8/18/2019 MME-504RR

1/2

Roll

No.

Total

No.

Total

No.

of

pages

:

02

of

Questions

08

M.Tech.(ME)

Sem._2)

COMPUTATIONAL

FLUID

DYNAMICS

I*

Subject

Code

MME_504

,;%J;

Paper

D

:

[E0429]

-

* ' , , . ' ' '

Time

3

Hrs.

Mil.

M*r.,

:

toO

*

:F '

INSTRUCTION

TO

CANDIDATES

:

,...'*.. ;

{ -,.x'

l. Attempt any FIVE questions. ,*' *1. :..t' l

2,

Atl

questions

arry

EeUAL

marks.

q

i

,

ir,a,*

.r,r.c.

*'lf'ul'-

1.

a)

what

are

different

gover4iiiq€{uations

used

or

solving

the

fluid

mechanics

nd

heat

ra rpre;yfr6blems?

rite

these

equations

n

cartesian

co-ordinates'.

lso.',

rite

different

oundary

onditions

used

or

solving

these

Boverning

grU$giohs.

u;

Exnlaiffi

t4d*fiT

turbulenceodelingndealing ithcFDproblems.

what

are'various

urburence

oders

sed

n

cFD

problems?

-

q'

d i-

2'

^)

)ffiW}.

different

methods

sed

or

solving

engineering

robrems?

;q$ry

their

rerative

merits

and

demerits.

what

are

differenr

steps

*{\Y lved

in

theoretical

modeling

f

a

physical

problem?

^\a

\#b)

Express

he

complete

Navier-stokes

quations

nd

derive

Bernoulli,s

equation

rom

t

explaining

he

assumptions

ade

n

the

process.

3

a)

Derive

he

finite

difference

expressionsor a secondorderderivative

with

forward,

backward

nd

central

difference

pproximations.

b)

Describe

n

brief

at Ieast

wo

techniques

hat

are

used

o

accelerate

the

convergence

f

the

solution

of

unsteady

uler's

equation

o

steady

state.

4

a)

Distinguish

etween

iscretization

nd

ound-off

errors.

compare

hem

with

suitable

examples.

lA-1211366

8/18/2019 MME-504RR

2/2

Describe

riefly

:

consistency,

onvergence

nd

stability

of

a

numerical

solution.

Explain

the

finite

difference

method

or

any

governing

equation

with

suitable

Cs.

5'

a)

using

Taylors

xpansion

erify

hat

he

cell

centred,fiqlteftgrume

discretization

ives

a

second

rder

accurate

artial

d.pti$A*,ivb

t o

::::::1T ::^:'r

a

se^cond

:'.d.'

ac

urate

;-#

b)

c)

point

in

2D

space

or

uniform

grid.

a'T

a2T

---:-

f

0x'

Ar'

t a

.,

-l.J'

i

+

O(h'?)

f lain

why,

n practice,

t

is

necessary

o

solve

or

the

rection

and

not

ust

the

velocity

corrections

n

order

pressure

to

satisfy

c)

8.

a)

b)

mass

conservation.

Describe

he

Tri-Diagonal

Matrix

Algorithm

for

solution

of

set

of

linear

algebraic

quations.

Describe

he

SIMpLE

pressure-correction

method

or

the

solution

of

coupled

mass

and

momentum

quations.

Explain,

briefly,

he

origin

of

the

odd-even

ecoupring

robrem

n

the

discrete

pressure

ield

that

may

occur

with

co-rocated

torage

f

velocity

and pressure

n

a

finite_volume

mesh.

b)

Show

that

forward

time

and

c

niii'

rr'$

wave

q

arion

es

rts

n

un,tuf

l:i:T:

:l,ff.ffi$.*,fi

':

Hl;

riterion

and

comment. ,. ,,d, * .

'

6'

a)

Verify

he

following

differen..

uppr&irJpo;

fo1

se

n

rwo

dimensions

at

the

point

(i,

j).

Assume

Ax

: 11y

ftd

l'*&r'\,

b)

Explain

he

at,fffi;C'1hods

with

suitable

xample

nd

give

heir

merits

nd

dgffi1f

:

r

)

Expricit

ethod

)

Irnpricii

ethod

)

semi_

impticiffirhffip

 

f rw

-/

L\ttpltvtl

rusrrlo(l

J/

Iteml.

rmpucrffi

7

r,

:ffi ,

trs

main

principres

f pressure-co*ection

methods

or

the

.

ffiFl

solution

f

the

ncompressible

luid-flow

quations.

lA-1211366