Gas Turbine Off-Design

Question 1

What is the ideal turbojet cycle

Answer 1

Intake nozzle - isentropic compression
Compressor - isentropic compression
Combustor - constant pressure heat addition
Turbine - isentropic expansion
Propelling nozzle - isentropic expansion

Question 2

What are the key differences between a aircraft gas turbines and a shaft power gas turbine

Answer 2

The useful power output of an aircraft is produced wholly or mostly by expansion in a propelling nozzle - shaft power gas turbine systems have two turbines, one to drive compressor and one to generate power

Also have to include the effect of forward speed and altitude on the engine performance

Question 3

What considerations are employed for intakes

Answer 3

To is constant
Po is constant if isentropic
Forward air speed
Considerate pressure increase
Requirements to minimise pressure loss while ensuring uniform pressure and velocity at compressor inlet - to avoid surge and vibrations

Question 4

Why do mechanical losses occur between turbine and compressor

Answer 4

Bearing friction
Windage

Question 5

What is the relationship between number of stages and overall isentropic efficiency for compressors and turbines

Answer 5

Compressors - Efficiency decreases as stages increase
Turbines - Efficiency increases as stages increase

Question 6

What is the role of the combustion chamber

Answer 6

Provide smooth stream of uniformly heated gas to turbine
Requires minimum losses in pressure and maximum heat release

Question 7

What difficulties occur in combustion chambers

Answer 7

Burning large quantities of fuel
Coping with extensive volume of air
Coping with high speed air
Working at very high temperature

Question 8

What does off design mean

Answer 8

Often case that one component works reasonably at certain operating conditions while others encounter undesirable conditions - turbine and compressor have to be run at same rotational speed - off design matches values to find the best design point

Question 9

How can you avoid surge during start-up

Answer 9

Bleed off air from compressor
Increase nozzle area

Question 10

How does a constant speed propeller work

Answer 10

Has a variable pitch that automatically adjusts to maintain chosen rotational speed meaning gas turbine can function at its optimum operation conditions both thermodynamically and aerodynamically

Question 11

Why might a gas turbine be combined with a diesel engine

Answer 11

To get optimum operation at a range of operating conditions for a significant time

Question 12

Why does altitude play a part in gas turbine design

Answer 12

Altitude determines the ambient pressure and temperature
These have strong impact on gas turbine performance

Question 13

Why is off design important

Answer 13

Variation in SFC with reduced power is important especially where large times are spent at this condition

Question 14

Give an example of off design

Answer 14

Water sprays injected into gas turbine inlet to cool down intake air on hot day - increases power output

Surplus electricity used to produce ice and applied to cool inlet air during day time - better than having a larger unit whole year round working away from design point

Question 15

List three gas turbine configurations

Answer 15

Single shaft gas turbine delivering shaft power
Free turbine engine where gas generator turbine drives compressor and power turbine drives load
Simple jet engine with propelling nozzle

Question 16

What is dimensional analysis

Answer 16

Means of simplifying physical problem by appealing to dimensional homogeneity to reduce number of relevant variables

Question 17

What are the two non-dimensional parameters

Answer 17

Non dimensional flow
Non dimensional rotational speed

Question 18

What is equilibrium point matching

Answer 18

Finding corresponding points on characteristics of each component when engine is running at a steady speed or in equilibrium

Question 19

What is the impact of connected compressor and turbine shafts

Answer 19

Turbine pressure ratio and non-dimensional speed can be used to get turbine efficiency

Question 20

What is flow compatibility/matching

Answer 20

Checking the compatibility of non-dimensional flow between compressor and turbine

Question 21

What is work compatibility

Answer 21

Equating the thermal work of the compressor with turbine (including mechanical efficiency)

Question 22

Summarise the calculations for a gas generator

Answer 22

Select point on compressor characteristic and use values to determine temperature ratio
Guess turbine pressure ratio to obtain non-dimensional mass flow for turbine from turbine characteristics and temperature ratio from flow compatibility
Calculate non-dimensional speed
Find turbine efficiency from turbine characteristic
Non-dimensional temperature drop can be calculated and used to calculate another value of temperature ratio
Compare values of temperature ratio - if they don’t agree guess another value for turbine pressure ratio

