Assessment of Engine Breathing Capacity
P M V SubbaraoProfessor
Mechanical Engineering Department
Measure of Filling & Emptying Effectiveness….
Stream Tube formed by Flow Through Valves
Equivalent Converging-Diverging Nozzle Configurations:
Mild Separation.Severe Separation
Capacity of A Valve Passage
Mass flow rate through any cross section of area A
)()()( xuxAxm
Invariant non-Uniform Area Flow Paths
0
111
dx
dA
Adx
du
udx
d
dx
uAd
0dx
dp
dx
duu
Conservation of mass
Conservation of Momentum
Conservation of Energy
0dx
duu
dx
dh
Isentropic Flow Through Variable Area
Bell The Cat : A Story for Kids
Engineering Understanding of Accoustics
• The fact that the engineer knows about the chocking is great but it is not enough for today's sophisticated industry.
• A cat is pursuing a mouse and the mouse escape and hide in the hole.
• Suddenly, the mouse hear a barking dog and a cat yelling.
• The mouse go out to investigate, and cat is catching the mouse.
• The mouse ask the cat I thought I hear a dog. • The cat reply, yes you right. • My teacher was right, one language is not enough
today.
Speed of Travel of A Disturbance
• The people had recognized for several hundred years that sound is a variation of pressure.
• The ears sense the variations by frequency and magnitude which are transferred to the brain which translates to voice.
• Thus, it raises the question: what is the speed of the small disturbance travel in a quiet medium.
• This velocity is referred to as the speed of sound.
• Let us generate and analyze a disturbance.
Valve Opening : A Disturbance for Cylinder
Expansion Stroke
Exhaust Stroke
c
High pressure and High temperature fluid in a closed Cylinder closed.
Role of Sonic Velocity in Engineering
0000 &,, hpT Stagnation Conditions.
pmanifold
wc+uc-u
u
Role of Sonic Velocity in Engineering
c
Velocity of sound at any give flow velocity u.
pmanifold
Role of Sonic Velocity in Engineering
Velocity of sound when flow velocity w=c.
wc+cc-c
u=c
c
pmanifold
Exhaust Gas Flow Through VALVES
Choking of Nozzle
Extent of Valve Opening
m
Mach Number
Velocity Sonic
flow ofVelocity NumberMach c
VM
Mach number of a flight
RT
V
c
VM acac
ac
For an ideal and calorically perfect gas:
RTd
dpc
Actual Geometry of Valve Stream Tube
p
dpM
u
du
2
p
dp
M
M
A
dA
11
2
2
p
dpd
1
p
dp
T
dT
1
Minimum Area
Specific Mass flow Rate through Valve PassageMass flow rate per unit area of cross section:
12
1
20
0
)(2
11
)(
)(
xM
xM
T
p
RxA
m
)()()(
xuxxA
m
121
0 1)(1
2
xp
pxM
Conditions for Choked Flow
1
0*
21
pp
121
0 1)(1
2
xp
pxM
p
dp
M
M
A
dA
11
2
2
Isentropic Compressible Flow Through Inlet Valve
2
1
,0
1
,02/1
,0
,0 11
2
inlet
cyl
inlet
cyl
inlet
inletR
p
p
p
p
RT
pAm
12
1
2/12/1
,0
,0
1
2
inlet
inletR
RT
pAm
When the flow is chocked:
AR Instantaneous Reference inlet valve flow area
Resource : The total pressure in the inlet manifold – Cylinder pressure
Isentropic Compressible Flow Through Exhaust Valve
2
1
,0
1
,02/1
,0
,0 11
2
cyl
exhaust
Cyl
exhaust
cyl
cylR
p
p
p
p
RT
pAm
12
1
2/12/1
,0
,0
1
2
cyl
cylR
RT
pAm
When the flow is chocked:
AR Instantaneous Reference exhaust valve flow area
Resource : The total pressure in the cylinder – Static Pressure in Exhaust manifold
Early Choking of Valve Passage
Extent of Valve Opening
m
Frictional Subsonic Flow
Sonic Efects
Effect of Sonic Conditions and Irreversibilities
Isentropic Subsonic Flow
Mas
s of
Fre
sh a
ir :I
ntak
e P
roce
ss
Typical Intake Poppet Valve Geometry
Typical Exhaust Poppet Valve Geometry
Effect of Frictional Losses: Intake System
Effect of Frictional Losses: Exhaust System
Frictional Compressible Flow Through Inlet Valve
• The real gas flow effects are included by means of an experimentally determined discharge coefficient CD.
• The air flow rate is related to the upstream stagnation pressure p0 and stagnation temperature T0, Static pressure just down stream of the valve and a reference area AR.
• AR is a characteristic of the valve design.
12
1
2/12/1 1
2
inlet
inletRD
RT
pACm
2
1
0
1
2/1 11
2
p
p
p
p
RT
pACm cyl
inlet
cyl
inlet
inletRD
When the flow is chocked:
Discharge Coefficient:
idealf
actf
d
m
mC
,
,
The value of CD and the choice of reference area AR are linked together.
The product CD . AR is the effective flow area of the valve assembly, AE.
In general valve head area or port area or curtain area are used as reference areas.
Friction & Turbulent Gas Flow through INLET VALVES
ab c
EXHAUST VALVES