Thermodynamics Propulsion Systems JCI 030314

THERMODYNAMICSPropulsion SystemsJoseph O. CamachoS00954886

THRUST EFFICIENCY

• In aircraft and rocket design, overall propulsive efficiency is the efficiency,

in percent, with which the energy contained in a vehicle's propellant is

converted into useful energy, to replace losses due to air drag, gravity,

and acceleration.

THRUST EFFICIENCY

• It can also be stated as the proportion of the mechanical energy actually

used to propel the aircraft. It is always less than 100% because of kinetic

energy loss to the exhaust, and less-than-ideal efficiency of the

propulsive mechanism, whether a propeller, a jet exhaust, or a fan. In

addition, propulsive efficiency is greatly dependent on air density and

airspeed.

THRUST EFFICIENCY

• The first performance parameter is the thrust of the engine that is

available for sustained flight (thrust = drag), accelerated flight (thrust >

drag), or deceleration (thrust < drag).• The uninstalled thrust F of a jet engine (single inlet and single exhaust) is

given by:

THRUST EFFICIENCY

• Where

• rho, rhf = mass flow rates of air and fuel, respectively

• Vo, V~ = velocities at inlet and exit, respectively

• Po, Pe = pressures at inlet and exit, respectively

THRUST EFFICIENCY

• It is most desirable to expand the exhaust gas to the ambient pressure,

which gives Pe = Po. In this case, the uninstalled thrust equation

becomes:

THRUST EFFICIENCY

• The installed thrust T is equal to the uninstalled thrust F minus the inlet drag Dinlet and minus the nozzle drag Dnoz, or:

• Dividing the inlet drag Dinle t and nozzle drag Dnoz by the uninstalled

thrust F yields the dimensionless inlet loss coefficient φinlet and nozzle

loss coefficient φnoz, or:

THRUST EFFICIENCY

• Thus the relationship between the installed thrust T and uninstalled thrust F is simply:

THRUST EFFICIENCY

• The second performance parameter is the thrust specific fuel

consumption (S and TSFC). This is the rate of fuel use by the propulsion

system per unit of thrust produced. The uninstalled fuel consumption S

and installed fuel consumption TSFC are written in equation form as:

THRUST EFFICIENCY• Where

• F = uninstalled thrust• S = uninstalled thrust specific fuel consumption• T = installed engine thrust• TSFC = installed thrust specific fuel consumption• mf = mass flow rate of fuel

• The relation between S and TSFC in equation form is given by

THERMAL EFFICIENCY

• The thermal efficiency of an engine is another very useful engine

performance parameter. Thermal efficiency is defined as the net rate of

organized energy (shaft power or kinetic energy) out of the engine

divided by the rate of thermal energy available from the fuel in the

engine. The fuel's available thermal energy is equal to the mass flow rate

of the fuel times the fuel lower-heating value hpR.

THERMAL EFFICIENCY

• Thermal efficiency can be written in equation form as:

• Where• Η = thermal efficiency of engine• Wout = net power out of engine• Qin = rate of thermal energy released

THERMAL EFFICIENCY

• Note that for engines with shaft power output, Wout is equal to this shaft power.

• For engines with no shaft power output (e.g., turbojet engine), Wout is equal to the

net rate of change of the kinetic energy of the fluid through the engine.

• The power out of a jet engine with a single inlet and single exhaust (e.g., turbojet

engine) is given by:

THERMAL EFFICIENCY

• The propulsive efficiency ηp of a propulsion system is a measure of how

effectively the engine power Wout is used to power the aircraft.

• Propulsive efficiency is the ratio of the aircraft power (thrust times velocity)

to the power out of the engine Wout. In equation form, this is written as:

THERMAL EFFICIENCY

• Where• ηp = propulsive efficiency of engine• T = thrust of propulsion system• Vo = velocity of aircraft• Wout = net power out of engine

THERMAL EFFICIENCY

• For a jet engine with a single inlet and single exhaust and an exit

pressure equal to the ambient pressure, the propulsive efficiency is given

by:

THERMAL EFFICIENCY

• For the case when the mass flow rate of the fuel is much less than that of

air and the installation losses are very small, the previous equation

simplifies to the following equation for the propulsive efficiency:

THERMAL EFFICIENCY

• The previous equation is plotted vs the velocity ratio V~/Vo in the next

slide and shows that high propulsive efficiency requires the exit velocity

to be approximately equal to the inlet velocity.

THERMAL EFFICIENCY

• Turbojet engines have high values of the velocity ratio Ve/Vo with

corresponding low propulsive efficiency, whereas turbofan engines have

low values of the velocity ratio Ve/Vo with corresponding high propulsive

efficiency.

THERMAL EFFICIENCY

THERMAL EFFICIENCY

• The thermal and propulsive efficiencies can be combined to give the

overall efficiency ηo of a propulsion system. Multiplying propulsive

efficiency by thermal efficiency, we get the ratio of the aircraft power to

the rate of thermal energy released in the engine (the overall efficiency of

the propulsion system):

RAMJET

• A ramjet engine is conceptually the simplest aircraft engine and consists

of an inlet or diffuser, a combustor or burner, and a nozzle.

