Non Isentropic Flow 1
Post on 07-Oct-2015
14 Views
Preview:
DESCRIPTION
Transcript
NON-ISENTROPIC FLOW
2
MENU
1. Non-Isentropic flow : Real flow 2. Shockwave & Expansion waves Normal shockwave Oblique shockwave Prandtl Meyer expansion
3. Duct Flow with Friction without Heat Transfer (Fanno flow)
4. Duct Flow with Heat Transfer and Negligible Friction Force (Reyleigh Flow)
3
Non-Isentropic flow : Real flow
What is Non-Isentropic Flow ?
1. Irreversible ( there is viscous effect) only 2. Non Adiabatic ( There is heat transfer) only 3. Combination of Both
4
Non-Isentropic flow : Real flow
What is Non-Isentropic Flow ?
2 1 = ln0201
ln0201
1. Irreversible ( there is viscous effect) only 01 02 and 01 = 02
2. Non Adiabatic ( There is heat transfer) only 01 02 and 01 = 02
3. Combination of Both 01 02 and 01 02
5
Isentropic flow
Flow through Convergent Divergent Duct
(1) 0= 1 ,
0= 1 ,
0= 1
Flow conditions
Is there an flow through the duct?
How is about the following flow through the duct?
(2) 0= 1 ,
0= 0.9725,
0= 0.7 5
(3) 0= 0.95 ,
0= 0.85,
0= 0.528
(4) 0= 0.95 ,
0= 0.1278,
0= 0.528
6
Isentropic flow
Flow through Convergent Divergent Duct
Mach number and Mass flow rate
7
Non-Isentropic flow
Flow through Convergent Divergent Duct
Normal shock wave
If the pressure at exit , pe is less than p3 and greater than pd so the normal shock wave will appear inside the divergent duct
The shock wave occurs in supersonic speed
The Mach number change from supersonic to subsonic
The flow properties change abruptly
pc
8
Non-Isentropic flow
Normal Shock Normal shockwave : shock waves that
occur in a plane / cross section normal to the direction of flow
A supersonic flow across a normal shock wave becomes subsonic
Total enthalpy remains constant across the shock (conservation energy principle)
01 = 02 = 1 + 1
2
2= 2 +
22
2
Continuity equation
= 11 = 22
Momentum equation
1 2 =
(2 1)
Entropy
2 1 > 0
01 = 02
9
Non-Isentropic flow
Prandtl Relation
Flow relation between before shock wave and after shock wave
2 =
1
1
1 2
5.0
2
*
)1(2
1
MMM
where
22 =
2 + ( 1)12
2 12 ( 1)
()2 = 12
10
Non-Isentropic flow
Prandtl Relation
Flow relation between before shock wave and after shock wave
1 2
22 =
2 + ( 1)12
2 12 ( 1)
What is happen if M1
11
Non-Isentropic flow
Prandtl Relation
Flow relation between before shock wave and after shock wave
2
1
12
Non-Isentropic flow
Static Properties Relation
Properties relation between before shock wave and after shock wave
Pressure
21
=2 1
2 ( 1)
( + 1)
Density
21
=12
=( + 1)1
2
2 + ( 1) 12
Temperature
21
= 2 1
2 1 [2 + 1 12]
( + 1)2 12
What is happen if M1
13
Non-Isentropic flow
14
Non-Isentropic flow
Entropy
2 1
= ln0102
0201
=21
2 ( 1)
( + 1)
1/(1)( + 1)1
2
2 + ( 1) 12
/(1)
2 1
=1
( 1)
2 12
( + 1) 1
+ 1+
( 1)
2 + ( 1) 12
( + 1)12
15
Non-Isentropic flow
Entropy
1
16
Non-Isentropic flow
Air Speed Measurement in Supersonic flight
17
Non-Isentropic flow
1. A blunt nose missile is flying at Mach 2 at standard sea level. Calculate the temperature and pressure at the nose of the missile
18
Non-Isentropic flow
Air Speed Measurement in Supersonic flight
Pressure ratio
1
)1(2
124
1 211
2
1
2
1
2
1
02
M
M
M
p
p
19
Non-Isentropic flow
2. Air with initial stagnation conditions of 700 kPa and 530 K passes through a frictionless CD nozzle Th troat area is 5 cm2 and the exit area is 12.5 cm2. The back pressure is 350 kPa, and a normal shock wave occurs within the diverging section. determine
(a) The Mach number at the exit (b) The change in stagnation pressure (c) Mach number before and after the shock (d) the nozzle area at the point of shock (e) The back pressure if the flow were isentropic throughout
20
Non-Isentropic flow
QUIZ 3 Air with initial stagnation conditions of 700 kPa and 330 K passes
through a CD nozzle at the rate of 1 kg/s. At the exit are of the nozzle the stagnation pressure is 550 kPa and the stream pressure is 550 kPa. The nozzle is insulated and there is no irreversibility except for the occurrence of a shock
(a) What is the nozzle throat area ? (b) What is Mach number before and after the shock ? (c) What is the nozzle area at the point of shock and at the exit (d) What is the stream density at the exit (e) The back pressure if the flow were isentropic throughout
21
Non-Isentropic flow
Rankine-Hugoniot Relations
Combining continuity equation and momentum equation
2 1 = 112 22
2 = 112(1
12)
21
=
+ 1 1
12
1
+ 1 1
12
21
=
+ 1 1
21
1
+ 1 1
21
Non-Isentropic flow
Duct Flow with Heat Transfer (Reyleigh Flow)
Combining continuity, momentum and energy equations
21 00TCqTC pp
Is the following isentropic gas law still valid ?
