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In this lecture...

• Turbine Blade Cooling

• Blade cooling requirements

• Fundamentals of heat transfer

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Turbine blade cooling

• Thrust of a jet engine is a direct function of the

turbine inlet temperature.

• Brayton cycle analysis, effect of maximum cycle

temperature on work output and efficiency.

• Materials that are presently available cannot

withstand a temperature in excess of 1300 K.

• However, the turbine inlet temperature can be

raised to temperatures higher than this by

employing blade cooling techniques.

• Associated with the gain in performance is the

mechanical, aerodynamic and thermodynamic

complexities involved in design and analysis of

these cooling techniques.

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Turbine blade cooling

• The environment in which the nozzles and

rotors operate are very extreme.

• In addition to high temperatures, turbine

stages are also subjected to significant

variations in temperature.

• The flow is unsteady and highly turbulent

resulting in random fluctuations in

temperatures.

• The nozzle is subjected to the most severe

operating conditions.

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Turbine blade cooling

• There are several modes of failure of a

turbine blade.

• Oxidation/erosion/corrosion

• Occurs due to chemical and particulate

attack from the hot gases.

• Creep

• Occurs as a result of prolonged

exposure to high temperatures.

• Thermal fatigue

• As a result of repeated cycling through

high thermal stresses.

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Turbine blade cooling

Combustion products Stator (^) Rotor

Average radial

temperature profile

Average temperature profile entering a turbine stage

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Fundamentals of heat transfer

• There are three modes of heat transfer

• Conduction

• Convection

• Radiation

• Conduction

• Heat transfer between two bodies or two parts of

the same body through molecules which are more or

less stationary.

• In liquids and gases, conduction results from

transport of energy by molecular motion near the

walls and in solids it takes place by a combination of

lattice vibration and electron transport.

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Fundamentals of heat transfer

• Conduction involves energy transfer at a

molecular level with no movement of

macroscopic portions of matter relative to one

another.

• Convection

• Involves mass movement of fluids

• When temperature difference produces a

density difference – leads to mass movement –

Free convection

• Caused by external devices like a pump, blower

etc. Forced convection

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Fundamentals of heat transfer

• Heat transfer by conduction

• The rate of heat transfer by conduction

can be written as (Fourier’s conduction

law)

temperature gradient.

conductedper unit timeper unit areaper unit negative

kis the thermalconductivity defined as theamount of heat

surface, anddT/dy is the temperaturegradient.

Where, Q/Ais therate of heat transferper unit areaof the

dy

dT q k A

Q

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Fundamentals of heat transfer

over the yearsby severalresearcher s.

Simplified forms of thisequationhasbeenusedextensively

material.

called thermal diffusivity and is aproperty of theconducting

is c

k ThisisknownastheFourier equation.Theparameter

t

T

T

c

k

Poissonequation

Thegeneralizedgoverningequationis athreedimensional

p

p

ρ

ρ ∂

2

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Fundamentals of heat transfer

• In a typical turbine blade, the boundary layer

developing on the blade surface and the

freestream temperature are of interest.

• The boundary layer that acts as a buffer

between the solid blade and the hot

freestream, offers resistance to heat transfer.

• Heat transfer occurs in this viscous layer

between the blade and the fluid through both

conduction and convection.

• The nature of the boundary layer (laminar or

turbulent) plays an important role in the heat

transfer process.

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Fundamentals of heat transfer

Stagnation point

Possibility of

shock-boundary

layer interaction

Unsteady wake

flow

Possibility of transition followed by

relaminarisation

Variation of heat transfer around a turbine blade

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Fundamentals of heat transfer

• The heat transfer coefficient is non-

dimensionalised by the thermal conductivity

and characteristic length:

• In addition to Nusselt number there are other

important non-dimensional groups namely,

Reynolds number (Re), Prandtl number (PR),

Eckert’s number (Ec), Grashof number (Gr)

Richardson number (Ri) and Stanton number

(St).

• All these numbers play a significant role in a

transfer analysis depending upon the

application.

Nu is the Nusselt number.

y

T

T T

L

k

h(x)L

Nu x

e w w

x 

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Laminar boundary layer (forced

convection)

0 0 1

2

= = = → ∞ = = =

= = = − −

∂

∂

∂

∂

∂

∂

φ φ θ

φ θ α μ ρ ρ θ

φ α

φ φ

y , v and y , u

The boundary conditions being:

where, u or , / or k / c and (T T )/(T T )

y y

(v )

x

(u )

case as:

plate.Wecanwritethetransport equation for sucha

Consider anincompressiblelaminar flow over aflat

p w e w

2

• The transport equations for velocity and

temperature are similar and therefore the

coupling is obvious.