1.UNITGas Dynamics and Jet propulsion

8/18/2019 1.UNITGas Dynamics and Jet propulsion

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Syllabus

SKCET / MECH / GAS DYNAMICS AND JET PROPULSION 1


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UNIT – I

COMPRESSIBLE FLOW- FUNDAMENTALS

SRI KRISHNA COLLEGE OF ENGINEERING AND

TECHNOLOGY

DEPARTMENT OF MECHANICAL ENGINEERING

GAS DYNAMICS AND JET PROPULSION



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Fluid

– Substance capable of owing.

Eg: Liquid, gases and vapourFluid Statics

– The stud of uid at rest.

Fluid !ine"atics

– The stud of uid in "otion withoutconsidering

the pressure.

Int!"u#t$!n

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Fluid dna"ics

– The stud of uid in "otion where

pressure force is considered.

Int!"u#t$!n

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#o"pressible uid dna"ics – $as dna"ics

$as dna"ics – The branch of uid dna"ics whichis concerned

with the causes and e%ect arising fro" the

"otion of co"pressible ow.

Gas Dyna'$#s

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*un"a'+ntal la,sStead ow energ equation – rst law ofther"odna"ics

Entrop relations – second law of ther"odna"ics

#ontinuit equation – law of conservation of "ass

-o"entu" equation – ewton/s second law of"otion

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.as$# D+$n$t$!ns#losed sste"

– There is no "ass transfer between the sste" into the

surroundings but energ 3or4 heat transfer ta+es place.

5pen sste"

– 1oth energ and "ass transfer ta+es place fro" the

sste" into the surroundings.

2solated sste"

– if there is no "ass transfer and energ transfer to

and fro" the sste"

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.as$# D+$n$t$!ns6ropert

– &n observable characteristics of the sste".

2ntensive propert

– The propert which is independent on "ass of the

sste".

Eg. pressure, te"perature, densit, viscosit

E0tensive propert– The propert which depends on the "ass of the sste".

Eg. 7olu"e, enthalp, wor+ done



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.as$# D+$n$t$!ns6ressure – the nor"al force per unit area. S2 unit 8"9.

8"9 ; 6ascal ;6a

bar ; @ " of water colu"n

Te"perature – when two sste" are in contact with each other

and are in ther"al equilibriu", the propert co""on to both the

sste"s having the sa"e value is called te"perature.

o# ; A9?> !



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.as$# D+$n$t$!nsBensit – the "ass of the substance per unitvolu"e.

' S2 unit !g8">.

Cor+ – 2t is an energ which is the product offorce and the

distance travelled in the direction of force.

' it is path function not a propert.

' (nit ." 3or4 *oule.

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.as$# D+$n$t$!nsSpecic heat – the a"ount of heat that required to risethe

te"perature of unit "ass of substance b one degree.

Specic heat capacit at constant volu"e 3#v4

' if te"perature rise occurs at constant volu"e

Specic heat capacit at constant pressure3#p4

' if te"perature rise occurs at constant pressure

The characteristic gas constant

D ; #p ' #v

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.as$# D+$n$t$!ns The characteristic gas constant

Bivide throughout b #p

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.as$# D+$n$t$!ns&diabatic process

– Buring a process if there is no heat transferbetween the

sste" and the surroundings.

– Dotodna"ic "achines 3or4 turbo "achinesassu"ed to

followed onl adiabatic process.

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.as$# D+$n$t$!ns2sentropic process – in which there is no change inentrop, such

process is a reversible adiabatic process orisentropic process.

This is governed b the following relations:

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Stead and unstead ow (nifor" and non'unifor" ow

La"inar and turbulent ow

#o"pressible and inco"pressible ow Dotational and irroational ow

5ne di"ensional, two di"ensional and threedi"ensional

ow

Ty3+s ! *l!,



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Steady flow is that type of flow, in which the fluid

characteristics like velocity, pressure and density at

a point do not change with time.

