Past Papers 1

Question 1

what are the two ways you can increase the stagnation pressure ratio in a compressor

Answer 1

• increase the stage loading coefficient
• increase the blade speed

Question 2

what are the impacts of increasing the stage loading coefficient

Answer 2

• high stage loading requires lots of turning which is limited by diffusion
• careful blade design can keep the boundary layers healthy, but the diffusion factor of 0.6 is the limit

Question 3

what are the impacts of increasing the blade speed

Answer 3

• if the relative inlet mach number rises to 0.7 the peak mach number will become supersonic on the suction surface (50% thing)
• the resulting shock-boundary layer interacts downstream and can separate the flow

Question 4

what is the formula for the number of stages of a compressor using logs

Answer 4

• n_stage = log10(p03/p01) / log10(p02/p01)

Question 5

what does it mean if theres no inlet swirl into a compressor

Answer 5

• V_θ1 = 0

Question 6

what does it mean if youre given data at design conditions

Answer 6

• theres zero incidence at the inlet
• so V_1 = V_x1

Question 7

what is the relationship between stagnation temperatures T_01 and T_02 within a stationary blade row (like stators)

Answer 7

• T_01 = T_02

Question 8

what is the most common use of the stagnation pressure loss coefficient formula Yp if youre given Yp

Answer 8

• to factorise and rearrange the formula for p1/p01
• if you have the mach number this can be found in the databook

Question 9

what does it mean if the flow is assumed to be isentropic though a stator row

Answer 9

• there is no stagnation pressure loss

Question 10

what is the formula for pitch s

Answer 10

• s = 2pi*r

Question 11

explain what is meant by a rotating stall cell

Answer 11

• a local flow perturbation causes one blade passage to exhibit separation
• flow is diverted around this blockage, increasing incidence onto the blades on the left (inducing separation)
• incidence is reduced for he blades on the right, meaning separated flow can recover
• this pattern grows to cover a number of passages to make a stall cell
• which then propagates (rotates) around the annulus

Question 12

what type of stall is likely to occur in low hub-to-tip ratio axial compressors

Answer 12

• its likely to be part span stall
• this is stall confined to one or a few blade stages

Question 13

what type of stall is likely to occur in high hub-to-tip ratio axial compressors

Answer 13

• its likely to be full span stall
• this is where the stall cell blocks the annulus entirely from hub to casing
• there is likely one one cell which extends axially through all stages

Question 14

what is the visual difference between a low and high hub-to-tip ratio annulus

Answer 14

• the high ratio one is like a skinny donut
• the low ratio one is like a thick donut with a smaller hole

Question 15

what is the relationship between γ, c_p and R

Answer 15

• c_p / R = γ/γ-1

Question 16

when told to sketch the stage characteristics of a multistage compressor, what graph are you plotting (axes and curve shape)

Answer 16

• a graph of ΔP_0 / ρU^2 against V_x/U
• the curve is like a -x^2 shape but starts about halfway to max y-axis and ends at about y_axis = 0

Question 17

you are given the overall characteristic of a multistage axial compressor as a plot with a bunch of contours. the focus is on a high speed and low speed mach contour. on the high speed mach contour, the point a is within the highest efficiency contour and marks the design point.

if you were to plot the stage characteristics for the first and last stage, where would you place the point a on the curve and why

Answer 17

• for the first stage characteristic, a would be on the RHS of the curve’s peak, not too close but not too far
• for the last stage characteristic, a would be in the same position
• a is the design point at maximum speed so all stages are well matched with constant flow coefficient and low incidence

Question 18

point b is on the high mach contour but is below a, further from the surge line. where would you place b on the same stage characteristic curves and why

Answer 18

• for the first stage, b would be on the RHS of the peak slightly after a
• for the last stage, b would be on the RHS of the peak lower than before
• this is because b has increased flow through the first stage, so pressure rise drops and Vx increases across the stage
• this amplifies through the stages with lower density and higher Vx so it gets worse until to the last stage

Question 19

point c is on the high mach contour but is above a, closer to the surge line. where would you place c on the same stage characteristic curves and why

Answer 19

• for the first stage, c would be on the RHS of the peak slightly above a
• for the last stage, c would be on the LHS of the peak still higher than a
• the reasons are opposite for b, decrease flow through first stage = dP_0 rises and Vx decreases
• this amplifies through the stages

Question 20

point d is on the low mach contour but on the same efficiency contour as a. where would you place d on the same stage characteristic curves and why

Answer 20

• for the first stage, d would be on the LHS of the peak above a
• for the last stage, d would be on the far RHS of the peak near the bottom
• point d has a reduced blade speed so p rise is reduced
• the annulus is too small for the low density air passing through it
• the rear stage chokes with high Vx limiting the mass flow through the machine
• so the front stage is pushed up towards stall

Question 21

which is the likely form of stall and at which stages are largely responsible for instability at 60%, 80% and 100% of compressor speeds (Vx/U)

Answer 21

• 60% = part span, front stage stall
• 80% = full span, all stage stall
• 100% = surge, rear stage stall