Past Papers 1 Flashcards
what are the two ways you can increase the stagnation pressure ratio in a compressor
- increase the stage loading coefficient
- increase the blade speed
what are the impacts of increasing the stage loading coefficient
- 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
what are the impacts of increasing the blade speed
- 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
what is the formula for the number of stages of a compressor using logs
- n_stage = log10(p03/p01) / log10(p02/p01)
what does it mean if theres no inlet swirl into a compressor
- V_θ1 = 0
what does it mean if youre given data at design conditions
- theres zero incidence at the inlet
- so V_1 = V_x1
what is the relationship between stagnation temperatures T_01 and T_02 within a stationary blade row (like stators)
- T_01 = T_02
what is the most common use of the stagnation pressure loss coefficient formula Yp if youre given Yp
- to factorise and rearrange the formula for p1/p01
- if you have the mach number this can be found in the databook
what does it mean if the flow is assumed to be isentropic though a stator row
- there is no stagnation pressure loss
what is the formula for pitch s
- s = 2pi*r
explain what is meant by a rotating stall cell
- 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
what type of stall is likely to occur in low hub-to-tip ratio axial compressors
- its likely to be part span stall
- this is stall confined to one or a few blade stages
what type of stall is likely to occur in high hub-to-tip ratio axial compressors
- 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
what is the visual difference between a low and high hub-to-tip ratio annulus
- the high ratio one is like a skinny donut
- the low ratio one is like a thick donut with a smaller hole
what is the relationship between γ, c_p and R
- c_p / R = γ/γ-1
when told to sketch the stage characteristics of a multistage compressor, what graph are you plotting (axes and curve shape)
- 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
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
- 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
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
- 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
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
- 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
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
- 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
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)
- 60% = part span, front stage stall
- 80% = full span, all stage stall
- 100% = surge, rear stage stall
