Fluid Mechanics for Power Generation by nikeborome


									             Fluids in Motion
                     P M V Subbarao
                   Associate Professor
             Mechanical Engineering Department
                         IIT Delhi

An Unique Option for Many Power Generation Devices..
              Velocity and Flow Visualization
• Primary dependent variable is fluid
  velocity vector V = V ( r ); where r is
  the position vector.
• If V is known then pressure and
  forces can be determined.
• Consideration of the velocity field
  alone is referred to as flow field
  kinematics in distinction from flow
  field dynamics (force considerations).
• Fluid mechanics and especially flow
  kinematics is a geometric subject and
  if one has a good understanding of
  the flow geometry then one knows a
  great deal about the solution to a fluid
  mechanics problem.
Flow Past A Turbine Blade

                          Particle p at time t1
  Particle p at time t2
                                        Uniform Flow
    Velocity: Lagrangian and Eulerian Viewpoints

There are two approaches to analyzing the velocity field:
Lagrangian and Eulerian

Lagrangian: keep track of individual fluids particles.

Apply Newton’s second law for each individual particle!

 Say particle p is at position r1(t1) and at position r2(t2) then,
Of course the motion of one particle is insufficient to describe
the flow field.
So the motion of all particles must be considered
simultaneously which would be a very difficult task.
Also, spatial gradients are not given directly.
Thus, the Lagrangian approach is only used in special
                     Eularian Approach

Eulerian: focus attention on a fixed point in space.

 In general,

 where, u = u(x,y,z,t), v = v(x,y,z,t), w = w(x,y,z,t)
This approach is by far the most useful since we are
usually interested in the flow field in some region
and not the history of individual particles.

This is similar to description of A Control Volume. We need to apply newton
Second law to a Control Volume.
                     Eularian Velocity

• Velocity vector can be expressed in any coordinate
  system; e.g., polar or spherical coordinates.
• Recall that such coordinates are called orthogonal
  curvilinear coordinates.
• The coordinate system is selected such that it is
  convenient for describing the problem at hand (boundary
  geometry or streamlines).
Fluid Dynamics of Coal Preparation & Supply

                  P M V Subbarao
               Associate Professor
          Mechanical Engineering Department
                      I I T Delhi

 Aerodynamics a means of Transportation ……
Major Components of Coal Fired Steam
Schematic of typical coal pulverized system

                             A Inlet Duct;
                             B Bowl Orifice;
                             C Grinding Mill;
                             D Transfer Duct to Exhauster;
                             E Fan Exit Duct.
Velocity through various regions of the mill during
                steady operation
             Cyclone-type classifier.

Axial and
radial gas
                            Centrifugal Classifiers

•   The same principles that govern the
    design of gas-solid separators, e.g.
    cyclones, apply to the design of
•   Solid separator types have been used
    preferentially as classifiers in mill
•   centrifugal cyclone-type and gas path
    deflection, or
•   louver-type classifiers.
•   The distributions of the radial and axial
    gas velocity in an experimental cyclone
    precipitator are shown in Figures.
•   The flow pattern is further characterized
    by theoretical distributions of the
    tangential velocity and pressure, the
    paths of elements of fluid per unit time,
    and by the streamlines in the exit tube
    of the cyclone.
       Particle Size Distribution--Pulverized-Coal
• The pulverized-coal classifier has
  the task of making a clean cut in
  the pulverized-coal size
• returning the oversize particles to
  the mill for further grinding
• but allowing the "ready to burn"
  pulverized coal to be transported
  to the burner.
• The mill's performance, its safety
  and also the efficiency of
  combustion depend on a
  sufficiently selective operation of
  the mill classifier.
                       Mill Pressure Drop
   • The pressure loss coefficients for the pulverized-coal system
     elements are not well established.
   • The load performance is very sensitive to small variations in
     pressure loss coefficient.