Unsteady flow is that type of flow, in which the fluid

characteristics like velocity, pressure and density at a

point changes with respect to time.

St+a"y 4 Unst+a"y l!,



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Uniform flow, in which velocity of fluid particles at all

sections are equal.

Non – uniform flow, in which velocity of fluid particles

at all sections are not equal.

Un$!' 4 N!n 5 Un$!'



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La'$na 4 Tubul+nt *l!, Laminar flow or stream line flow, the fluid moves in

layers and each particle follows a smooth and

continuous path.

Turulent flow, the fluid particles move in very

irregular path



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C!'3+ss$bl+ 4 In#!'3+ss$bl+ *l!,

!ompressile flow in which density of fluid changes

from point to point "#ases, $apours%. "&'(.)%

*ncompressile flow in which density of fluid is

constant "Liquids%. "&+(.)%

&ach Numer -low velocity$elocity of sound



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R!tat$!nal 4 I!tat$!nal l!, /otational flow in which the fluid particles flowing

along stream lines and also rotate aout their own

a0is.

*rrotational flow in which the fluid particles flowing

along stream lines ut don1t rotate aout their own

a0is "without turulences, whirlpool, vortices, etc.,%.

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234 flow, in which the flow parameter such as velocity is a

function of time and one space co3ordinate "0% only "stream

lines 3 straight line%.

534 flow, in which the flow parameter such as velocity is a

function of time and two space co3ordinate "0, y% only

)34 flow, in which the flow parameter such as velocity is a

function of time and three mutual perpendicular a0is "0, y,

6% only.

15D6 25D 4 %5D *l!,

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The first law of thermodynamics state that, when a system e0ecute a

cyclic process, the algeraic sum of work transfer is proportional to

the algeraic sum of heat transfer.

En+7y +8uat$!n

7hen heat and work terms are e0pressed in the same units

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The quantities 8d91 and 8d71 will follow the path function, ut the quantity

"d93d7% does not depands on the path of the process. Therefore the

change in quantity "d93d7% is a property called :nergy ":%.

En+7y +8uat$!n

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En+7y +8uat$!n

Sustituting eqn. "iii% in "i%



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:nergy equation for a flow processflowprocess?

:g<

i. -low through no66les, diffusers and duct etc.,

ii.:0pansion of steam and gases in turines

iii.!ompression of air and gases in turo compressor etc.,

*n such flow processes the work term "7% includes flow work also

7here, 7s Shaft work @ "p5v53p2v2% -low work



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:nergy equation for a flow process


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:nergy equation for a flow process<

7here,

:quation "vii% is a steady flow energy equation per unit Cg

mass.

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=diaatic energy equation<

!ompared to other quantities, the change in elevation g"D53D2% is

negligile in flow prolems of gases and vapours.

*n a reversile adiaatic process the heat transfer 8q1 is negligily

small and can e ignored.

:0pansion of gases and vapours in no66les and diffusers are

e0ample for this process.

-or this process eqn."vii% reduced to



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=diaatic energy transfer and energy

transformation< =diaatic energy transfer<

shaft work will present in an adiaatic energy transfer process

:0ample<

i. :0pansion of gases in turines

ii.!ompression of gases in compressor

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=diaatic energy transfer and energy

transformation<

=diaatic energy transformation<

*n adiaatic energy transformation process the shaft work is 6ero.

