ME436 Applied Fluid Mechanics

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Oct 24, 2013 (3 years and 11 months ago)

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ME436 Applied Fluid
Mechanics

Spring 201
2

Lecture 3:
Euler
Turbomachinery Equation

Turbomachinery type


Axial


Mixed


Radial

Velocity Components

r

a

w

inlet

outlet

At any point in the pump, velocity is in


axial (a),


radial (r) and


tangential (w) directions.


Any change in


C
a

=> Axial force; thrust bearing
to the stationary rotor casing


C
r

=> Radial force


C
w

=> angular motion; rotational
effect

Axial


Compact


Same inlet and outlet area


High rpm


Axial Pumps

Axial Pumps

Axial Pumps

Radial


Flow direction changes

Technical Drawings

Meridional Direction


In the flow direction


May be axial or radial or a combination


Definition


U: rotor speed


V: relative velocity


C: absolute velocity



Rotation

Velocity

Triangles

Euler’s Turbomachinery Equation

Assumptions:


Steady flow in a turbomachinery


Neglect turbulence effects, instabilities
etc.


Constant mass flow rate

Front View

inlet

outlet

Mass Balance:

Angular Momentum Balance:

Angular momentum balance

Torque


Power


Per unit mass:


w
r = U (rotor speed) :

Euler’s Turbomachinery
Equation

Velocity Triangles


inlet

outlet

Change of absolute kinetic
energy

Virtual pressure rise

Pump or compressor: c
2
2
may
be important


External effect + Internal diffusion effect

Change of relative kinetic
energy

Change in static pressure, if
the losses are neglected

V2>V1 : nozzle
-
like

V1>V2 : diffuser
-
like

Centrifugal effect

(energy produced by impeller)

ME436 Applied Fluid
Mechanics

Spring 201
2

Lecture
4
: Centrifugal
Turbomachinery with an
incompressible working fluid
(Pumps and Fans)

PUMP

FAN

Working fluid

Liquid (eg. Water)

Gas (eg. Air)

Material

Eg. Steel, titanium


Erosion due to
impurities

or cavitation
is a major issue

Eg. Plastik

Sealing

Important
. Leakage
may cause problems

Not important. Since

sealing increases cost,
usually avoided.

Cost

higher

Low

Pumps and fans

Hydraulic Pumps

Side and front views

tongue

Volute,
casing,
housing

Blade

Technical Drawings

Open
impeller

Closed
impeller

Open impeller

Blade


Length


Thickness or width


Breadth


Inlet angle


Outlet angle


Leading edge


Trailing edge


Tip


Blade channel


Pressure side


Suction side


Ideal Impeller


Infinitely many blades with zero
thickness


This way fluid follows the geometry of
the blades perfectly,


And also blades causes no occlusion
in the flow geometry.

Effect of the number of blades


As number of blades increases impeller can guide the fluid
better, i.e. Fluid velocity vector and blade angle will be the
same. Thus, all the work from the shaft can be transferred to
the fluid => High pressure increase.


As number of blades increases, the area that the blades
occupy due to their thickness increases. At the same flow rate
a higher fluid velocity occurs for the impeller with more blades.
Viscous losses rise with the square of the fluid velocity. =>
Large losses.


A comprimise between the two results has to be found.

Open vs. Closed Impellers

Open vs. Closed Impellers

CLOSED IMPELLER

OPEN IMPELLER

Can compensate for shaft thermal growth, but if there is too
much axial growth the vanes may not line up exactly with the
discharge nozzle.

The impeller to volute or back plate clearance must be adjusted
when the pump is at operating temperature and all axial
thermal growth has occurred



Good for volatile and explosive fluids because the close
clearance wear rings are the parts that will contact if the shaft
displaces from its centerline

You would have to use soft, non
-
sparking materials for the
impeller and that is not very practical.



The impeller is initially very efficient, but looses its efficiency as
the wear ring clearance increases

Efficiency can be maintained through impeller clearance
adjustment.



No impeller adjustment is possible. Once the wear ring
clearances doubles they have to be replaced. This means the
pump had to be disassembled just to check the status of the
wear rings.

