MODULE TITLE: Further Aerodynamics, Propulsion and Computational

Techniques.

ASSIGNMENT TITLE: Jet Engine Propulsion

NAME OF LECTURER: H. Adjali

DATE: 9th December 2013

NAME OF STUDENT: Chris Chikadibia Esionwu

COURSE: Aerospace Engineering, Astronautics and Space Technology

ROUTE: NUEAS

STUDENT 1D: K1114745

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Question 1

1.1. Propulsive efficiency, np is the ratio of the thrust power and the rate at which work is done on

the air in an engine (Power output).2

𝑛𝑝 =𝑡ℎ𝑟𝑢𝑠𝑡 𝑝𝑜𝑤𝑒𝑟

𝑝𝑜𝑤𝑒𝑟 𝑜𝑢𝑡𝑝𝑢𝑡 =

𝑡ℎ𝑟𝑢𝑠𝑡 𝑝𝑜𝑤𝑒𝑟

𝑡ℎ𝑟𝑢𝑠𝑡 𝑝𝑜𝑤𝑒𝑟 + 𝑟𝑒𝑠𝑖𝑑𝑢𝑎𝑙 𝑘𝑖𝑛𝑒𝑡𝑖𝑐 𝑒𝑛𝑒𝑟𝑔𝑦

Thrust power = Fnet x Ca, which is the rate of work that must be present in order to keep an aircraft

moving at a constant forward velocity (Ca) against any drag.2

Power output = net work output = 1

2 (𝑚𝑎 + 𝑚𝑓)𝐶𝑗2 − 𝑚𝑎𝐶𝑎2). This the rate of change of kinetic

energy for the flow through the energy.2

Thrust power = = 𝐹𝑛𝑒𝑡 𝑥 𝐶𝑎 = ((𝑚𝑎 + 𝑚𝑓 )𝐶𝑗 − 𝑚𝑎𝐶𝑎)𝐶𝑎

𝑡ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒, 𝑛𝑝 =((𝑚𝑎 + 𝑚𝑓)𝐶𝑗 − 𝑚𝑎𝐶𝑎)𝐶𝑎

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(𝑚𝑎 + 𝑚𝑓)𝐶𝑗2 − 𝑚𝑎𝐶𝑎2)

Neglecting effect of fuel, mf

𝑛𝑝 =(𝑚𝑎𝐶𝑗 − 𝑚𝑎𝐶𝑎)𝐶𝑎

12 (𝑚𝑎𝐶𝑗2 − 𝑚𝑎𝐶𝑎2)

𝑛𝑝 =2𝐶𝑎

𝐶𝑎 + 𝐶𝑗 𝑒𝑞𝑢. 1

Where ma = mass flow rate of air, mf = rate of fuel consumption, Ca = forward velocity

Cj = jet velocity, Fnet = net force

𝑤ℎ𝑒𝑛𝐶𝑎

𝐶𝑗 = 𝑟

𝑡ℎ𝑒𝑛, 𝐶𝑎 = 𝑟𝐶𝑗

𝑠𝑢𝑏𝑠𝑡𝑖𝑡𝑢𝑡𝑒 𝐶𝑎 = 𝑟𝐶𝑗 𝑖𝑛𝑡𝑜 𝑒𝑞𝑢. 1

3

𝑛𝑝 = 2𝑟𝐶𝑗

𝑟𝐶𝑗 + 𝐶𝑗 =

𝐶𝑗(2𝑟)

𝐶𝑗(1 + 𝑟) =

2𝑟

1 + 𝑟

Question 2

2. This is a concise comparison between pure jet, ramjet and rocket engines. The following

headlines illustrates the differences and also similarities between these engines

2.1 . Engine Layout/Construction: The table below identifies the differences and

similarities in the design of the engines as shown in fig.1-3.

Pure Jet Engine (fig.1) Ramjet Engine (fig.2) Rocket Engine (fig.3)

Has a compressor No compressor No compressor

Turbine present No turbine Turbine present

No injection pump No injection pump Has an injection pump

Has moving parts No moving parts No moving parts

Nozzle present Nozzle present Nozzle present

Has two openings; intake and nozzle

Two openings; intake and nozzle

Has just one opening, the nozzle.

