Ship Jet Rocket Engine Propulsion

Propulsion of a Ship

Jet propulsion of ship is found to be less efficient than propulsion by screw propeller due to the large amount of frictional losses in the pipeline and the pump, and therefore, it is used rarely. Jet propulsion may be of some advantage in propelling a ship in a very shallow water to avoid damage of a propeller.

Consider a jet propelled ship, moving with a velocity V, scoops water at the bow and discharges astern as a jet having a velocity V_r relative to the ship. The control volume is taken fixed to the ship as shown in Fig. 1.
 

Following the momentum theorem as applied to the control volume shown. We can write

Where F_c is the external force on the control volume in the direction of the ship’s motion.

The forward propulsive thrust F on the ship is given by



Propulsive power is given by  


 
Jet Engine

A jet engine is a mechanism in which air is scooped from the front of the engine and is then compressed and used in burning of the fuel carried by the engine to produce a jet for propulsion. The usual types of jet engines are turbojet, ramjet and pulsejet.
 

 


A turbojet engine consists essentially (Fig. 2) of -
    
(i) a compressor,
    
(ii) a combustion chamber,
    
(iii) a gas turbine and
    
(iv) a nozzle.

A portion of the thermal energy of the product of combustion is used to run the gas turbine to drive the compressor. The remaining part of thermal energy is converted into kinetic energy of the jet by a nozzle. At high speed fiight, jet engines are advantageous since a propeller has to rotate at high speed to create a large thrust. This will result in excessive blade stress and a decrease in the efficiency for blade tip speeds near and above sonic level. In a jet propelled aircraft, the spent gases are ejected to the surroundings at high velocity usually equal to or greater than the velocity of sound in the fluid at that state.

In many cases, depending upon the range of fight speeds, the jet is discharged with a velocity equal to sonic velocity in the medium and the pressure at discharge does not fall immediately to the ambient pressure. In these cases, the discharge pressure p₂ at the nozzle exit becomes higher than the ambient pressure patm. Under the situation of uniform velocity of the aircraft, we have to use Eq. as the momentum theorem for the control volume as shown in Fig. 3 and can write

     
where, Fx is the force acting on the control volume along the direction of the coordinate axis ”OX” fixed to the control volume, V is the velocity of the aircraft, u is the relative velocity of the exit jet with respect to the aircraft, and  are the mass flow rate of air, and mass burning rate of fuel respectively. Usually is very less compared to   usually varies from 0.01 to 0.02 in practice).

The propulsive thrust on the aircraft can be written as


                                  
The terms in the bracket are always positive. Hence, the negative sign in FT represents that it acts in a direction opposite to o_x, i.e. in the direction of the motion of the jet engine. The propulsive power is given by


 
Non-inertial Control Volume

Rocket engine

Rocket engine works on the principle of jet propulsion.

(i) The gases constituting the jet are produced by the combustion of a fuel and appropriate oxidant carried by the engine. Therefore, no air is required from outside and a rocket can operate satisfactorily in a vacuum.
    
(ii) A large quantity of oxidant has to be carried by the rocket for its operation to be independent of the atmosphere.
    
(iii) At the start of journey, the fuel and oxidant together form a large portion of the total load carried by the rocket.
    
(iv) Work done in raising the fuel and oxidant to a great height before they are burnt is wasted.
    
(v) Therefore, to achieve the efficient use of the materials, the rocket is accelerated to a high velocity in a short distance at the start. This period of rocket acceleration is of practical interest.



Let   be the rate at which spent gases are discharged from the rocket with a velocity u relative to the rocket (Fig. 4) both and u are assumed to be constant.

Let M and V be the instantaneous mass and velocity (in the upward direction) of the rocket. The control volume as shown in Fig. 4 is an accelerating one. Therefore we have to apply the momentum theorem of the control volume. This gives
     


where ΣF is the sum of the external forces on the control volume in a direction vertically upward. If p_e and p_a be the nozzle exhaust plane gas pressure and ambient pressure respectively and D is the drag force to the motion of the rocket, then one can write



where, A_e is outlet area of the propelling nozzle.
 
Then Eq. (5) can be written as

     
In absence of gravity and drag, Eq (6) becomes

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