Past Paper 2 Flashcards
how does the diffusion factor relate to the choice of pitch to cord ratio
- 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
why is the standard expression for the diffusion factor difficult to use at the prelim design stage and what is the alternative
- 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
what variable is the blade span referring to
- the height of the blade h
- typically used in 𝑚̇ = ρV_x*hs
what common assumptions are made about the turbine and nozzle of a turbojet
- the stator of the turbine and the nozzle exit is choked
- M3 = M5 = 1
what assumptions are made about the nozzle of turbojet
- 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
what assumption is made about the mass flow rate through a turbojet
- the mass flow rate of the fuel is negligible
- so the work of the turbine is the same 𝑚̇ going through the compressor
what do you need to remember about the γ-relations when working with given polytropic efficiencies
- if youre including the efficiency in the power you do NOT use any isentropic values in the fractions
what assumption is made about the combustor in a turbojet
- the pressure loss across it is negligible
- so p_02 = p_03
what is the formula for the fuel flow rate 𝑚̇_f in a turbojet
- 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
what is the negative impact of stall cells (other than the engine not working)
- 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
what is the compressor surge margin
- 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)
why is the surge margin necessary
- 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
what does the general velocity triangle for a radial compressor look like
- 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
what is the slip factor σ in words and a general equation
- 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
what does it mean for X2 if the rotor blades have backsweep
- X2 is -ve
what is dh_0 equal to
- dh_0 = U*dV_θ
why is it desirable to chose the inlet tip radius r_t to minimize the blade tip inlet relative velocity
- because it means you can avoid choking, separation and loss due to shocks
what is the assumption that allows you to say W_C = W_T for a gas generator
- that mechanical losses are negligible
what is referred to as the compressor map
- 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
why does the working line of a gas turbine change when accelerating form idle to full speed
- 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
what would you do if you wanted to increase the surge margin for a gas turbine
- 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
what would be the effect of increasing the turbine NGV to increase the surge margin for a gas turbine
- 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
