CLASSIFICATION SPACE PROPULSION SYSTEM

The space propulsion system is classified by the type of energy sourced used. in this blog, we will talk about the chemical space propulsion system. it is classified in two different types 1. solid 2. liquid 3. hybrid. Liquid space propulsion system is classified as 1. pressure fed,2. pump-fed, 3. bipropellant 4. monopropellant.

A propellant is a chemical substance used in the production of energy. The propellant consists of fuel+oxidizer+ additives (in a very less quantity). 

  SOLID PROPELLANT 

The solid propellant is in which fuel, oxidizer, additives all are in the solid phase.  

for example 

Sucrose+ KNo3 

(fuel)        (oxidizer)

SOLID PROPELLANT  IS CLASSIFIED INTO  

1.Homogenous (colloidal) propellant

• Single base propellant
• Double base propellant 
• Triple base propellant 

2.Non- homogenous (composite) propellant 

HYBRID PRPELLENT 

The hybrid propellant is in which fuel and oxidizer both are in a different phase.

for example 

  LIQUID PROPELLANT

The liquid propellant is in which fuel and oxidizer  both are in liquid form

for example 

liquid hydrogen (fuel)+liquid oxygen(oxidizer)

LIQUID PROPELLANT IS CLASSIFIED INTO 

1. mono-propellant

• simple
• composite 

2. Bi-propellant

• hypergolic
• non-hypergolic

CLASSIFICATION OF PROPULSIVE DEVICES

Propulsive devices are the device which is used especially used for air and space vehicles. Propulsive devices are broadly classified into two parts air-breathing and non-air-breathing. The rocket motor is a non-airbreathing propulsive device.

CLASSIFICATION OF PROPULSIVE DEVICES

propulsive devices are broadly classified into two parts

1.     Air-breathing

for example 

a)      Ramjet

b)      Scramjet

c)       Turbojet

d)      Turboprop

e)      Turbofan

      2.   Non- air-breathing

for example 

a)      Chemical

b)      Nuclear

c)       Electric

We are more concerned about non-air-breathing propulsive devise which are basically of 3 types 

         1.       Photons

         2.    Rockets

a.       Chemical

                                              i.            Solid

                                             ii.            Liquid

                                           iii.            Hybrid

b.      Non-chemical

                                            I.            Electric

                                          II.            Nuclear

                                        III.            Solar

           3.    Solar sail

 DIFFERENCE BETWEEN AIRBREATHING AND NON-AIR BREATHING

AIR BREATHING

•         Air breathing propulsive  devise take oxygen from atmosphere
•        They operated only in the atmosphere, not in a vacuum
•         These device can’t operate at the flight speed not more than M 5.
•        The rate of climb decrease with altitude in the air breathing propulsive devices  
•       The thrust developed by the air-breathing   engine is dependent on flight speed

NON AIR BREATHING

•        Non-air breathing propulsive devices have its fuel and oxygen with its self
•        They can operate both in atmosphere and vacuum(space)
•        These devices can operate at any flight speed
•        The rate of climb increases with altitude
•        The thrust developed by non-air breathing devices are independent of flight speed

LEVEL TURN / V-n DIAGRAM

Which is the maximum speed at which an aircraft fly?  Well, it is defined at the time of manufacturing only. We will see how to obtain maximum speed of aircraft at the maximum lift with the help of V-n diagram. It is a very important diagram, and every aircraft has its own V-n diagram. We will first derive the formula for angular velocity and radius required for a turning flight.

Case 1.  A-LEVEL TURN FLIGHT

As u can see in the figure

A

Φ Is bank angle

L is lift

R is radius

W is weight

 From figure

Components figure will be made

B

We can say from the figure  

A plane is at a constant altitude and horizontal plane

From the force diagram in figure B.The magnitude of the resultant force is

We will now introduce a new term “load factor”

n=L/W…1

The load factor is usually quoted in terms of “g’s”; for example, an aeroplane with lift equal to 10 times the weight is said to be experiencing a load factor of 10 g’s.

Hence, the equation can be written as,

From newton’s law of motion

Combining 2 and 3

The angular velocity is denoted by w=V∞/R called a turn rate.

 For both the civil aircraft and jet aircraft we required, The highest possible load factor, The lowest possible velocity.