The impeller can be adjusted to compensate for wear and stay
close to its best efficiency. No pump disassembly is necessary.

The impeller can clog if you pump solids or "stringy material".
It's difficult to clean out these solids from between the shrouds
and vanes.

The open impeller is less likely to clog with solids, but if it does,
it is easy to clean.



The impeller is difficult to cast because the internal parts are
hidden and hard to inspect for flaws

The open impeller has all the parts visible, so it's easy to
inspect for wear or damage



The closed impeller is a more complicated and expensive
design not only because of the impeller, but the additional wear
rings are needed.

The pump is less costly to build with a simple open impeller
design.



The impeller is difficult to modify to improve its performance.

The vanes can easily be cut or filed to increase the capacity.



The specific speed choices (the shape of the impeller) are
limited

You have a greater range of specific speed choices.

Examples


Determine the work required for a
pump with no pre
-
whirl at the inlet?





For the best efficiency: Cw1=0

Example

at the inlet and outlet

Radial, Backward, Forward

Impeller Blade Shape


Value of C
w

=> Value of energy transfer

Degree of Reaction

For a radial turbomachinery:

Degree of Reaction

backward

radial

forward


for a given impeller tip speed, forward
-
curved vanes
have a highvalue of energy transfer.


Therefore, it is desirable to design for high values of
b
2

(over 90
0
),


but the velocity diagrams show that this also leads
to a very high value of C
2
.


High kinetic energy is seldom required, and its
reduction to static pressure by diffusion in a fixed
casing is difficult to perform in a reasonable sized
casing.


However, radial vanes (b
2

= 90
0
) have some
particular advantages for very highspeed
compressors where the highest possible pressure is
required.


Radial vanes are relatively easy to manufacture and
introduce no complex bending stresses.

Characteristic Curve


W=C
w2

U
2



Forward:


Cr2


Cw2


W



Radial:


Cr2


Cw2


W




Backward:


Cr2


Cw2


W



The effect on fan performance is shown in the different performace curves.

The forward curved type


run slower than the other types,


are the quietest in operation.


use higher horsepower at low resistance, and


the least amount of horsepower at the higher pressures and low flows.



The backward curved type of centrifugal fan performance characteristic curve
shows that


for increasing delivery volume, they startout at a lower horsepower,


rise to a peak on the horsepower curve near the point of highest efficiency on the
fan performance curve and


then drop off again.




Effect of blade thickness

t

Obstruction of the fow area

Slip

Stodola

Stanitz

c.a. 0.9;
evenif the
fluid is ideal!

Slip Factor


Losses


Slip



Viscous Losses


Losses in pipes


Mechanical Losses



Volumetric Losses (Leakage)

Efficiency

Efficiency

example

Volute

Vaneless Diffuser


A simple annular passage


Suited for a wide range of operations

Assuming
m
=0 ; angular momentum is constant:

Usually C
w

>> C
r
; thus

If
r
=const. => rC
r
=const.

Thus, the flow maintains a
constant inclination to radial lines,
the flow path traces a logarithmic
spiral.

for an incremental radius dr, the
fluid moves through angle d
q

Vaned Diffuser


Smaller size


KE transferred to P at a higher rate


More efficient


More friction


Any deviation from the design point =>
changes in velocity triangles =>
decrease in efficiency

Vaned Diffuser

Inlet vane of a radial turbine

Stator


Rotor

Cavitation


Local drops in pressure => cavitation



Suction Head:
hs = ps / γ + vs2 / 2 g



Liquids vapor head:
hv = pv / γ



NPSH:
NPSH = ps / γ + vs2 / 2 g
-

pv /
γ


Available NPSH:


NPSH
a

= patm / γ
-

he
-

hl
-

pv / γ



Required NPSH:



Thermodynamics of Cavitation

P

v

Bubble Collapse


In bulk flow


Near the wall

Cavitation Damages


Local pitting of the impeller and erosion of
the metal surface


Serious damage can occur from this
prolonged cavitation erosion.


Vibration of machine and noise is also
generated in the form of sharp cracking
sounds when cavitation takes place.


A drop in efficiency due to vapor formation,
which reduces the effective flow areas.