• The inlet or diffuser slows the air velocity relative to the engine from the

flight velocity Vo to a smaller value V2. This decrease in velocity

increases both the static pressure P2 and static temperature T2.

RAMJET

RAMJET

• In the combustor or burner, fuel is added and its chemical energy

is converted to thermal energy in the combustion process.

• This addition of thermal energy increases the static temperature

T4, and the combustion process occurs at a nearly constant

pressure for M4 << 1.

RAMJET

• The nozzle expands the gas to or near the ambient pressure and,

the temperature decreases from T4 to T9 with a corresponding

increase in the kinetic energy per unit mass.

RAMJET

RAMJET

RAMJET• However, P9 = P0 and m9 ≈ m0 for the ideal engine.

RAMJET• However, γ9=γ0=γ and R9 = R0 = R for and ideal engine.

RAMJET• However, πd = πb = π = 1 for an ideal engine. Thus Pt9 = P0πr and

RAMJET• However

• Thus

RAMJET

RAMJET

• Step 5: Application of the steady flow energy equation (first law of

thermodynamics) to the control volume about the burner or combustor

gives

RAMJET

• Where hpR is the thermal energy released by the fuel during combustion.

For an ideal engine,

• Thus the preceding equation becomes

RAMJET

RAMJET

• The fuel/air ratio f is defined as

RAMJET

• For the ideal ramjet, Tt0 = Tt2 = ToTr and rt4/Tt2 = Tb.

RAMJET• Step 6: This is not applicable for the ramjet engine•• Step 7: Since M9 = M0 and Tg/To = rb, then

• And the expression for thrust can be rewritten as

RAMJET

RAMJET

• Step 9: Development of the following efficiency expressions is left to the

reader.

RAMJET

TURBOFAN

• The propulsive efficiency of a simple turbojet engine can be improved by

extracting a portion of the energy from the engine's gas generator to

drive a ducted propeller, called a fan.

• The fan increases the propellant mass flow rate with an accompanying

decrease in the required propellant exit velocity for a given thrust.

TURBOFAN

• Because the rate of production of "wasted" kinetic energy in the exit

propellant gases varies as the first power with mass flow rate and as the

square of the exit velocity, the net effect of increasing the mass flow rate

and decreasing the exit velocity is to reduce the wasted kinetic energy

production and to improve the propulsive efficiency.

TURBOFAN

TURBOFAN

• The gas flow through the core engine is mc, and the gas flow through the fan is mf. The ratio of the fan flow to the core flow is defined as the bypass ratio and given the symbol alpha a. Thus

ENGINE PERFORMANCE

• When a gas turbine engine is designed and built, the degree of variability of

an engine depends on available technology, the needs of the principal

application for the engine, and the desires of the designers.

• Most gas turbine engines have constant-area flow passages and limited

variability (variable Tt4; and sometimes variable Tt7 and exhaust nozzle throat

area).

ENGINE PERFORMANCE

• In a simple constant-flow-area turbojet engine, the performance (pressure ratio

and mass flow rate) of its compressor depends on the power from the turbine

and the inlet conditions to the compressor.

• As we will see in this chapter, a simple analytical expression can be used to

express the relationship between the compressor performance and the

independent variables: throttle setting (Tt4) and flight condition (M0, To, P0).

ENGINE PERFORMANCE

• When a gas turbine engine is installed in an aircraft, its performance varies with flight conditions and throttle setting and is limited by the engine control system. In flight, the pilot controls the operation of the engine directly through the throttle and indirectly by changing flight conditions.

• The thrust and fuel consumption will thereby change. In this chapter, we will look at how specific engine cycles perform at conditions other than their design (or reference) point.

ENGINE PERFORMANCE

• There are several ways to obtain this engine performance. One way is to look

at the interaction and performance of the compressor-burner-turbine

combination, known as the pumping characteristics of the gas generator.

• In this case, the performance of the components is known because the gas

generator exists. However, in a preliminary design, the gas generator has not

been built, and the pumping characteristics are not available.

ENGINE PERFORMANCE

• In such a case, the gas generator performance can be estimated by using first principles and

estimates of the variations in component efficiencies.

• In reality, the principal effects of engine performance occur because of the changes in

propulsive efficiency and thermal efficiency (rather than because of changes in component

efficiency).

• Thus a good approximation of an engine's performance can be obtained by simply assuming

that the component efficiencies remain constant.

BIBLIOGRAPHY• http://web.mit.edu/e_peters/Public/Rockets/

Rocket_Propulsion_Elements.pdf • Fundamentals of Compression Process, Chapter 2• http://

web.mit.edu/e_peters/Public/Rockets/Rocket_Propulsion_Elements.pdf• Elements of Propulsion Gas Turbines and Rockets. J D. Mattingly