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a. Commgnton CFD andparalleicomputing.., 0f velocity. for divergence b. Derivean expression

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Explain. a. Whatarephysicalboundaryconditions? form. in thenon-conservative b. DerivePDEof continuifyequation

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: Explainthefeatures of thefollorving grids. grids i) Structured ii) Unstructured b. WhatareadaptiveSrids? , a.

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(J)in thefollorvingform: Derivetheexpression for a Jacobian

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Explainthe grid stretching,with a typicalexample.

a. Whatis iinitevolumescheme? Explain. b, Elp!{n thecell centered technique.

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a. Explainthetime marchingtr:chnique. Expiain. b. Whatis alternating directorimplicit(ADI)technique?

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r N .6 06AE7s2 S e v e n t hS e m e s t e B r . E . n e g r e eE x a m i n a t i o n ,D e c . 0 9 / J a n . l 0 Gomputational

Fluid Dynamics

T i m e :3 h r s , Note: Answ,er on1,FIVE full questions,selectittg

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- ^ a. Explainrhevarious fluidflou,,roo.l^ot '. .': .::b. Dgpv..,e, gxpression.lbr strbstantial.ileriv-ar'ive.'.: ........

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'. .:' : tlro ,-.;'l',';. \ ] n a rr srhe-difference a :what'is r n ed r t f e r e n- clbeiu,een bee t * e c nshock shocK c a p t u r i r and'sirock capturiig r gr r d ' s h o fitting? a fcikr r i n e ? lrrrrrrl b' Whatisthe clifference betueett.onr.n'oii." unLl,ro,',-.o,.rservative lbrmsof equations? (10NIarks)

Apply eigen value method ro a Quasi- linear partial.differenrjalequationfor the mathematical classification ascllipric.parabolic. or hipcrboiic.. (201\larks)

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AvL .333 Meshfor the solutionof Laplaceequation, Boundan'conditjons are shorvnin the Fig4(b), i - e . g : o o n x : 0 a n d, v : 0 , 9 = I o nx = l , g : 0 o n l . (l2l\{arks) )j.: PART _ B

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What are the featuresof the structuredgrids? Explain the algebraicgrid generation.

Transform the follor.ving equation from ph1'sicalp lane in x, ), coordinatesinto a computational planein _{,I coordinates.

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06AE752

seventh semester B.E. DegreeExamination, June/July z0ll Gomputational Fluid Dynamics Time:3 hrs.

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Max.Marks:100

Explainthevariousflow models. b . Explaintheneedfor CFD. Deriveexpression for divergence of velocity.

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PART _ B Explainadaptivegrid generation. Explainalgebraicgrid generation.

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considerfollowing transformation for accomplishing grid stretching: €:x I=/n(y+l). Whatlappensto gov-eming flow equations in boththe physicalandthe computational plane with this abovetransformation? Showthis with z - o coniinultyequationfor-incompressible Briefly explainthe finite volumediscretization.

(20Marks)

what is successive over- relaxationandunder- relaxation? Whatis numericaldissipation anddispersion?

(08Marks) (12Mark)

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06A8752

seventh semester B.8,. f)egree Examination, December 2011

GomPutational Time:3 hrs.

Fluid DYnamics Max.Marks:100

Note: Answer any FIVE fuII questions,selecting from eachpart' ot leastTWO questions

an arbitraryvolttnte, Derive the equationsof conservationof a massand momentum,for (20 Marks) fixed in space,in the integralform. . that reflect different Explain the different mathematical behavior of the equations in CFD (20Marks) cases' behaviorsof a flow field. Give an examplefor the each one'of the

PART _ B in grid generation' of variousco - ordinatesystems Explaintheimportance b. Whatarethe adaptivegrids?Explain' of the grids. properties List the essential

(t0 Marks)

in brief' Whatis a jacobianmatrix?Explainits importance, areneeded?Explainb. Why transformations Transformthe laplaceeguationfrom (x,y)to ((, n) co ordinates'

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(05 Marks) (05 Marlc)

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Whatis a finite volumemethod?Explainandlist the importantfeaturesof an FVN4' fl0 Marks)

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Explain. why is it needbd? andvalidation? b . what is verification 8

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Writeshortnoteion: marchingin CFD Tineandspace of solutionof PDESnumerically schemes b. Variousgeneral in CFD c. Upwindschemes d. Fluxvectorsplitting.