Correlation of pressure
loss coefficient with
Reynolds number
through the mill section
of an exhauster-type
Polar Coordinates
     Volume Rate of Flow (flow rate, discharge)
• Cross-sectional area oriented normal to velocity vector (simple case
  where V . A).
Volume Rate of Flow in A General Control Volume

• The acceleration of a fluid particle is the rate of change of its
• In the Lagrangian approach the velocity of a fluid particle is a
  function of time only since we have described its motion in terms of
  its position vector.
 In the Eulerian approach the velocity is a function of both
 space and time; consequently,

x,y,z are f(t) since we must follow the total derivative approach
in evaluating du/dt.
 Similarly for ay & az,

In vector notation this can be written concisely
Basic Control-Volume Approach
                         Control Volume
• In fluid mechanics we are usually interested in a region of space, i.e,
  control volume and not particular systems.
• Therefore, we need to transform GDE’s from a system to a control
• This is accomplished through the use of Reynolds Transport
• Actually derived in thermodynamics for CV forms of continuity and
  1st and 2nd laws.
                 Flowing Fluid Through A CV

• A typical control volume for
  flow in an funnel-shaped pipe
  is bounded by the pipe wall
  and the broken lines.
• At time t0, all the fluid (control
  mass) is inside the control
The fluid that was in the control volume at time t0 will be seen
  at time t0 +dt as:       .
                The control volume at time t0 +dt       .

                 The control mass at time t0 +dt    .

The differences between the fluid (control mass) and the control volume
                          at time t0 +dt    .
• Consider a system and a control volume (C.V.) as follows:
• the system occupies region I and C.V. (region II) at time t0.
• Fluid particles of region – I are trying to enter C.V. (II) at time
  t0 .


  • the same system occupies regions (II+III) at t0 + dt
  • Fluid particles of I will enter CV-II in a time dt.
  •Few more fluid particles which belong to CV – II at t0 will occupy
  III at time t0 + dt.
     The control volume may move as time passes.

                III has left CV at time t0+dt

I is trying to enter CV at time t0

                                         II           At time t0+dt

                            At time t0
           Reynolds' Transport Theorem

• Consider a fluid scalar property b which is the amount of this
  property per unit mass of fluid.
• For example, b might be a thermodynamic property, such as the
  internal energy unit mass, or the electric charge per unit mass
  of fluid.
• The laws of physics are expressed as applying to a fixed mass
  of material.
• But most of the real devices are control volumes.
• The total amount of the property b inside the material volume M
  , designated by B, may be found by integrating the property per
  unit volume, M ,over the material volume :
                   Conservation of B
• total rate of change of any extensive property B of a
  system(C.M.) occupying a control volume C.V. at
  time t is equal to the sum of
• a) the temporal rate of change of B within the C.V.
• b) the net flux of B through the control surface C.S.
  that surrounds the C.V.
• The change of property B of system (C.M.) during Dt

add and subtract
The above mentioned change has occurred over a time dt, therefore
Time averaged change in BCM is
 For and infinitesimal time duration

• The rate of change of property B of the system.
                   Conservation of Mass

 • Let b=1, the B = mass of the system, m.

The rate of change of mass in a control mass should be zero.
              Conservation of Momentum

 • Let b=V, the B = momentum of the system, mV.

The rate of change of momentum for a control mass should be equal
to resultant external force.
                 Conservation of Energy

 • Let b=e, the B = Energy of the system, mV.

The rate of change of energy of a control mass should be equal
to difference of work and heat transfers.
        First Law for A Control Volume

• Conservation of mass:

• Conservation of energy:
Complex Flows in Power Generating Equipment

        Separation, Vortices, and Turbulence
Classification of Flows in Power Generation
Pipe Flows
                          Turbulent Flow
Turbulent flow: fuller profile due to turbulent mixing extremely complex
   fluid motion that defies closed form analysis.
• Turbulent flow is the most important area of power generation fluid
• The most important nondimensional number for describing fluid
   motion is the Reynolds number
• Internal vs. External Flows
• Internal flows = completely wall bounded;
• Usually requires viscous analysis, except
  near entrance.
• External flows = unbounded; i.e., at some
  distance from body or wall flow is uniform.
• External Flow exhibits flow-field regions
  such that both inviscid and viscous
  analysis can be used depending on the
  body shape and Re.

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