that this

historic steady flight laid the foundation to Ramjet technology, and that wouldn’t be totally wrong as the

first known references to Ramjets dates back to 1913, just a decade about the eventful flight.

Background:

RAMJET

The driving force for the invention of Ramjets was the dire need of fast-moving, high-speed, air-

breathing propulsion systems. In the age of World Wars, countries required high-speed vessels that

could propel the movement of missiles and bombers. Things first gained momentum in 1913 when the

Ramjet was originally conceived and was patented by Rene Lorin; however, he was not able to build a

prototype because of the shortage of adequate materials.

In 1928, Boris Stechkin presented a theory of supersonic ramjet engines; and finally in 1933, I.A.

Merkulov designed and tested the first Ramjet engine. However, the credit for the first powered ramjet

flight goes to French engineer René Leduc when his persistence and secrecy paid off on April 21, 1949,

when his Lorin-inspired 010 model. Carring aloft atop a Languedoc 161 airliner, the innovative ramjet

model flew for 12 minutes and reached 450 mph (724 kph) at half power.

Ramjets – The Mammoth, Super flying machines

Let’s start understanding the science and design of Ramjets by a simple observation: Have you ever

belly-flopped off a high dive and been hit by the surrounding air? Have you? The basic science revolving

around this phenomenon is when you hit a fluid without giving it time to get out of the way, it tends to

hit back. Deep-sea divers and swimmers beat physics by taking a more streamlined plunge, and faster

cars and aircraft do it by sporting more aerodynamic shapes. However, there is a constraint as we move

closer to the speed of sound. As we reach that ‘jinxed’ threshold, something strange happens as

streamlining is not enough anymore. Now, the speed at which the very air that kept the plane aloft

begins to hammer it down with seemingly insurmountable drag, teeth-rattling turbulence and brutal

shock waves. Now, that’s awful, isn’t it?

But wait, here’s something intriguing we can do that. What if this turbulent speed was put to some great

advantage? What if instead of churning through it with propellers or burning through it with rockets, we

could pack it into a specially shaped tube, pump it up with an explosion and fire it out a nozzle at

supersonic speeds, all with no major moving parts? Wonder how we’d do it? We’d probably be using a

Ramjet to do job for us!

For starters, Ramjet holds a very simple approach of owning no moving parts and yet compress the

incoming atmospheric subsonically then mix it with fuel which burns in a combustion chamber

downstream of a flame-holder. The resulting exhaust gases pass through a choked nozzle and are

exhausted to the atmosphere at supersonic speed. But here’s a deception! Unlike its main speed

competitor, viz., rocket, which utilizes chemicals such as potassium chlorate, ammonium nitrate among

others as its powering fuels, ramjets possess essentially air-breathing engines. Therefore, even though

ramjets can compete with rockets in terms of speed, they still cannot travel at vacuum and require to fly

through the atmosphere.

The main area where Ramjets can compete with rockets is Speed. However, rockets cannot start on

their own. They are handicapped with the need of thrust or energy boosters to propel to a supersonic

speed before they can fully take charge.

So, how do you define a Ramjet?

A ramjet is a type of turbojet that uses the forward direction of incoming air to compress it in the pre-

combustion phase without employing a compressor.

The Ramjet essentially has three main parts:

1. Inlet

2. Combustion Chamber

3. Nozzle

These three parts make up to a highly fast-moving giant that has now taken the world by storm.

How does a Ramjet Work?

The Inlet compresses and decelerates the incoming air flow by a network of shocks formed at the mouth

of the inlet. The incoming air is compressed before it enters into the combustion chamber. A majority of

ramjets use shock waves to slow down the air flow and make it suitable to enter the combustor.

The Combustor injects fuel and combines it with the air flow to ignite the mixture. An ideal fuel to an air

ratio needs to be achieved such that Stoichiometric balance is maintained. This can be done by keeping

a watch on the fuel pressure and the fuel flow to fuel injector optimization. Nevertheless, it is pivotal

fuel flow doesn’t exceed the stoichiometric ratio for the fuel flow may otherwise turn saturated, or fuel

rich, or may simply not ignite at all.

In order to facilitate the fuel ignition process, fuel injector atomizes the fuel that results in better mix

with the air flowing through the ignition, and therefore help in better combustion. To maintain flow

stability, flame holder is employed. It further slows down the flow and creates a recirculation region to

allow the flame to propagate. In some cases, a simple flat plate may find use as a flame holder. It

shelters the flame and improves fuel mixing.

The Nozzle is typically used to drive out the exhaust of the combustor at supersonic speeds to obtain the

expected high thrust. For supersonic flows, a converging-diverging nozzle is used; as for the subsonic

flow, a converging nozzle is ideal.