Has a combustion chamber Combustion chamber present

Combustion chamber present

Table 1: Engine layout of pure jet, ramjet and rocket.

Fig.1: Pure jet engine4 Fig.2: Ramjet engine4

Fig.3: Rocket engine.4

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2.2 Mode Of Operations

2.2.1 Pure Jet Engines: This is an air breathing engine which uses gas turbine to drive its

compressor, then the air is heated up in the combustion chamber and released via the

nozzle to produce a high speed forward thrust. An example is the turbojet that has lots of

moving parts; every air that travels through the intake into the core engine, exits as hot

gases (jet).2

2.2.2 Ramjet Engines: This is a form of an air breathing jet which produces thrust using forced

(ram) air or the forward motion and the Bernoulli effects to compress incoming air without a

rotating compressor (no gas turbine).5 Ramjet cannot produce thrust at zero airspeed, they

would need an assisted take-off to accelerate to a speed where it gains thrust.5 2.2.3 Rocket Engines: Just like the air breathing engines, thrust is produced according to Newton’s

Third Law of motion. High pressure and temperature gas (propellant) is expelled in a very

high exit velocity through the nozzle, then the rocket moves in the opposite direction.1

2.2.4 Tabular comparisons and similarities between engines

Pure Jet Ramjet Rocket

Source of Air Surroundings Surroundings Carries its own (stored oxygen).1

Thrust Gains thrust when throttled.

Can be throttled Always on a full thrust unless propellant run out (solid rocket) or the use of valve to stop injection of propellant (liquid rockets).

Net Momentum Force equation.

Fnet = (ma + mf)Cj - maCa

Fnet = (ma + mf)Cj – maCa

Fnet = mCj + Ae(Pc + Pa). Where Ae = area of nozzle, and Pc = combustion chamber pressure.7

Places to operate It’s a terrestrial engine, so cannot operate in a vacuum because of absence of air.

Cannot operate in a vacuum.

It’s a both terrestrial and space engine, so can operate in a vacuum because it carries its own oxygen.

Flight Path Angle Flight most efficient at cruise (180o), but would fall off the sky if it attains an angle greater than the maximum stall angle (15o).

Just like all jet engines cannot fly vertically.

Normally have its lift-off at a vertical angle, and then changes angle after it beats the atmospheric drag.

Cost Has a lower cost compared to rockets since it uses atmospheric air for

Has a lower cost than rockets, but cost difference between pure jets will depend

Cost of operation is very high, this is because it has to carry its own oxygen,

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compression and combustion. Also unlike rockets, jet engines is not designed for outer space conditions, like having a large tank to store both fuel and oxygen therefore increasing cost.5

on the purpose and size of the engine.

and also, it means it would need a large tank, thereby increasing its overall weight and of course cost.7

Fuel Source Stored fuel Stored fuel Stored fuel

Range and Performance

Because they use gas turbines, there’s a greater compression and high power even at low speeds compared to ramjets. They have a high altitude efficiency but the turbine limit temperature means a limit top speed. They are very noisy and inefficient if flown at a Mach number below 2.6

Ramjets gives little or no thrust at a lower or ½ the speed of sound. It is efficient if airspeed exceeds 100 km/h, this is due to low compression ratio.5 It works better than pure jet engines at supersonic speeds (Mach 2-4), but its performance fall off at M = 6 due dissociation and pressure loss caused by shock as intake air is slowed by subsonic velocities for combustion.5

Rockets have a very high performance, measured using their specific impulse (Isp). They can combine very high thrust, very high exhaust velocity, and a very high thrust to weight ratio to gain a few 1000 seconds Isp.7 But high temperature in the combustion chamber makes materials lower tensile strength, and temperature gradient between combustion chamber and nozzle is formed which causes differential expansion which then creates internal stress.7

Safety and Fuel Efficiency

Has high fuel efficiency than rockets, but very noisy.

Has high fuel efficiency than rockets over the entire useful working life of at least Mach 6.

Uses non air breathing oxidisers, so have a major safety issue in that the propellants are very poisonous, a good example is Hydrazine N2H4 (very toxic and unstable). Rockets are generally less fuel efficient in comparison to all jet engines.

