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