Case 2.  PULL – UP MANOEUVRE

In this case the initially L=W then there is a sudden increase in the lift, L>W Airplane will begin  to turn upwards in the vertical plane.

The resultant force is, from figure

Combine equation 6 and 3

         

      

Case3. PULL-UP MANEUVER.

In this case, initially L=W, suddenly flight rolls to invert position in such a manner Land W both are in downwards direction as shown in figure

Cobine 9 and 3 equations

High-performance aircraft are  designed in such a way that they have high load factor and low turn radius,n+1 ≅  n and n-1 ≅ n, the equation  will be reduced to

We know that lift is

Substituting equation 14 and 1 into 12 and 13

From the above Equation, it clearly shows that lower the wing loading smaller the turn radius and larger the turn rate everything else is constant

Designing of the wing loading is done by the following points

1. Payload
2.  Range
3.  Maximum velocity 

V-n DIAGRAM

At high speed, n is limited because of structural designed. V-n Diagram is a graph of load factor versus velocity of a given aircraft

  

The plane is at velocity V₁ and at an angle of attack where C_l<C_lmax, is point 1 in the diagram. Velocity remains the same V₁, angle of attack is increased to get max lift and max load factor that can be obtained at velocity V₁ is point 2 in the diagram. 

With the same velocity, we will again increase the angle of attack, wing stalls and load factor drops at point 3, it is called a stall region, is unobtained in flight. 

Now, we will increase the velocity to V₄ and max possible load factor also increases, is the point is 4.

Beyond a certain value of load factor, defined as the positive limit load factor and showed by the horizontal line in the diagram. Velocity corresponding to point B is V*. We will again increase the velocity to V₅, is the velocity where we fly at Cl<C_lmax, so that +limit load factor is not exceeding. Point 5 is a point where we get c_lmax at velocity V₅ with structural damage in aircraft. 

Vertical line CD is the high-speed limit, the velocity greater than this, the dynamic pressure becomes so large that again structure damage may occur to the aeroplane. AE&ED they are negative absolute angles of attack that is a negative load factor

Point B is called a manoeuvre point. At this point lift and load factor both simultaneously at the highest possible values, velocity corresponding to pint B is called the corner velocity V*  

    

AIRSPEED / PITOT TUBE

We have seen in the previous post that velocity in the test section is obtained with the help of pressure difference, this pressure difference is measured with the help of U shape manometer.
How do we calculate pressure difference in real life, hence how do we calculate the speed of an aircraft?   

Pitot tube, this is an aerodynamic instrument that actually measures the total pressure at a point of the flow.

TOTAL CONDITIONS 

Stagnation condition is when the fluid is brought to rest adiabatically.

• Total Temperature:  The value of the temperature of the fluid element after it has been brought to rest adiabatically is defined as the total temperature, denoted by T0.
• Total enthalpy: The value of the enthalpy of the fluid element after it has brought to rest adiabatically is defined as the total enthalpy denotes by h0.
• Total pressure: The value of the pressure of the fluid element is brought to rest isentropically, is called total pressure denoted by p0.
• Total density: The value of the density of the fluid element is brought to rest isentropically, called as total density denoted by ρ 0

TOTAL CONDITIONS  are imaginary quantities that would exist at a point in flow if the fluid element passing through that point was brought into rest adiabatically.

• Static temperature: Static temperature is measured of purely random motion of the molecules in a gas. It is the temperature u feel when you u are ride along with the gas at the local flow velocity.
•  Static pressure: Static pressure is measured of purely random motion of the molecules in a gas. It is the pressure u feel when you u are ride along with the gas at the local flow velocity.
• Static density: Static density is measured of purely random motion of the molecules in a gas. It is the density u feel when you u are ride along with the gas at the local flow velocity. 
  

It is an important equation in aerodynamic, it states that at any point in the flow, the total enthalpy is given by the sum of the static enthalpy and kinetic energy, all per unit mass.

EXAMPLE OF STATIC AND TOTAL PRESSURE

 Think that u are sitting in a car which is moving with the velocity of 100m/s, windows are closed and there is a fly inside the car moving with u in a random motion. your speed is 100m/s and in that mean, so is that fly. This fly hits u on your skin with this random motion, you will feel a slight impact .this slight effect is analogous to static pressure in flowing gas.
Now think there is a person standing along the side of the road and u open the window and the fly hits the skin of the person, the impact will be more. The strength of the impact is analogous to the total pressure.

PITOT TUBE

It consists of a tube placed parallel to the flow and open to the flow at the endpoint(A). the other end of the tube (point B) is closed, as shown in the figure1.

1

Now, imagine flow is started and some amount of gas is pile up inside the tube as the tube is closed from pressure gauge at point (B). There is no place for the gas to go hence, gas will pile up and stagnate everywhere inside the tube, including the open face of the tube at point (A). The gas is brought into reset isentropiclly as friction is negligible and no heat exchange. Hence, from the above discussion, we can say that pressure at point A is total pressure. point A is a stagnation point, according to the definition of stagnation point, any point of the flow where V=0.

CAN WE MEASURE BOTH THE PRESSURE (STATIC AND TOTAL PRESSURE ) IN ONE INSTRUMENT? 

Yes
As pitot tube only measure total pressure
 PITOT-STATIC PROBE is the instrument which measures both the pressure difference

HOW?

There is a small hole in the surface at point A called static pressure orifice or static pressure tab as shown in the figure2. Since the surface is parallel to the flow, only random motion of the gas molecule will be felt by the surface itself.

2

HOW TO CALCULATE AIRSPEED OF INCOMPRESSIBLE FLOW?

We know static pressure + dynamic pressure= total pressure

.......1

The above equation only holds for incompressible flow

HOW TO CALCULATE AIRSPEED OF SUBSONIC FLOW?

The formulas which we have derived till now are only valid for flow with Mach number less than 0.3 (M<0.3) where we can assume flow to be incomprehensible.
Now, if we increase our Mach number greater than 0.3 and less then 1, compressibility will be taken into account
We will now derive the formula  to calculate the velocity of air vehicle for subsonic flow

we know that, from considering the enthalpy

from energy equation 

substitute equation 1 into 2

Speed of the sound is

Thus, equation 3 becomes  

The Mach number M=V/a

These are the fundamental and important equations in aerodynamics to calculate total pressure, temperature, density and Mach number.

The above equation says the ratio of total pressure and static pressure is direct measure of Mach number. thus, individual measurements of total pressure and static pressure in conjunction of the equation can be used to calibrate an instrument in the cockpit of an aeroplane called as mach metre, where the dial reads directly in terms of the flight Mach number of the aeroplane.

To obtain actually velocity we know that M=V/a

....5

equation 5 can be rearranged algebraically as

...6

The static temperature in the air surrounding the aeroplane is difficult to calculate.  With the help of equation 6, we will calculate actually velocity assuming that a is equal to standard seal-level.

The airspeed indicator is designed to sense the actual pressure difference.
equation 6 is calibrated as

....7

HOW TO CALCULATE AIRSPEED OF SUPERSONIC FLOW?

Flow which has mach number greater than 1 is called a supersonic flow.
supersonic flow has shock waves, hence, the flow passing through shock wave is nonisentropic. There are very large friction and thermal conduction effects hence, neither adiabatic nor frictionless condition holds.

The equation number is called a Rayleigh Pitot tube formula.

WIND TUNNEL

The wind tunnel is a ground-based experimental facility, which gives us an enormous amount to experimental data of natural flow simulation. we will see two types of wind tunnel here 
1. Supersonic wind tunnel 
2. Subsonic wind tunnel 
 We have divergent nozzle in the supersonic wind tunnel and convergent nozzle in the subsonic wind tunnel.  How do we decide this?  

Let’s derive an equation

Differentiation we get

Recalling the moment equation and Euler’s equation

Substituting 6 into 7

Since the flow is isentropic

Equation becomes

Rearranging

The equation number 9 is a very important equation of aerodynamics

• Cases 1. Subsonic flow M<1, for the velocity to increase (dV positive) the area must decrease (dA negative ), from equation 9, when the flow is subsonic area must decrease to increase the velocity, hence we need a converging nozzle for subsonic flow  as shown in figure a
• Case 2. Supersonic flow M>1, for the velocity to increase (dV positive) the area must also increase, from equation 9, when the flow is supersonic area must increase to increase the velocity hence, we need a divergent nozzle for supersonic flow, as shown in figure b
• Case 3. Transient flow M=1   

dA/A = 0, stream tube has min area at M=1. This minimum area is called the throat.shown in figure c

SUBSONIC WIND TUNNEL 

1

Figure 1 is a subsonic  wind tunnel

Where

• V₁= velocity in the nozzle
• p₁=pressure at nozzle
• A₁=area of nozzle
• V₂=velocity in the test section
• p₂=pressure at the test section
• A₂=area of the test section
• V₃= velocity in the diffuser
• p₃=pressure at diffuser
• A₃= area of the diffuser   

                    

  Mach number will be less than 1 as we are dealing for subsonic wind tunnel, we will assume flow to be incompressible.

