model to schedule a flow path through a turbo-machine p m v subbarao professor mechanical...
TRANSCRIPT
Model to Schedule A Flow Path through A Turbo-machine
P M V SubbaraoProfessor
Mechanical Engineering Department
Description of the Journey is More Important than the Outcome ….
Complete Fluid Dynamics of Turbo-machinery
1
1
1
1
T
V
p
2
2
2
2
T
V
p
IntakeDelivery
Conservation Laws for a Fluid
..
pVV
t
V
0.
Vt
wqVet
e
.
Conservation of Mass : A Law for Sizing
0.
Vt
Conservation of Mass:
Conservation of Mass for SSSF:
0. V
Integrate from intake to delivery over entire volume :
onstant. CVdVV
Gauss Divergence Theorem
Constantˆ.. AV
dAnVVdV
The entire flow is only due to normal component of the velocity to the flow area :
ConstantflowA
f dAV
Specific Speed of the machine dictates the variation of Flow area
along the fluid path!
Flow Area through A Turbo Machine
Along the flow path, define area averaged mean velocity as:
flow
flow
A
A
f
fmdA
dAV
V
Define area averaged mean density as:
flow
flow
A
A
mdA
dA
path flow alongstation any at
Constant flowfmm AV
222111 AVAV ff
2,2,2,1,1,1, flowfmmflowfmm AVAV
Order of Velocity Vectors
• The real flow through any turbomachine is three dimensional.
• Axial, Radial and Circumferential.
• Axi-symmetry: Inter blade row space.
• Axi-symmetry assumes an average value to represent the state of working fluid in the blade-to-blade plane.
Meridional Plane
The momentum balance is considered in a plane constructed through axis of rotation and radial axis.
This Plane is called Meridional Plane.
1122 rVrVm
Euler Turbo-machinery Equation.
Axial Momentum Equations
Axial Momentum Equation:
A turbomachine cannot tolerate this force doing any work.
The axial force should be completely absorbed by a thrust bearing.
Any remaining traces of this force can cause mechanical or aerodynamic damages.
inaxialoutaxialx VVmF ,,
Concurrent Designs for Minimum Axial Thrust
1122 rVrVmP
Euler Turbo-machinery Power Equation.
WgzV
hgzV
hm
1
2
2
2
22
Conservation of Energy for Turbo-machines
1
2
2
2
1122 22gz
Vhgz
VhrVrV
1111
21
12222
22
2 22gzrV
VhgzrV
Vh
For a Turbomachine:
constatnt2
2
gzrVV
h
gzrVV
hIRothalpy 2:
2
Combination of Euler and SFEE
Over an ideal turbomachine blade along flow directionrothalpy remains constant
Conservation of Rothalpy
• A cornerstone of the analysis of steady, relative flows in rotating systems has, for many years, been the immutable nature of the fluid mechanical property rothalpy.
• "In a moving passage the rothalpy is therefore constant provided:– the flow is steady in the rotating frame;– no friction from the casing;– there is no heat flow to or from the flow.
gzUVV
hIRothalpy blade 2:
2
or
gzUVhIRothalpy blade 0: