Lec 04 Turbo machine
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Transcript of Lec 04 Turbo machine
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1
Lect- 4
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 2
Lect-4
In this lecture...
Performance parameters: cascadeanalysis
2-D losses in axial compressor stage primary losses
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 3
Lect-4
Performance parameters
Measurements from cascade: velocities,pressures, flow angles ...
Loss in total pressure expressed as totalpressure loss coefficient
Total pressure loss is very sensitive to
changes in the incidence angle. At very high incidences, flow is likely toseparate from the blade surfaces,eventually leading to stalling of the blade.
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12
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PPPLC
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 4
Lect-4
Performance parameters
Blade performance/loading can beassessed using static pressure coefficient:
The CPdistribution (usually plotted as CPvs. x/C) gives an idea about thechordwise load distribution.
inlet)cascadetheat
measured(usuallypressurestaticreferencetheisP
andpressurestaticsurfacebladetheisPWhere,V
PPC
ref
local
reflocalP 2
12
1
=
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 5
Lect-4
Performance parameters
Deflection,
degrees
Tota
lpressurelosscoeffic
ient
Position along cascade
Location of the
blade trailing edge
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Lect-4
Performance parameters
Incidence angle, degrees
Totalpressurelo
ss
coefficient
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Lect-4
Losses in a compressor blade
Nature of losses in an axial compressorViscous losses
3-D effects like tip leakage flows, secondaryflows etc.
Shock lossesMixing losses
Estimating the losses crucial designing losscontrol mechanisms.
However isolating these losses not easy andoften done through empirical correlations.
Total losses in a compressor is the sum ofthe above losses.
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Lect-4
Losses in a compressor blade
Viscous lossesProfile losses: on account of the profile or nature
of the airfoil cross-sections
Annulus losses: growth of boundary layer alongthe axis
Endwall losses: boundary layer effects in thecorner (junction between the blade surface andthe casing/hub)
3-D effects:Secondary flows: flow through curved blade
passages
Tip leakage flows: flow from pressure surface tosuction surface at the blade tip
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10
Lect-4
Losses in a compressor blade
The loss manifests itself in the form of stagnationpressure loss (or entropy increase).
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11
Lect-4
Losses in a compressor blade
The overall losses in a turbomachinery can besummarised as:
lossesEndwall:
lossleakagetip:
lossflowsecondary:
lossesshock:lossesprofile:Where,
E
L
s
sh
P
ELsshP
++++=
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12
Lect-4
2-D Losses in a compressor blade
2-D losses are relevant only to axial flowturbomachines.
These are mainly associated with bladeboundary layers, shock-boundary layerinteractions, separated flows and wakes.
The mixing of the wake downstreamproduces additional losses called mixing
losses. The maximum losses occur near the blade
surface and minimum loss occurs near theedge of the boundary layer.
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 13
Lect-4
2-D Losses in a compressor blade
2-D losses can be classified as:
Profile loss due to boundary layer, including
laminar and/or turbulent separation. Wake mixing losses
Shock losses
Trailing edge loss due to the blade.
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 14
Lect-4
2-D Losses in a compressor blade
The profile loss depends upon: Flow parameters like Reynolds number,
Mach number, longitudinal curvature of theblade, inlet turbulence, free-stream
unsteadiness and the resulting unsteadyboundary layers, pressure gradient, andshock strength
Blade parameters like: thickness, camber,
solidity, sweep, skewness of the blade,stagger angle and blade roughness.
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 15
Lect-4
2-D Losses in a compressor blade
The mixing losses arise as a result of themixing of the wake with the freestream.
This depends upon, in addition to theparameters mentioned in the previous slide,
the distance downstream. The physical mechanism is the exchange of
momentum and energy between the wake andthe freestream.
This transfer of energy results in the decay ofthe free shear layer, increased wake centre linevelocity and increased wake width.
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 16
Lect-4
2-D Losses in a compressor blade
At far downstream, the flow becomesuniform.
Theoretically, the difference between thestagnation pressure far downstream and the
trailing edge represents the mixing loss. Most loss correlations are based on
measurements downstream of the trailingedge (1/2 to 1 chord length) and therefore
do not include all the mixing losses. If there is flow separation, the losses would
include losses due to this zone and at itseventual mixing downstream.
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 17
Lect-4
2-D Losses in a compressor blade
edge.trailingtheatlayerboundarybladetheofthicknessmomentumandntdisplaceme
thetovelocitiesanddifferencepressurestaticthe
relatetonecessaryisitabove,thedetermineTo
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mp 21
0202
=+
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 19
Lect-4
2-D Losses in a compressor blade
Thus, in a simplified manner, we see thatthe profile loss can be estimated based onthe momentum thickness.
The above loss correlation includes both
profile and wake mixing loss. If flow separation occurs, additional losses
are incurred. This is because the pressuredistribution is drastically altered beyond
the separation point. The losses increase due to increase in
boundary layer displacement andmomentum thicknesses.
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 20
Lect-4
2-D Losses in a compressor blade
In addition to the losses discussed above,boundary layer growth and subsequent decay ofthe wake causes deviation in the outlet angle.
An estimate of this is given as:
Hence, viscous effect in a turbomachine alwaysleads to decrease in the turning angle.
The values of displacement and momentumthicknesses, depend upon, variation of freestreamvelocity, Mach number, skin friction, pressuregradient, turbulence intensity and Reynoldsnumber.
ttan)(tan 12
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 21
Lect-4
2-D Losses in a compressor blade
In general, the loss estimation may be carriedout using one of the following methods:
Separate calculation of the potential orinviscid flow and the displacement andmomentum thicknesses. Subsequently, usethe equation discussed previously.
Using a Navier-Stokes based computational
code. Here the local and the integratedlosses can be computed directly.
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 22
Lect-4
Mach number and shock losses
The static pressure rise in a compressorincreases with Mach number.
Thus the pressure gradient increases withincrease in Mach number.
This means that the momentum thickness andhence the losses increase with Mach number.
Increasing Mach numbers also lead to
increase in shock losses. At transonic speeds, the shock losses are very
sensitive to leading and trailing edgegeometries.
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 23
Lect-4
Mach number and shock losses
An estimate of the 2-D shock losses for acompressor must include:
The losses due to the leading edge bluntnesswith supersonic upstream Mach number.
The location of the passage shock can bedetermined from inviscid theories. If the shockstrength is known, the losses can beestimated.
The losses due to boundary layer growth andthe shock-boundary layer interaction are mostdifficult to estimate. The contribution howeveris small for weak shocks.
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 24
Lect-4
Mach number and shock losses
One of the empirical correlations for the shockloss was given by Freeman and Cumpsty(1989).
This is valid for an incidence angle upto 5o
. These empirical correlations are however,
derived using the 2-D assumption.
Actual flows are seldom 2-D in nature.
[ ].angleinletbladetheis,where
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losslosssh
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=
=
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Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 25
Lect-4
In this lecture...
Performance parameters: cascadeanalysis
2-D losses in axial compressor stage primary losses
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Prof Bhaskar Roy Prof A M Pradeep Department of Aerospace IIT Bombay 26
Lect-4
In the next lecture...
Tutorial: solved examples and tutorialproblems.