M E 320 Professor John M. Cimbala Lecture 26
Today, we will:
โข
Discuss dimensional analysis of turbines
โข
Do an example problem โ dimensional analysis with turbines
โข
Discuss piping networks โ how to deal with pipes in series or in parallel
b. Dimensionless parameters in turbine performance
We perform exactly the same dimensional analysis for turbines as we did for pumps. Result:
322 35
Dimensionless Parameters:
Capacity coefficient Head coefficient Power coefficient
QH P
gH bhp
CC C
DD D
ฯฯ ฯฯ
== =
๎
V
Example: Scaling up a hydroturbine
Given: An existing hydroturbine (A): Fluid is water at 20
o
C, D
A
= 1.95 m,
120 rpm,
A
n=
๎
bhp
A
= 220 MW, and
3
335 m /s at 72.4 m
AA
H==
๎
V. We are designing a new
turbine (B) that is geometrically similar, still uses water at 20
o
C, and 120 rpm,
B
n=
๎
but
97.4 m
B
H=. [Dam B has a higher gross head available than Dam A.]
To do: (a) Calculate D
B
and
B
๎
V for operation of turbine B at a homologous point.
(b) Calculate bhp
B
and estimate the turbine efficiency of both turbines.
Solution:
(a) At homologous points, the two turbines are dynamically similar. Apply the affinity laws:
,,
22 22
solve for
AB ABAB
HA HB B A A
AA BB BA BA
gH gH H n H
CC DDD
D
DHnH
ฯ
ฯฯ ฯ
โโ โโ
=== โ = =
โโ โโ
โโ โโ
๎
๎
Plug in numbers:
Similarly,
33
,,
33
AB BBBB
QA QB B A A
AA BB A A A A
DnD
CC
DD DnD
ฯ
ฯฯ ฯ
โโโโ โโโโ
=== โ= =
โโโโ โโโโ
โโ โโ โโ โโ
๎
๎
๎
๎
๎
๎
๎
VV
VV V
Plug in numbers:
(b) Similarly,
35
,,
35 35
AB BBB
PA PB B A
AA A BB B A A A
bhp bhp n D
C C bhp bhp
DD nD
ฯ
ฯฯ ฯฯ ฯ
โโโโโโ
=== โ=
โโโโโโ
โโ โโ โโ
๎
๎
Plug in numbers:
