Propulsion - Introduction and fundamentals
71 flashcards · Physics · by Zack Phipps
How is thrust generated?
Thrust is generated whenever the momentum flux leaving an engine is larger than the momentum flux entering the engine
What is momentum flux?
Transport of momentum that acts in a direction perpendicular to flow.
The momentum conservartion equation is: Mx,out -Mx,in = Σ F
MX,out is the momentum flux in the x direction leaving the control volume, Mx,in is the momentum flux in the x direction entering the control volume, Fx is the sum of all forces in the x direction
Total thrust for a rocket is F = m*Vj + Aj ( Pj- PA)
This means that thrust is dependant on atmospheric pressure and therefore altitude m is mass flow rate
What is the momentum flux entering the control volume? [words] Mx,in = mass flow rate of air x velocity
What is the momentum flux leaving the control volume? [words] Mx,out = mass flow rate of air and fuel x jet velocity
Total thrust equation for a jet engine: F = (ma +m f ) Vj - maV + Aj ( Pj- PA )
How can the lift to drag ratio be replaced in the Breguet range equation?
CL/CD
What is Breguet range equation?
s = -L/D ( V / TSFC) (1/g0) ln(W2/W1)
What is thrust specific fuel consumption?
TSFC = Mass flow rate of fuel / Thrust
In steady flight at constant velocity, what is the relations between: Weight, Lift, Drag, and Thrust
W = L F =D W = D (L/D) W = F (L/D)
What is the fuel to air ratio?
mass flow rate of fuel / mass flow rate of air
What is propulsive Efficiency?
A measure of how well an engine can convert the kinetic energy into displacement work
What is Thermal Efficiency?
How well an engine can convert heat into kinetic energy
What is thrust equation using the fuel air ratio?
F = ma [(1 + f ) Vj - V ]+ Aj ( Pj- PA )
For a rocket, what is the momentum flux entering the control volume?
Zero, a rocket has no inlet
Propulsive efficiency is defined as:
The ratio of aircraft power to the rate of kinetic energy of the working fluid produced by the engine
Aircraft power is defined as:
Waircraft = F x V = V ( ma [(1 + f ) Vj - V ]+ Aj ( Pj- PA ) )
Wjet is defined as:
Wjet = 1/2( (ma +mf) Vj2 - maV2)
Using the fuel to air ratio what can Wjet be defined as?
Wjet = ma/2 ( (1 + f ) Vj2 - V2)
The simplified equation of propulsive efficiency is Np = 2 /( (Vj / V) +1)
This is a simplified version assuming that: f <<1 Pj = Pa
What is the simplified version of the thrust equation?
F = ma ( Vj - V)
What happens to the thrust when propulsive efficiency?
Thrust decreases as propulsive efficiency increases this is because Vj = V for 100% efficiency and for this thrust would equal zero
Why cant an engine be 100% propulsively efficient?
This would mean thrust is equal to practically zero, and thrust is needed to overcome drag.
How do you increase propulsive efficiency without reducing thrust
Increasing the mass flow rate of air allows the thrust to remain constant whilst decreasing the jet velocity. This is why engines are getting bigger.
what is the overall efficiency in terms of thermal and propulsive efficiency? No =Np x Nth
By separating the two it allows easier optimisation of each component to increase overall efficiency
Overall efficiency can be defined using mass flow rate of fuel:
No = F x V / mf LCV
When the exhaust is fully expanded and f<<1 what can the overall efficiency be simplified to?
No = (Vj - V)V / f * LCV
Using TSFC how can the overall efficiency be written?
No =V / (TSFC *LCV)
What is the equation for thermal efficiency?
Nth = 1/2 ((Vj2 - V2) / (f * LCV))
How can the thermal efficiency be increased? and what is it limited by?
increasing the pressure ratio increasing the temperature ratio It is limited by the material used in the turbine blades being able to handle to temperature and pressure , this can be handled using cooling methods
What is thermal equilibrium
a uniform temperature and therefore no tenancy for heat transfer
What is Mechanical equilibrium
all forces are balanced, and therefore no tendency to accelerate.
What is phase equilibrium
no tendency for phase changes.
What is chemical equilibrium
no tendency for chemical change.
What is the Zeroth Law of Thermodynamics
If two systems are in thermal equilibrium with a third system, then they are in thermal equilibrium with each other
Thermodynamic equilibrium requires: Thermal Mechanical Phase Chemical
What is a intensive properties?
Intensive properties do not depend on the amount of material
What is an extensive properties?
Extensive properties do depend on the amount of material
are specific properties upper or lower case
lower
What is the two-property rule?
The state of a simple compressible system is completely specified by two independent, intensive properties
When are two properties independent?
Two properties are independent when one property can be kept constant, while the changing the other one.
What do the different processes mean: • Isothermal (constant temperature) • Isobaric (constant pressure) • Isochoric (constant volume) • Adiabatic (no heat transfer) • Isentropic (constant entropy, valid when a process is adiabatic and reversible) • Isenthalpic (constant enthalpy)
what is the first law of thermodynamics?
∆U = Q −W Q is positive when heat is added to the system, and the work W is positive when the system is doing work (i.e., work output from the system).
what is the ideal gas euqation of state?
PV = nR---T PV = mRT, P = ρRT
Assumptions for ideal gas model
• The volume occupied by the molecules is negligible • Intermolecular forces are negligible • Molecules carry only translational kinetic energy (i.e., no energy is stored as vibrations or rotation)
enthalpy equation: H =U +P*V
specific heat at constant volume:
the specific heat at constant pressure is defined as:
the ratio of specific heats
For a perfect gas Cv and Cp are:
Constant
for a perfect gas assumption the specfific heats can be used to relate the change in internal engery or the change in enthalpy for finite changes in temperature are:
mass fraction is: xi= mi/m
molar fraction is: yi= ni/n
molar and mass fractions are related by:
what is the pressure fraction Pf?
volume fraction is equal to:
Steady Flow Energy Equation (SFEE)
Specific total energy is
how does the SFEE simplifications apply to the diffuser
how does the SFEE simplifications apply to the compressor
how does the SFEE simplifications apply to the burner
how does the SFEE simplifications apply to the turbine
how does the SFEE simplifications apply to the nozzle
how is does pressure change with temperature when in a perfect gas and isentropic relationship
changes in entropy (using temp and pressure) is equal to:
changes in entropy (using temp and volume) is equal to:
changes in entropy (using pressure and volume) is equal to:
Isentropic efficiency of a compressor
Isentropic efficiency of a turbine
how to check the right isentropic efficiency equation was used?
• The isentropic efficiency is always less than 1 • The outlet temperature of the real process is always higher than the outlet temperature of the isentropic process • The work done by a real compressor is always higher than the work done by an isentropic compressor • The work done by a real turbine is always less than the work done by an isentropic turbine