Dual-Combustion Supersonic Ramjet

During an interesting study on combustion in external supersonic streams, NASA pioneers came out with

several intriguing results. As part of this investigation, highly reactive fuels were injected adjacent to

wedge airfoils and vigorous burning was observed. However, one interesting observation was although

considerable lift and thrust was observed at Mach number 5, this external burning endeavor marked

high lift and low drag but acceptably low efficiency! This led to a new consensus that prompted the

NASA scientists to try an internally burning supersonic combustion ramjet, better known to us as

Scramjet.

The initial efforts in this direction were highly successful, and investigations over ducted combustion

supersonic ramjets were in full swing. In the beginning phases, asymmetric external-internal contraction

inlet was designed. However, with difficulties relating to weight and complexity of variable geometry, a

fixed-geometry inlet was introduced.

In the past studies, supersonic combustion in ramjet has been observed to solve several problems

associated with the severe stagnation conditions within a ramjet engine at high flight Mach number.

Diffuser momentum loss, dissociation, non-equilibrium expansion losses, and structural loading are all

relieved by transition to a supersonic combustion process. In general, the cross-sectional area of the

supersonic combustor increases in the downstream direction to avoid thermal choking and excessive

pressure gradients. The subsequent nozzle expansion process requires a more dramatic increase in

cross-sectional area and is usually integrated with the vehicle aft end to provide the maximum possible

area ratio. In order to battle these issues, a ‘dual-mode’ ramjet was patented by Curran in the year

1972.

An interesting aspect of the Dual-mode Scramjet is that it gives thrust even at zero speed.

In a dual mode ramjet, a thermally-choked combustion process is established in the aft regions of the

scramjet flow path where the cross-sectional areas are greatest. The diverging scramjet duct acts as a

subsonic diffuser, and the thermal throat is positioned so as to effect the required back-pressure. The

cross-sectional area of the thermal throat must increase as flight Mach number decreases, unless fuel-

to-air ratio is reduced.

Dual-Mode Scramjet

For a given duct, this effect determines the minimum flight Mach number for dual-mode operation. At

Mach 3, the required thermal throat area approaches that of the inlet capture area and necessitates

that combustion extend into the nozzle region.

Alternatively, we can also define a dual-mode supersonic ramjet as a Propulsion System, which being

dependent on the Flight Mach Number, operates in two Modes. The flow path can be Fixed Geometry

and is slightly diverging.

The following are the two major modes of the Dual-mode Supersonic Ramjet:

Mode 1: As a Ramjet with a high Mach but Subsonic Combustion; here, the “Throat” is provided

through Thermal Choking. An “Isolator” is required for lower Mach operation to provide a combustor

entrance pressure higher than the combustion Pressure.

Mode 2: As a Scramjet with Supersonic Combustion

Ramjets do exist in subsonic flow, however, supersonic ramjets are used on a wider scale and are deemed to be more efficient.

Subsonic Ramjet Behavior Illustration

Ideal Ramjet Cycle Analysis:

A typical Ramjet works on the principle of a Brayton Cycle. Using the turbine engine station

numbering system, we begin with free stream conditions at station 0. In cruising flight, the inlet

slows the air stream to compress it to station 2 conditions. As the flow slows, some of the

energy associated with the aircraft velocity increases the static pressure of the air and the flow

is compressed. Ideally, the compression is isentropic and the static temperature is also

increased as shown by the dashed lines on the plot. For an ideal, isentropic compression a

vertical line on the T-s diagram describes the process. In reality, the compression is not

isentropic and the compression process line leans to the right because of the increase in

entropy of the flow. The non-isentropic effects are the result of shock waves in the inlet. For

the ramjet, there is a terminal normal shock in the inlet that brings the flow to subsonic

conditions at the burner. As speed increases, the losses through this shock eventually decrease

the level of pressure that can be achieved in the burner, and this sets a limit on the use of

ramjets. For supersonic combustion ramjets (scramjets) there is no normal shock and the inlet

shock losses associated with the normal shock are avoided. The combustion process in the

burner occurs at constant pressure from station 3 to station 5. The temperature increase

depends on the type of fuel used and the fuel-air ratio. For scramjets, there may be additional

entropy losses associated with the mixing of the fuel and the air. Following combustion, the hot

exhaust is then passed through the nozzle. Ideally, the nozzle brings the flow isentropically back

to free stream pressure from station 5 to station 8. Since ramjets and scramjets often use

converging-diverging nozzle designs, there is often a mismatch between the external flow

pressure and the free stream. The area under the T-s diagram is proportional to the useful work

and thrust generated by the engine.

Below is a systematic definition of processes at each station:

Station 1

Here we have undisturbed air, just before entering the inlet of the engine. The stagnation temperature can be determined from the static temperature and the Mach number using the isentropic relation.

, and

, and

Isentropic diffuser, from Station 1 to Station 2:

Adiabatic, and no work done except that of volume change:

Isentropic (reversible, adiabatic, therefore no losses):

Constant-Pressure Heat Addition, from Station 2 to Station 3:

is specified, for a given thrust setting. For maximum thrust, this value is limited by the limiting temperature of the combustor material.

To find the fuel/air ratio needed to achieve this temperature, we consider the enthalpy balance across the combustor.

Stagnation enthalpy of the air + burned products leaving the combustor = Stagnation enthalpy of the air entering the combustor + sensible enthalpy of the fuel + heat released by reaction.

We neglect the sensible enthalpy of the fuel, since it is very small compared to the heat released by reaction.

Solving for the fuel/air ratio,

Isentropic Nozzle, from Station 3 to Station 4:

Fully expanded flow at the nozzle exit: static pressure is the same as the ambient atmospheric pressure.

Relating temperature ratio and pressure ratio,

Also, the exit Mach number can be found from:

Let us pause for a moment and consider what the exit Mach number will be. Since stagnation pressure is constant throughout this ideal engine, and the specific heats are assumed constant,

Obviously, the exit Mach number will be equal to the flight Mach number!

Exit velocity is

and the flight velocity is

Thrust per unit air mass flow rate:

and Thrust Specific Fuel Consumption

TSFC = f*m/T

Ramjet Performance and Efficiency:

Although ramjets may be run as slow as 45 meter per second below about Mach 0.5, they give little

thrust and are highly inefficient due to their low pressure ratios.

However, above this speed, given sufficient initial flight velocity, a ramjet will be self-sustaining. Indeed,

unless the vehicle drag is extremely high, the engine/airframe combination will tend to accelerate to

higher and higher flight speeds, substantially increasing the air intake temperature. As this could have a

detrimental effect on the integrity of the engine and/or airframe, the fuel control system must reduce

engine fuel flow to stabilize the flight Mach number and, thereby, air intake temperature to reasonable

levels.

Due to the stoichiometric combustion temperature, efficiency is usually good at high speeds (around

Mach 2–Mach 3), whereas at low speeds the relatively poor pressure ratio means the ramjets are

outperformed by turbojets, or even rockets.

Applications of Dual-Mode Scramjet:

As illustrated above, dual-mode scramjet can address several high-speed problems for the aerospace

industry. Additionally, when considered with the current breed of common applications of dual-mode

scramjet, they are extensively employed in Long Range Missiles and Reusable Heavy Commercial

Vehicles (HCVs).

Limitations of Dual-Mode Scramjet:

The primary technical challenges in practical application of the dual-mode scramjet scheme are

modulation of the thermal throat location, fuel distribution, ignition, and flame-holding in the large

cross-section. Any in-stream devices must be retractable or expendable so as not to inhibit supersonic

combustion operation. As per the cycle analysis, the dual-mode scramjet is central to most combined-

cycle schemes.

Related versions of Ramjets:

We’d a brief study of a typical ramjet and its faster cousin, scramjet. However, there is more than what

meets the eye. In addition to these two air breathing engines in the ramjet family, there are a few more

that belong to the same space:

Nuclear-powered ramjets

During the Cold War, the United States designed and ground-tested a nuclear-powered ramjet called

Project Pluto. This system used no combustion; a nuclear reactor heated the air instead. The project was

ultimately canceled because ICBMs seemed to serve the purpose better, and because a low-flying

radioactive missile could cause problems for any allied soldiers.

Ionospheric ramjet:

The upper atmosphere above about 100 kilometers contains monatomic oxygen produced by the sun

through photochemistry. A concept was created by NASA for recombining this thin gas back to diatomic

molecules at orbital speeds to power a ramjet.

Bussard ramjet:

The Bussard ramjet is a spacecraft propulsion concept intended to fuse interstellar wind and exhaust it

at high speed from the rear of the vehicle.

Modern Applications:

Ramjets have found their applications across various fields. In aviation, ramjets have definitely

attained a foothold as several of the heavy commercial aircraft as well as the military aircraft

and missiles now deploy ramjet technology. In addition to these applications, the ramjet has

also been used in a very innovative science of Anti-matter.

For beginners, antimatter comprises of positron (positively charged electrons). It is similar to

matter with respect to almost all properties including mass with a difference lying in its charge

value.