Table 2: A comparison of mode operations, range and efficiency of Pure Jet, Ram Jet and

Rocket Engines.

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Question 3

3.1.a Bock diagram and cycle of the propulsion unit

Fig. 4: a scanned block diagram showing all stages of the propulsion unit.

Fig. 5: a scanned temperature versus entropy co-ordinates of the above block diagram (not to scale).

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3.2 At the Intake According to the ISA table3, at 500m altitude Ta = 284.9K, Pa = 0.9546 bar. Ca = 60 m/s, Po1 =? To1 =?

𝑇𝑜𝑎 = 𝑇𝑎 +2𝐶𝑎2

2𝐶𝑝= 284.9 +

602

2 𝑥 1005 = 286.7𝐾

To1 = Toa = 286.7K ni = 100%, Cp = 1005, r = 1.4

𝑃𝑜1

𝑃𝑎 =

(𝑇𝑜11

𝑇𝑎 )

𝑟𝑟−1

𝑟= (1 + 𝑛𝑖

𝐶𝑎2

2𝐶𝑝𝑇𝑎)

𝑟𝑟−1

𝑃𝑜1

0.9546= (1 + 1

602

2 𝑥 1005 𝑥 284.9 )

1.41.4−1

𝑃𝑜1 = 0.9546 𝑥 1.0063.5 = 0.9748 𝑏𝑎𝑟

Po1 = 0.9748 bar

3.3. At the Compressor

To1 = 286.7K, Po1 = 0.9748 bar, rPHPC = 12, nHPC = 0.88

To2 =? Po2 =?

𝑃𝑜2

𝑃𝑜1 = 12, 𝑃𝑜2 = 𝑃𝑜1 𝑥 12 = 0.9748 𝑥 12 = 11.6976 𝑏𝑎𝑟

𝑇𝑜21

𝑇𝑜1= (

𝑃𝑜2

𝑃𝑜1)

𝑟−1𝑟

= (11.6976

0.9748)

1.4−11.4

= 2.03

𝑇𝑜21 = 𝑇𝑜1 𝑥 2.03 = 286.7 𝑥 2.03 = 583.1𝐾

nHPC = (𝑇𝑜21 − 𝑇𝑜1)/(𝑇𝑜2 − 𝑇01 )

0.88 =583.1 − 286.7

𝑇𝑜2 − 286.7 𝑇𝑜2 =

296.4 + 252.3

0.88 𝑇𝑜2 = 623.6𝐾

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3.3b. at the Combustion Chamber

To2 = 623.6K, Po2 = 11.6976 bar, nb = 0.98, Cp = 1155, LCV = 44000 x103

To3 = HP inlet temperature = 1200K, Po3 =? mf =?

5% pressure loss in c.ch

Po3 = 0.95 x Po2 = 0.95 x 11.6976 = 11.1127 bar

nb =(𝑚𝑎+𝑚𝑓 )𝐶𝑝 (𝑇03−𝑇𝑜2)

𝑚𝑓 𝑥 𝐿𝐶𝑉 , 𝑚𝑓 =

𝑚𝑎𝐶𝑝(𝑇𝑜3−𝑇𝑜2)

𝑛𝑏𝐿𝐶𝑉−𝐶𝑝(𝑇𝑜3−𝑇𝑜2)

𝑚𝑓 =𝑚𝑎 𝑥 1155(1200 − 623.6)

0.98 𝑥 44000𝑥103 − 1155(1200 − 623.6)

=665742𝑚𝑎

43120000 − 665742 = 0.0157𝑚𝑎, 𝑚𝑓 = 0.0157𝑚𝑎

𝑇ℎ𝑒𝑟𝑒𝑓𝑜𝑟𝑒,𝑚𝑓

𝑚𝑎= 0.0157

3.3b. at the High Pressure Turbine

To3 = 1200K, Po3 = 11.1127 bar, mf = 0.0157ma, nHPt = 0.85, nM = 0.99

To4 =? Po4 =?

nM x WHPt = WHPc

0.99 (𝑚𝑎 + 𝑚𝑓)𝐶𝑝𝑔(𝑇𝑜3 − 𝑇𝑜4) = 𝑚𝑎𝐶𝑝𝑎(𝑇𝑜2 − 𝑇𝑜1)

