Past Paper 2

Question 1

how does the diffusion factor relate to the choice of pitch to cord ratio

Answer 1

• the blade force has to balance the ROCO momentum
• for a given turning at a given mass flow rate, a higher pitch to cord ratio gives a higher required blade force
• to match the higher blade force, the avg v difference between the PS and SS must be higher
• which leads to more diffusion as the peak v must diffuse back to to match exit conditions

Question 2

why is the standard expression for the diffusion factor difficult to use at the prelim design stage and what is the alternative

Answer 2

• because the blade shape is not known at the prelim design stage
• instead correlations based on angles are used
• which is Lieblein’s expression for DF = 1 - V2/V1 +1/2ΔV_θ/V1s/c

Question 3

what variable is the blade span referring to

Answer 3

• the height of the blade h
• typically used in 𝑚̇ = ρV_x*hs

Question 4

what common assumptions are made about the turbine and nozzle of a turbojet

Answer 4

• the stator of the turbine and the nozzle exit is choked
• M3 = M5 = 1

Question 5

what assumptions are made about the nozzle of turbojet

Answer 5

• there are no losses or heat transfer in the nozzle (specifically before the throat)
• so its adiabatic: T_04 = T_05
• and isentropic: p_04 = p_05

Question 6

what assumption is made about the mass flow rate through a turbojet

Answer 6

• the mass flow rate of the fuel is negligible
• so the work of the turbine is the same 𝑚̇ going through the compressor

Question 7

what do you need to remember about the γ-relations when working with given polytropic efficiencies

Answer 7

• if youre including the efficiency in the power you do NOT use any isentropic values in the fractions

Question 8

what assumption is made about the combustor in a turbojet

Answer 8

• the pressure loss across it is negligible
• so p_02 = p_03

Question 9

what is the formula for the fuel flow rate 𝑚̇_f in a turbojet

Answer 9

• 𝑚̇_f = 𝑚̇(T_03 - T_02)
• not really, this is specifically as a ratio of old to new values
• the temperature difference is between the combustor

Question 10

what is the negative impact of stall cells (other than the engine not working)

Answer 10

• blades moving into and out of stall cells experience large dynamic pressure loads
• this forcing can cause fatigue and blade cracking
• if the performance drop with part span stall is slight, this may go unnoticed

Question 11

what is the compressor surge margin

Answer 11

• its a margin that measures the ‘distance’ that the compressor operating point is from stall at a given speed (relating back to the contoured plot)

Question 12

why is the surge margin necessary

Answer 12

• its necessary because of engine-to-engine manufacturing tolerances
• in-service deterioration, which tends to raise the working line and reduce the stall p ratio
• and to allow for engine acceleration when the compressor o.p. moves above the steady state operating line

Question 13

what does the general velocity triangle for a radial compressor look like

Answer 13

• V is pointing bottom left
• U is pointing from end of V to the right, but not past the origin
• V_rel links V origin to the end of U, still pointing bottom left
• the horizontal vertical length is V_m
• the entire horizontal length (V to origin) is V_θ

Question 14

what is the slip factor σ in words and a general equation

Answer 14

• the ratio of the actual V_θ2 at impeller exit to the ‘ideal’ value that would be produced if the flow followed the blade angle X2
• σ = V_θ2 / U_2 + V_θ2,ideal

Question 15

what does it mean for X2 if the rotor blades have backsweep

Answer 15

• X2 is -ve

Question 16

what is dh_0 equal to

Answer 16

• dh_0 = U*dV_θ

Question 17

why is it desirable to chose the inlet tip radius r_t to minimize the blade tip inlet relative velocity

Answer 17

• because it means you can avoid choking, separation and loss due to shocks

Question 18

what is the assumption that allows you to say W_C = W_T for a gas generator

Answer 18

• that mechanical losses are negligible

Question 19

what is referred to as the compressor map

Answer 19

• the contoured plot with p03 or p02/p01 against 𝑚̇*sqrt(T01)/p01
• there is the full version of this but you can be asked to draw a mini version
• you just need to draw the lines of constant mach with lines of constant T_03 increasing to the left from the origin
• the surge line needs to be shown on the very left
• the working line is the ‘path’ the performance of the machine takes on this plot

Question 20

why does the working line of a gas turbine change when accelerating form idle to full speed

Answer 20

• because fuel flow is increased to accelerate the engine
• this raises combustor outlet temperature T_03
• As the turbine is always choked (so f(M) = c), this reduces the mass flow rate
• thereby increasing compressor exit temperature
• this changes the turbine work and therefore the compressor work (Wc = Wt) to give the curve of increasing through T03 contours back down to the starting contour
• the steady state contour is just a straight line along a T03 contour

Question 21

what would you do if you wanted to increase the surge margin for a gas turbine

Answer 21

• increase the size of the turbine nozzle guide vane throat
• this would reduce T_03, giving you a working line on a lower T_03 contour further from the surge line

Question 22

what would be the effect of increasing the turbine NGV to increase the surge margin for a gas turbine

Answer 22

• p02 is lower so the gas turbine operates at a lower pressure ratio
• gas turbine operates are higher T_03 (?)
• lower compressor and turbine efficiencies
• specific work and total work are likely to reduce (despite mass flow rate being restored to ideal operating conditions)
• overall cycle efficiency lower