For centuries antimatter has been a baffling topic for physicists and scientists. So, although it is

real and account their presence in the universe, they constitute of sub-atomic particles that are

the opposite of normal matter. And therefore, when a particle and antiparticle meet, they

mutually annihilate each other and release their entire mass as energy.

In amidst of all this, ramjet still manages to find application in this mysterious science in the

form of Advanced Ramjet Propulsion System using Antimatter.

This intriguing concept relates to the generation of antimatter by ultra-intense laser pulses

incident on a high atomic number target. In this experiment, the high atomic number is used as

Gold.

Derivation of Ideal Ramjet Using Ultra-Intense Laser Derived In-Situ Antimatter

The primary difference between the conventional ideal ramjet and the ideal ramjet using in-situ

ultra-intense laser derived antimatter is the fuel air ratio will be set to zero. The stagnation

temperature of the combustion chamber is obtained using an energy balance. The energy

balance involves the incoming flow stagnation temperature at station 2 with antimatter

annihilation per kilogram of airflow determining the stagnation temperature.

Qantimatter = Cp(To4 – T02)

Q Antimatter – annihilation heat antimatter addition per kilogram of airflow

Cp – Constant pressure specific heat

T02 – Stagnation temperature at station 2

The stagnation pressure of station 4 should be derived as a function of Mach Number

T0/T = 1+((K-1)/2)*M2)

T0 – Stagnation Temperature

T – Static Temperature

The energy balance equation gives away the following equation:

T04 = QAntimatter/Cp + Ta((K-1)/2)*M2)

The combustion chamber heat addition is based on in-situ antimatter annihilation derived from

an ultra-intense laser system that is incident on a 1 mm thick gold target. The following ideal

ramjet thrust equation is derived for an antimatter ideal ramjet using ultra-intense laser

derived in-situ antimatter with the fuel air ratio set to zero.

In-Situ Antimatter Derived from an Ultra-Intense Laser

The Titan laser of Lawrence Livermore National Laboratory is an ultra-intense laser (1020

W/cm2) with ~1 ps pulses that has demonstrated the capacity to generate 2 × 1010 positrons

incident on a ~1 mm thick gold target.

Approximately 90% of the positrons are emitted anisotropic and aft to the laser target through

predominantly the Bethe-Heitler process, which is resultant of interaction between electrons

and the nuclei through bremsstrahlung photons. Therefore, each ~1 ps pulse yields 1.8 × 1010

positrons to the aft of the laser target with about 2 MeV of kinetic energy.

The rest mass of the positron and electron pair is 2 mc2 = 1.02 MeV, and m is the electron rest

mass equivalent to the positron rest mass and c is the speed of light. The positron kinetic

energy is 2 MeV. Assuming the collisions are elastic, such that kinetic energy is conserved, the

energy of a positron and electron annihilation is 3.02 MeV. For each ultra-intense laser ~1 ps

pulse 8.71 × 10−6 kJ of energy is released aft to the laser target. Extrapolating the current state

of technology, up to 1.8 × 1022 positrons could be emitted aft to the laser target.

Model and Results for Ramjet Propulsion Involving Ultra-Intense Laser

Derived In-Situ Antimatter

Antimatter ramjet thrust as a function of Flight Mach Number

The antimatter ramjet model assumed future extrapolations and improvements in laser energy,

pulse rate, and the possibility for multiple ultra-intense lasers to generate antimatter. A total of

108 pulses on the picosecond time scale using an ultra-intense laser (1020 W/cm2) are

assumed. The antimatter annihilation produces 871 kJ

aft to the laser target and adjacent to the ramjet propulsive flow. For the flight profile, the

ambient air mass flow is scaled to 1 kg/s. A profile addressing the antimatter ramjet thrust as a

function of Mach number is presented.

The ambient conditions of Table 1 are incorporated into the model. As illustrated in Figure 1,

the optimal thrust occurs in the supersonic regime. The antimatter ramjet produces a maximum

thrust of 471 N at a Mach number of 2.77; and the antimatter annihilation achieves a station 4

stagnation temperature of 1494 K. Based on the model results, the antimatter ramjet

propulsion application would be suitable for integration with a UAV propulsion system. The

thrust is directly proportional to the number of ultra-intense laser pulses. Given the scalable

nature of the ultra-intense laser derived antimatter generation, the antimatter ramjet

propulsion system is also applicable for Micro-UAV propulsion applications.

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Le Moyne, R. and Mastroianni, T. (2014) Advanced Concept Ramjet Propulsion System Utilizing In-Situ

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