Biomedical Engineering Reference
In-Depth Information
(4)
k
k
U
U
U
U
U
2
(
U
k
)
(
eff
)
i
i
j
j
j
(
)
(
k
)
j
t
t
t
x
x
x
x
x
x
3
x
x
j
j
k
j
j
j
i
j
j
And,
eff
(
U
)
(
)
j
t
x
x
x
j
j
j
U
U
U
(5)
U
U
2
j
j
j
i
i
(
C
(
(
)
(
k
))
C
)
1
t
t
2
k
x
x
x
3
x
x
j
j
i
j
j
where ζ
k
and ζ
ε
are k-ε turbulence model constants and are equal to 1.0 and 1.3
respectively, and C
ε1
and C
ε2
are equal to 1.45 and 1.92, respectively:
Energy Equation:
T
(
)
(
U
h
)
X
(6)
j
tot
j
S
E
X
X
j
j
where h
tot
is defined as the specific total enthalpy, which for the general case
of variable properties is given in terms of the specific static enthalpy, h, by:
1
U
;
(7)
h
h
(
p
,
T
)
h
tot
h
2
2
And S
E
is the source term, which represents the work done by the viscous
and pressure forces. The equation of state for an ideal gas is given as:
(8)
p
RT
where T is the temperature of the fluid and R is the gas constant.
Pressure Coefficient
The parameter ―pressure coefficient‖ was defined to determine the
pressure variation on the rotor,
P
P
Pressure coefficient =
(9)
max
P
min
inlet
