ME436 Applied Fluid Mechanics

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ME436 Applied Fluid Mechanics

• Spring 2012
• Lecture 3 Euler Turbomachinery Equation

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Turbomachinery type

• Axial
• Mixed
• Radial

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Velocity Components

• At any point in the pump, velocity is in
• axial (a),
• radial (r) and
• tangential (w) directions.
• Any change in
• Ca gt Axial force thrust bearing to the
  stationary rotor casing
• Cr gt Radial force
• Cw gt angular motion rotational effect

inlet
w
a
r
outlet
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Axial

• Compact
• Same inlet and outlet area
• High rpm

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Axial Pumps
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Axial Pumps
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Axial Pumps
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Radial

• Flow direction changes

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Technical Drawings
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Meridional Direction

• In the flow direction
• May be axial or radial or a combination

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Definition

• U rotor speed
• V relative velocity
• C absolute velocity

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VelocityTriangles
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Eulers Turbomachinery Equation

• Assumptions
• Steady flow in a turbomachinery
• Neglect turbulence effects, instabilities etc.
• Constant mass flow rate

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Front View
Mass Balance
Angular Momentum Balance
inlet
outlet
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Angular momentum balance
Torque Power Per unit mass wr U (rotor
speed)
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Eulers Turbomachinery Equation
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Velocity Triangles
outlet
inlet
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Change of absolute kinetic energy Virtual
pressure rise Pump or compressor c22 may be
important
Centrifugal effect (energy produced by impeller)
Change of relative kinetic energy Change in
static pressure, if the losses are
neglected V2gtV1 nozzle-like V1gtV2
diffuser-like
External effect Internal diffusion effect
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ME436 Applied Fluid Mechanics

• Spring 2012
• Lecture 4 Centrifugal Turbomachinery with an
  incompressible working fluid (Pumps and Fans)

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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

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Hydraulic Pumps
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Side and front views
tongue
Volute, casing, housing
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Blade
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Technical Drawings
Closed impeller
Open impeller
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Open impeller
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Blade

• Length
• Thickness or width
• Breadth
• Inlet angle
• Outlet angle
• Leading edge
• Trailing edge
• Tip
• Blade channel
• Pressure side
• Suction side

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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.

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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 gt
  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. gt Large losses.
• A comprimise between the two results has to be
  found.

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Open vs. Closed Impellers
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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.
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Examples

• Determine the work required for a pump with no
  pre-whirl at the inlet?
• For the best efficiency Cw10

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Example
at the inlet and outlet
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Radial, Backward, Forward
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Impeller Blade Shape

• Value of Cw gt Value of energy transfer

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Degree of Reaction
For a radial turbomachinery
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Degree of Reaction
backward
radial
forward
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• 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 b2 (over 900),
• but the velocity diagrams show that this also
  leads to a very high value of C2.
• 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 (b2 900) 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.

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Characteristic Curve

• WCw2 U2
• Forward
• Cr2 ? Cw2 ? W ?
• Radial
• Cr2 ? Cw2 ? W ?
• Backward
• Cr2 ? Cw2 ? W ?

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• 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.

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Effect of blade thickness
Obstruction of the fow area
t
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Slip
c.a. 0.9 evenif the fluid is ideal!
Slip Factor
Stodola
Stanitz
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Losses

• Slip
• Viscous Losses
• Losses in pipes
• Mechanical Losses
• Volumetric Losses (Leakage)

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Efficiency
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Efficiency
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example
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Volute
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Vaneless Diffuser

• A simple annular passage
• Suited for a wide range of operations

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Assuming m0 angular momentum is constant
Usually Cw gtgt Cr thus
If rconst. gt rCrconst.
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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 dq
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Vaned Diffuser

• Smaller size
• KE transferred to P at a higher rate
• More efficient
• More friction
• Any deviation from the design point gt changes in
  velocity triangles gt decrease in efficiency

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Vaned Diffuser
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Inlet vane of a radial turbine
Stator
Rotor
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Cavitation

• Local drops in pressure gt cavitation

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• Suction Head hs ps / ? vs2 / 2 g
• Liquids vapor head hv pv / ?
• NPSH NPSH ps / ? vs2 / 2 g - pv / ?
• Available NPSH
• NPSHa patm / ? - he - hl - pv / ?
• Required NPSH

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Thermodynamics of Cavitation
P
v
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Bubble Collapse

• In bulk flow

• Near the wall

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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.