𝑚𝑎 =𝑚𝑓

0.0157

0.99 (𝑚𝑓

0.0157+ 𝑚𝑓) 1155(1200 − 𝑇𝑜4) =

𝑚𝑓

0.01571005(623.6 − 286.7)

𝑚𝑓

0.0157+ 𝑚𝑓 =

𝑚𝑓 + 0.0157𝑚𝑓

0.0157=

(1 + 0.0157)

0.0157𝑚𝑓 = 64.7𝑚𝑓

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0.99(64.7𝑚𝑓)1155(1200 − 𝑇𝑜4) =𝑚𝑓

0.0157𝑥1005 𝑥336.9

73981.215𝑚𝑓(1200 − 𝑇04) = 21565891.7𝑚𝑓

1200 − 𝑇04 =21565891.7𝑚𝑓

73981.215𝑚𝑓

1200 − 𝑇𝑜4 = 291.5, 𝑇𝑜4 = 908.5𝐾

nHPt = 𝑇𝑜3−𝑇04

𝑇03−𝑇041 , 0.85 =1200−908.5

1200−𝑇𝑜41 , 1020 − 0.85 𝑇𝑜41 = 291.5, 𝑇𝑜41 = 857.1𝐾

𝑃𝑜4

𝑃𝑜3= (

𝑇𝑜41

𝑇𝑜3)

𝑟𝑟−1

, 𝑃𝑜4

11.1127= (

857.1

1200)

1.33/0.33

= 0.2576,

𝑃𝑜4 = 11.1127 𝑥 0.2576 = 2.86 𝑏𝑎𝑟

𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑎𝑡 𝑡ℎ𝑒 𝑒𝑥𝑖𝑡 𝑜𝑓 𝑡ℎ𝑒 ℎ𝑖𝑔ℎ 𝑝𝑟𝑒𝑠𝑠𝑢𝑟𝑒 𝑡𝑢𝑟𝑏𝑖𝑛𝑒 = 𝑃𝑜4 = 2.86𝑏𝑎𝑟

3.3d. Fuel Consumption, mf

𝑚𝑎 =𝑚𝑓

0.0157, 𝑖𝑓 𝑚𝑎 = 20 𝑘𝑔/𝑠

𝑚𝑓 = 20 𝑥 0.0157 = 0.314𝑘𝑔

𝑠/𝑁

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3.3e. the Net Momentum Thrust, Fnet

𝐹𝑛𝑒𝑡 = (𝑚𝑎 + 𝑚𝑓 )𝐶𝑗 − 𝑚𝑎 𝐶𝑎

Cj = 500 m/s, Ca = 60 m/s, ma = 20 kg/s, mf = 0.314kg kg/s/N

𝐹𝑛𝑒𝑡 = (20 + 0.314)𝑥 500 − 20 𝑥 60 = 10157 − 1200 = 8957 𝑁

𝑁𝑒𝑡 𝑀𝑜𝑚𝑒𝑛𝑡𝑢𝑚 𝐹𝑜𝑟𝑐𝑒, 𝐹𝑛𝑒𝑡 = 8.957 𝑘𝑁

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References

1. Seller, J. Jerry (2005). Understanding Space: An Introduction to Astronautics. Quebecor World, New York: McGraw-Hill Companies. ISBN 0-07-340775-5

2. Adjali, H. (2013). Air Breathing Cycles and Gas Turbine Lecture Notes. Kingston University, London.

3. ,.(2012) The Engineering Tool Box {online}. Last accessed 24th November 2013 at http://www.engineeringtoolbox.com/international-standard-atmosphere-d_985.html#.UpI4OMTBqzQ

4. ,.(2003) Gas Turbines Propulsion {online}. Last accessed 24th November 2013 at 5. ,.(2013) Ramjets Engines {online}. Last accessed 24th November 2013 at

http://en.wikipedia.org/wiki/Ramjet

6. ,.(2013) Turbojet Engines {online}. Last accessed on 24th November 2013 at

http://en.wikipedia.org/wiki/Turbojet

7. ,.(2013) Rocket Engines {online}. Last accessed 24th November 2013 at

http://en.wikipedia.org/wiki/Rocket_engine