Air is passed in the nozzle with the help blower at low velocity. The nozzle converges to a small area A₂ at the test section, velocity increase, from equation 1 (the continuity equation). Then the air is passed into a diffuser or diverging duct, where the area (A₃) is increased and velocity (V₃) decreases, from equation 2 (the continuity equation) 

The pressure at various location in the wind tunnel is related to the velocity through Bernoulli’s the equation for incompressible flow

As V increases p decreases hence, p₂<p₁ i.e. is the test section the pressure is smaller than the reservoir pressure upstream of the nozzle. In much subsonic wind tunnel, all or part of the test section is open, or vent, to the surrounding air. In such cases, the outside air pressure is communicated directly to the flow of the test section, and p₂=1atm. Downstream of the WindTunnel is a diffuser, where the pressure (p₃) increases and velocity (V₃) decreases.

If A3=A1 then, from equation 1, V₃=V₁; and from equation 3, p₃=p₁ 

Note: In the actual wind tunnel, the aerodynamic drag created by the flow over the model in the test section causes a loss of momentum not included in the derivation of the Bernoulli’s equation; hence, in reality, p₃ is slightly less than p₁, because of such losses

The test section of the velocity is derived as, from equation 3

Substitute equation 1 into 4

ρ1 in the above equation is called as dynamic pressure 

Solve for V2

In equation 5 area the ratio is fixed A₂/A₁ quantity, as it is given at the time of design only. The controlling nob is basically, pressure difference (p₁-p₂) which allows the wind tunnel to operate to control the value of the test section velocity V₂

WHERE WILL WE GET PRESSURE DIFFERENCE FROM?

Manometer we will get the pressure difference, how?

We will use u tube manometer, the left side of the tube is connected to p1 and the right side is connected to pressure p2. The difference in height of the fluid on both side gives us the pressure difference as shown in figure 2

In the modern wind tunnel, the manometer has been replaced to pressure transducers and electrical digital display

How to different obtain values of pressure difference?

Well, we can obtain different values of pressure difference by increasing and decreasing velocity. For example, if I want to double the pressure difference I have to increase the velocity by approximately 42%.

If we increase the contraction ratio while keeping the pressure constant, velocity difference across the nozzle is increased, although the actual velocity at the t and exit of the nozzle. 

SUPERSONIC WIND TUNNEL 

 Supersonic flow M>1, for the velocity to increase (dV positive) the area must also increase, from the equation 9, when the flow is supersonic area must increase to increase the velocity hence, we need a divergent nozzle for supersonic flow.

Just passing the air from the divergent nozzle is enough to generate supersonic flow in wind tunnel

No, it’s not enough

HOW TO GENERATE SUPERSONIC FLOW IN WIND TUNNEL??

Starting with the stagnant gas in a reservoir, the preceding discussion says that a duct of sufficiently converging- diverting shape must be used, as shown in figure  

The flow starts out with very low-velocity V @ 0 in the reservoir, expands to high subsonic speeds in the convergent section reach Mach 1 at the throat, then it is passed through a divergent nozzle to get supersonic flow.

For rocket engines, the flow quality is not important, but the weight of the nozzle is a major concern, for the Wight to be minimized, the engine’s length is minimized, which gives rise to a rapidly diverging, bell-like shape for a supersonic section.

The real flow through the nozzle is closely approximated by isentropic flow because little or no heat added or taken away through the nozzle walls and the vast the core of the flow is virtually frictionless. Equation 10 to 12 apply to nozzle flow .these equation demonstrates the power of Mach number in aerodynamic calculation.

Mach number continuously increases through the nozzle, going from near zero in the reservoir to M=1 at the throat and to supersonic valises of downstream of the throat.