Experimental technique of fluid machinery

P

decreases. Figure 5.3: Linear open loop suction type wind tunnel.

Blow down wind tunnel

This wind tunnel is used for high speed testing. It uses a compressed air

volume that passes through a drier to reduce the amount of water stored

inside the flow. Once the air enters the cylinder it must expands and this

expansion lead to a reduction in pressure and temperature and the water

vapour can become ice, affecting all the measurement or even stuck the fa-

cility.

Similarity rules

In order to be sure of what is happening inside the wind tunnel i have to

observe the similarty rules. These similarity rules are very important because

in wind tunnels we are used to study models and not a 1:1 replica, so we

must be sure that the obtained results can be scaled to the original object.

Similarity rules prescribe to keep the same values of

• Reynolds number,

• Mach number, 53

• turbulence intensity level,

• temperature ratio.

Moreover, the same flow structure must be reproduced

• flow periodicity in linear cascade,

• 2D flow region at mid-span section.

Flexible operating conditions

Wind tunnels should be flexible in order to be able to investigate different

flow phenomena on different models

• incidence,

• periodicity control,

• turbulence control,

• channel shape modification.

At UniBg we have three mid speed open loop, suction type facilities

• 2 for Nozzle vane cascade testing,

• 1 for rotor blade cascade.

Every facility must be equipped with instrumentation allowing to define its

operating condition in terms of and can be measured either

M a, Re T u. M a

at the inlet or outlet of the test section, far enought from the model to assure

an undisturbed flow condition

✓ ◆ ✓ ◆

P 1 P 1

1 1

t,1 t,1

2 2

= 1+ M a = 1+ M a

1 2,is

P P

1 2 (5.1)

is typically computed using the true chord as characteristic dimension

Re c

and the isoentropic velocity at cascade exit U 2,is

U c

2,is (5.2)

Re =

2,is ⌫

is measured upstream at several locations to also estimate its decay. It

T u

is typically based only on the stream wise fluctuating velocity component,

assuming isotropy p 0 2

(ū ) (5.3)

0 !

U (t) = Ū + u T u =

1 Ū

54

Figure 5.4: measurement.

M a

Turbulence can be increased by installing a turbulence generator at the inlet

section of the wind tunnel. There are other tests to characterize the flow

condition, for example the boundary layer traverse, if the BL is very thick i

cannot expect a good behaviour of the flow. If the BL is too thick i must open

the bleed ports upstream. The last thing to check is the flow periodicity.

The flow periodicity must be assured in the cascade middle section, and it

is influenced by the number of blades and by the shape of the outlet duct.

To verify if the flow is periodic or not, static pressure distribution along the

tangential direction downstream of the cascade must be periodic. Pressure

taps are used with movable walls in order to adjust the flow direction.

Testing condition

The inlet flow characterization and periodicity tests have to be done each time

a modification is made to the wind tunnel/test section. For each run M a,

and must be known. To get these data, the following measuremets

T u Re

must always be performed to assess the cascade operating condition

• and (3-holes probe) ,

!

P P M a

t1 1 1

• ,

P 2

• ( using a thermocouple) for compressible flow to get .

T U

2,is

55

Chapter 6

Boundary layer

In real world tangential forces are exchanged among fluid layers and between

fluid and walls. Thanks to the viscosity the fluid stays attached to the wall,

this condition is said to be a "no slip condition". Inside the boundary layer

we have losses and that’s why is important to study it. There are different

Figure 6.1: Boundary layer.

kind of boundary layer

• laminar boundary layer,

• transition boundary layer,

• turbulent boundary layer,

and we make velocity measurements at different stream wise locations inside

the boundary layer,

• in the laminar part,

• at the beginning of transition, 56

• at the end of transition,

• in the fully turbulent part.

Figure 6.2: Boundary layer regimes.

Different flow regimes require different equipment, frequency response is very

important because the frequency of the laminar BL is completely different

from the frequency of the turbulent BL. Usually when i perform a BL mea-

surement i move the probe along the BL because i want to compute the

velocity gradient in the best possible way. I have to adapt the measurement

grid in order to have the highest resolution inside the BL because the velocity

gradient is very strong. In laminar BL the number of measurement point i

need is lower respect to the turbulent BL. For a laminar BL, flattened Pitot

probe can be used, as no fluctuations are superimposed to the signal and

no frequency response is required. For transitional and turbulent boundary

layers, high frequency response is require, as the probe must detect high ve-

locity fluctuations. It is very difficult to perform measurements up to the wall

because of the reduced spatial resolution available and due to the very small

thickness of the boundary layer. So it’s mandatory to predict the boundary

layer shape close to the wall, in order to be able to extrapolate the measured

data up to the wall. Let’s consider a generic turbulent boundary layer. In

the direction, it can be divided into two main regions

y

1. the outer layer which is the most external part and here we are able to

perform measurement, so it is not so important y

0.2 < < 1,

2. the inner layer y

0 < < 0.2.