u1 u2
p1, r1 p2, r2
Fire
q
With Heat Addition
Non-Isentropic flow
Static Properties relations
2
2
2
1
1
2
1
1
M
M
p
p
Pressure Temperature
2
1
2
2
2
2
2
1
1
2
1
1
M
M
M
M
T
T
Density
2
2
1
2
1
2
2
1
2
1
1
M
M
M
M
r
r
Total Properties relations
1
2
12
1
2
22
1
2
2
2
1
10
20
1
1
1
1
M
M
M
M
p
p
Total Pressure Total Temperature
2
12
1
2
22
12
1
2
2
2
2
2
1
10
20
1
1
1
1
M
M
M
M
M
M
T
T
Non-Isentropic flow
Critical Static Properties relations
Pressure Temperature Density
Critical Total Properties relations
Total Pressure Total Temperature
2* 1
1
Mp
p
2
2
2
* 1
1
MM
T
T
r
r
1
112
2*
M
M
1
1
)1(2
1
12
2*
0
0
M
Mp
p
2
22
2
*
0
0 121
1M
M
M
T
T
Non-Isentropic flow
Graph of Total Temperature at Various Mach number
Adding heat will increase flow velocity or Mach number in Subsonic flow and decrease flow velocity of Mach number in Supersonic flow
Extracting heat (cooling of the flow) will decrease flow velocity or Mach number in Subsonic flow and increase flow velocity of Mach number in
Supersonic flow
0.0
1.0
2.0
3.0
0.0 0.5 1.0 1.5
T0/T0*
Mach
2
22
2
*
0
0 121
1M
M
M
T
T
Supersonic
Subsonic
Non-Isentropic flow
Graph of Total Pressure at Various Mach number
Supersonic
Subsonic
1
1
)1(2
1
12
2*
0
0
M
Mp
p
0
1
2
3
0 1 2 3 4 5 6
p0/p0*
Ma
ch
Non-Isentropic flow
Graph of Static Pressure at Various Mach number
0.0
1.0
2.0
3.0
0.0 0.5 1.0 1.5 2.0 2.5 3.0
p/p*
Ma
ch
2* 1
1
Mp
p
For subsonic flow (M1), adding heat will increases pressure
Supersonic
Subsonic
Non-Isentropic flow
Graph of Density at Various Mach number
Supersonic
Subsonic
r
r
1
112
2*
M
M
0.0
1.0
2.0
3.0
0.0 2.0 4.0 6.0 8.0 10.0 12.0
r /r *
Mach
Non-Isentropic flow
Graph of Static Temperature at Various Mach number
2
2
2
* 1
1
MM
T
T
0.0
1.0
2.0
3.0
0.0 0.5 1.0 1.5
T/T*
Mach
0.0
1.0
2.0
3.0
0.0 0.5 1.0 1.5
T/T*
Mach
Supersonic
Subsonic
30
31
Non-Isentropic flow
Rankine-Hugoniot Relations
Combining continuity equation and momentum equation
1 2 + 12 =1
2 (1 2)(
1
2+
1
1)
1 2 + 12 =1
2 (1 2)(2 + 1)
1 2 + 12 =1
2 (1 + 2)(
1
1
1
2)
1 2 + 12 =1
2 (1 + 2)(1 2)
top related