:0ample<

i. :0pansion of gases in no66le

ii.!ompression of gases in diffuser

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Stagnation state and stagnation

properties


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Stagnation enthalpy EhoF<

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Stagnation temperature EToF<Stagnation temperature of a gas or vapour is defined as temperature

when it is adiaatically decelerated to 6ero velocity at 6ero elevation.

for perfect gas, eqn "0i% can e written as,

4ivide the equation throughout y !p

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2

0

2 p

cT T

C

∴ = +


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Stagnation temperature EToF<



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Stagnation pressureEGoF<Stagnation temperature is the pressure of gas when it is adiaatically

decelerated to 6ero velocity at 6ero elevation.

for perfect gas, the adiaatic reaction is

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Stagnation velocity of sound EaoF<we know that the acoustic velocity of sound

-or the given value of stagnation temperature the stagnation velocity of

sound



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Stagnation density EHoF<

-rom adiaatic relation

-or the given value of stagnation pressure and temperature the stagnation

density is given y

SKCET / MECH / GAS DYNAMICS AND JET PROPULSION &1

( ) ( ) ( )11

1120 0

11

2

T M

T

γ γ γ ρ

ρ

−− − = = + ÷ ÷


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$arious regions of flow<



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SKCET / MECH / GAS DYNAMICS AND JET PROPULSION &&

The adiaatic energy equation for a perfect gas is derived in terms of fluid

velocity "c% and sound velocity "a%.

-orm adiaatic energy equation

7e know that,

;y sustitution this in equation "i%

=t T(@ h(@ a( and ccma0


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SKCET / MECH / GAS DYNAMICS AND JET PROPULSION &(

Therefore equation "ii% ecomes

=t c(@ aao

Therefore, form equation "iii%


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=coustic velocity "or%

Sound velocity<

SKCET / MECH / GAS DYNAMICS AND JET PROPULSION &-

&oving 7ave Stationary 7ave

7ave front – a plane cross

which pressure and

density changes suddenly

and there will ediscontinuity in pressure,

temperature and density.


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=coustic velocity "or% Sound velocity<


*f small impulse is given to the piston the gas immediately adKacent to

the piston will e0perience a slight rise in pressure "dp% or in other word

it is compressed.

The change in "dH% takes place ecause the gas is compressile and

therefore, there is lapse of time etween the motion of the piston and

the time this is oserved at the far end of the tue.

Thus it will take certain time to reach far end of the tue or in other

words there is finite velocity of propagation which is acoustic velocity.


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*n this case the segment gas at pressure p on the right side moving

with velocity 8a1 toward left and thus its pressure is raised to "pBdp%

and its velocity lowered to "a3dc%.

This ecause of the velocity of piston acts opposite to the movement

of gas.

;efore deriving following assumption made<

2. The fluid velocity is assumed to e acoustic velocity.

5. There is no heat transfer in the pipe and the flow is through aconstant area pipe.

). The change across an infinitesimal pressure wave can e assumed

as reversile adiaatic "or% isentropic.


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SKCET / MECH / GAS DYNAMICS AND JET PROPULSION (1

Gressure force *mpulse force

-rom continuity equation for the two sides of the wave


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The product of dH dc is very small, hence it is ignored. The eqn "ii%

ecomes

Sustituting this in equation "i%, we get

-or an isentropic flow,


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SKCET / MECH / GAS DYNAMICS AND JET PROPULSION (%

4ifferentiating aove equation


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SKCET / MECH / GAS DYNAMICS AND JET PROPULSION (&

Sustitution this in equation "iii%

The velocity of sound in normal amient temperature is aout )( ms.


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&ach angle and &ach cone

SKCET / MECH / GAS DYNAMICS AND JET PROPULSION ()

a% *ncompressile flow

% Susonic flow

c% Sonic flow

d% Supersonic flow


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&ach angle

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&ach angle


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&a0imum velocity of fluid, !ma0


-rom adiaatic energy equation

*t has two components one is enthalpy "h% and the another is kinetic

energy . 7hen the static enthalpy is 6ero "or% when the entire energy is

mad up of kinetic energy only the aove equation ecomes

and


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&a0imum velocity of fluid, !ma0


( ) ( )

2 22 2

max

1 2 2 1

oo

c aa ch

γ γ

= + = = − −


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!rocco Numer, E!r F

!rocco numer is a non3dimensional fluid velocity which is defined as

the ratio of fluid velocity to its ma0imum fluid velocity.

1.UNITGas Dynamics and Jet propulsion

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