(10Marks)

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0648752

Seventh Semester B.E. Degree Examination, January 2Ol3

Gomputational Fluid Dynamics Time: 3 hrs.

Max. Marks:100 Note: Answer FIVEfull questions, selecting atleast TWO questions from each pait.

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Derive the equation lor substantialdbrivativeoperarorin vector rotation and explain the physical significanceof eachterm. (08Marks) c. List few CFD applicationsis non aerospacefield. (04Marks)

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a. Derive the continuity equation by consideringthe model of finite control volume fixed in space.

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Describethe essentialfeaturesof hyperbolicequationimpact on physical behaviourof CFD --:-(AG Marks) problems. b. For the one dimensionalunsteadythermal conductiontlrough a semi infinite fluid, write the governing equatid-n,Toindaryconditionsand plot the typical solution characteristics.

Consider theinotationa,l, 2 -?.-*g1"tional,steady flowof a compresstofi;ffi#* field is slightlyFert-uffedfromTeesTieu* iit"-flo* over a-Thinpiont":Tind the roots of equationsinvolvedin suchkind of flow problem,usingeigenhetltodl (08 Marks) PART - B 5a.

Explainthe boundaryfittedcoordinate systemfor thedivergentduct. b. Explain the elliptic grid generdtion,with suitableexample. Write short noteson adaptivegrids.

6a.

(06 Marks) (08 Marks) (06 Marks)

For the two dimensionalsteadyflow, continuity equationin Cartesiancoordinatesobtain the transformation from physical plane to computational plane, using direct and inverse transformations. (10Marks) b. Derive the genericform of the governingflow equationwith strong conservativeform in the transformedspacefor two dimensionalunsteadyflow with no sourceterm. (10Marks) I ot2

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l0AE752

SeventhSemesterB.E. DegreeExamination, Dec.2013 /Jan.2ol4

Gomputational Fluid Dynamics Time: 3 hrs. "i

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PART _ A Briefly explainthe needof parallelcomputingandexplainits types.

(06 Marks)

b. Derive an expressionfbr substantialderivativeand explain its physicalmeaning. (06Marks) Explain the varioustypesof fluid flow model with suitablesketchand bring out what type of model leadsto what type of governingequationsforms. (08Marks)

C)

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Max. Marks:100 Note: Answer FIVEfull questions, selecting at least TWO questions from euch part.

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a. What is Euler's form of NS equation?Derive the same for a finite volume Eulerian flow model along x-direction. (06Marks) b. Differentiatebetween: i) Shock fitting and shock capturing methods ii) Neumannand Dirichlet boundaryconditions. (04Marks) c. Representthe generic form of governing equation suitable for CFD in case of steady. inviscid flow, expand the terms involved in it. Also describethe procedure of obtaining primitive variablesof suchgenericform of equations. (t0 Marks)

3

a. Assuming a system of quasi-linearequations,with the help of a characteristiccurve at a point p(x, y), classifythe different typesof PDE's, statingexamplefor eachtype. (t0 Mart<s) b. Determinethe typeol PDE for the followingequation: DuAv^AuAv ^ - ^ =0: ^ - ^ =0 ox oy ay ox

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a. Considera laplaceform of steadyheatconductionequation,and obtain the discretevaluesof temperatureat grid points indicated in the Fig.Qa(a). Assume the grid ds structuredwith Ax: Ay. Use a FDM schemewhich hasa Truncationerror of order O[(Ax)2,(ny)']. v

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Fig.Qa(a) (12Marks) b. What is CFL criterion?Obtain the CFL criterion for a first order wave equation. (08Marks)

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