lec 04 turbo machine

8/9/2019 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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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.

2

12

1

0201

V

PPPLC

=


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Lect-4


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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Lect-4


Deflection,

degrees

Tota

lpressurelosscoeffic

ient

Position along cascade

Location of the

blade trailing edge


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7/26Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay 7

Lect-4


Incidence angle, degrees

Totalpressurelo

ss

coefficient


8/26Prof. Bhaskar Roy, Prof. A M Pradeep, Department of Aerospace, IIT Bombay

8

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


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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Lect-4


The loss manifests itself in the form of stagnationpressure loss (or entropy increase).

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Lect-4


The overall losses in a turbomachinery can besummarised as:

lossesEndwall:

lossleakagetip:

lossflowsecondary:

lossesshock:lossesprofile:Where,

E

L

s

sh

P

ELsshP

++++=



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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Lect-4


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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Lect-4


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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Lect-4


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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Lect-4


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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Lect-4


edge.trailingtheatlayerboundarybladetheofthicknessmomentumandntdisplaceme

thetovelocitiesanddifferencepressurestaticthe

relatetonecessaryisitabove,thedetermineTo

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)PP(

:aswrittenbecanstreamline

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Lect-4


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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Lect-4


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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Lect-4


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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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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Lect-4


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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Lect-4


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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Lect-4

In this lecture...

Performance parameters: cascadeanalysis

2-D losses in axial compressor stage primary losses


26/26

Prof Bhaskar Roy Prof A M Pradeep Department of Aerospace IIT Bombay 26

Lect-4

In the next lecture...

Tutorial: solved examples and tutorialproblems.

lec 04 turbo machine

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