Question 23

Summarise the calculations for a choked propelling nozzle

Answer 23

Calculate pressure ratio and see if nozzle is choked
Choked - pressure and temperature found from critical relations
Perform static matching of gas generator turbine and nozzle - same mass flow between the components and fixed by compressor characteristics and turbine pressure ratio
Compare mass flow from nozzle characteristic with gas generator value - if not the same then compressor characteristic point needs to be changed

Question 24

Summarise the calculations for an unchoke propelling nozzle

Answer 24

Calculate pressure ratio and see if the nozzle is unchoked
Pressure is the same as atmospheric pressure

Question 25

Why do we look at forward speed as a function of Mach number

Answer 25

Forward speed increase ram pressure Increased pressure before nozzle so higher pressure ratio Nozzle non-dimensional flow maximum when nozzle is choked then independent of pressure ratio (and forward speed) Turbine unchanged due to flow compatibility

Question 26

What are the components of thrust

Answer 26

Momentum thrust (change in velocity) Pressure thrust (change in pressure)

Question 27

Why is mechanical speed important to engine life

Answer 27

Turbine stresses Turbine entry temperature Maximum don-dimensional speed decreases as ambient temp increases so reduced mass flow and pressure ratio (and so red. thrust)

Question 28

How can fuel consumption dependence on ambient conditions be ignored

Answer 28

Use non-dimensional values based on ambient conditions

Question 29

What does SFC identify

Answer 29

The efficiency of the engine Obtained from thrust and fuel consumption curves Improves with altitude as ambient temperature decreases

Question 30

What is the specific thrust equation for gas turbine engine

Answer 30

Choked F/m = (u5 - ua) + (1/(rho_c * u5))*(Pc - Pa) Unchoked F/m = (u5 - ua) --- No pressure thrust

Question 31

What is the work compatibility equation

Answer 31

Cpg * (To3 - To4) = nm * Cpa * (To2 - To1)

Question 32

What is the general procedure for gas turbine calculations

Answer 32

Start from atmospheric condition and move along each component sequentially i.e. intake -> compressor -> combustor -> turbine -> nozzle

Question 33

Give example steps for simple gas turbine calculation

Answer 33

Given initial conditions Find To1 from standard relation Find Po1 using Po/P relation in LBOTF Find Po2 from compressor ratio Find the compressor temperature rise from LBOTF Find the turbine temperature drop (work matching) Find turbine inlet pressure (either stated or same as compressor outlet) Find To4' from definition of expansion isentropic efficiency Find Po4 using isentropic flow relation of pressure and temperature ratios Find nozzle to atmospheric pressure ratio Find critical pressure ratio and check if choked or unchoked Find nozzle static temperature Find nozzle static pressure Find nozzle density Find nozzle velocity Find area/mass flow - A5/m = 1/(rho_c * u5) Find the specific thrust (pressure in pascals) Find the theoretical far from combustor temperature rise from LBOTF figure Find actual far = theoretical/combustor efficiency Find TSFC = f/Fsp

Question 34

Give steps for choked nozzle

Answer 34

T5 is critical temperature so found from relation P5 is critical pressure so found from relation U5 is the sonic speed F/m = (u5 - ua) + (1/(rho_c * u5))*(Pc - Pa)

Question 35

Give steps for unchoked nozzle

Answer 35

To4 - T5 can be found from standard expansion equation To4 = To5 = Static + Dynamic temperatures To4 - T5 = (u5^2)/2Cp so can find u5 (u5 - ua) --- No pressure thrust

Question 36

What is the mass flow parameter

Answer 36

mass flow rate * sqrt(T)/P

Question 37

What is the rotational speed parameter

Answer 37

N/sqrt(RT)

Question 38

What does compatibility of rotational speeds mean

Answer 38

Compressor and turbine shafts are connected so rotational speeds are the same N/sqrt(To3) = N/sqrt(To1) * sqrt(To1/To3)

Question 39

What does flow compatibility mean

Answer 39

Mass flow of air through components is the same mass flow rate * sqrt(To3)/Po3 = (mass flow rate * sqrt(To1)/Po1) * Po1/Po2 * Po2/Po3 * sqrt(T/To1) Same can be done to find the turbine exit non-dimensional flow and compare with nozzle flow

Question 40

What is the nozzle non-dimensional flow

Answer 40

C5 * A5 * rho_5 * sqrt(To4)/Po4