We are interested in the inner layer description, so we move from the global

coordinate to the wall coordinate system (y )

+ +

, u

u y u

⌧ (6.1)

+ +

y = u =

⌫ u ⌧

57

where the shear velocity is r ⌧ w (6.2)

u =

⌧ ⇢

The inner layer can be devided into three main regions, starting from the

wall

1. The linear sub-layer (y + < 0.3) (6.3)

+ +

u = y ,

2. The buffer region " #

2 3

+ +

(k u ) (k u )

+ (6.4)

+ + k c k u

y = u + e e 1 ,

2 6

3. The Log-law region 1 (6.5)

+ +

u = ln y + C c =5 k = 0.4

k

Figure 6.3: Linear-Buffer-Log law regions.

In the right part of the picture (6.4) we can see all the points layed on the log

law region, this means that the BL is fully turbulent, while on the left side of

the picture we see points laying on the linear part so laminar BL. If we are

able to put at least one measuring point inside the laminar sub-layer or inside

a laminar boundary layer, we can directly extrapolate the velocity profile up

to the wall, obtaining . If we can’t do that we can use the Clauser chart.

⌧ w

This chart allows to predict the friction coefficient from measurements

C f

performed in the log-law region. ⌧ w (6.6)

C =

f 1 2

⇢ U 1

2

58

Figure 6.4: Linear-Buffer-Log law regions.

Another way to look at the velocity distribution to understand if the

boundary layer is laminar or turbulent is through the definition of the integral parameters.

They are:

• ,

Displacement thickness ⇤

• ,

Momentum thickness ⇤⇤

⇤

• .

Shape factor H =

12 ✓

The is the distance by which the solid would have

displacement thickness

to be displaced in a frictionless flow to give the same mass deficit as the

boundary layer ✓ ◆

Z Z Z u (6.7)

⇤

!

u dy = U dy = 1 dy.

1 U 1

⇤

0 0

Figure 6.5: Displacement thickness.

It compares two flow conditions the real one on the left side and a

theoretical one (frictionless flow) on the right.

59

The compares two flow conditions too. It tells us

Momentum thickness

how much we have to move the wall (beside ) to get the same momentum

⇤

defect ✓ ◆

Z u u (6.8)

⇤

✓ = 1 dy < .

U U

1 1

0

Figure 6.6: Momentum thickness.

The gives information about the BL state, infact

shape factor

• if the BL is laminar,

H = 2.6!

12

• if the BL is turbulent.

!

1.3 < H < 1.5

12

Another useful parameter is the momentum Reynolds number

✓ U 1 (6.9)

Re = .

✓ ⌫

CFD codes use this parameter to estimate the transition.

Transition

Transition is not an instantaneous and localized phenomenon, it takes time

and space to develop and it can be:

• natural transition it takes place at low value of turbulence (not

!

visible in turbomachines because of the high turbulence values),

• by-pass transition! happens in turbomachines, is a laminar–turbulent

transition in a fluid flow over a surface. It occurs when a laminar

boundary layer transitions to a turbulent one through some secondary

instability mode, bypassing some of the pre-transitional events that

typically occur in a natural laminar–turbulent transition.

60

• separation induced transition happens at low if the laminar

! Re,

boundary layer separates due to a strong adverse pressure gradient.

When we have a laminar BL that undergoes a very strong recompression we

can have separation. If we are lucky we have a separation bubble, while if we

are not, the separation doesn’t reattach anymore and a huge wake develops.

If we have a separation bubble the flow will reattach but it will be turbulent.

(typical of the suction side because here we have strong pressure gradients).

Some influencing parameters are:

• Re,

• Turbulence,

• Roughness,

• pressure gradient,

• curvature.

Transition due to pressure gradient

To introduce this phenomena let’s write down the BL equations for a 2D

incompressile flow 8 2

@u @v 1 @P @ u

>

> u + v = + µ ,

>

>

< 2

@x @y ⇢ @x @y (6.10)

>

> @u @v

>

>

: + = 0.

@x @y

Boundary conditions are

8

> u = v = 0 f or y = 0,

< (6.11)

>

: u = U f or y = .

1

In the BL @P 1 @P @U 1 (6.12)

!

=0 = U .

1

@y ⇢ @x @x

While at the wall we have 2

@P @ u @U 1 (6.13)

= µ = ⇢ U 1

2

@y @y @x

y=0

61

Separation takes place when @u (6.14)

⌧ = µ

w @y y=0

Figure 6.7: Boundary layer separation.

62

Chapter 7

Advanced measurement

techniques

7.1 LDV, Laser Doppler Velocimetry

The LDV is an indirect non intrusive measurement technique of instantaneous

flow velocity through the detection of particle