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Computational Fluid Dynamics (April 2010)

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Total No. of Questions : 12] [Total No. of Pages : 3 [3764]-145 P1315 B.E. (Mech.) COMPUTATIONAL FLUID DYNAMICS (2003 Course) Time : 3 Hours] [Max. Marks : 100 Instructions to candidates : 1) Answers to the two sections should be written in separate books. 2) Neat diagrams must be drawn wherever necessary. 3) Figures to the right indicate full marks. 4) Use of logarithmic tables, slide rule, Mollier charts, electronic pocket calculator and steam tables is allowed. 5) Assume suitable data, if necessary. SECTION - I Unit - I Q1) a) b) Derive the continuity equation in differential form for in compressible flow. [10] Define & develop expression for substantial derivative. [6] OR Q2) Derive an expression for energy equation for infinitesimally small, moving fluid element. [16] Unit - II Q3) List the full procedure for the solution of Blasius equation using shooting method. [16] OR Q4) How characteristics lines are related to Courant number from stability view? Explain. [16] Unit - III Q5) a) Derive 2u ui + 3, j + 4 ui + 2, j 5 ui+ 1, j + 2 ui, j + O 2 . 2 2 = ( ) i, j ( ) [10] P.T.O. b) Write short note on: i) [8] Consistency. ii) Stability. iii) Convergence. OR Q6) a) Derive the forward and central difference, approximations to the first derivative, along with the leading error term. [8] b) Derive the stability criterion (CFL conditions) for the first order wave equation. [10] SECTION - II Unit - IV Q7) For the following equation: = t [16] 2 2 a) Obtain discretised form of finite difference quotient. b) Using explicit method, write algebraic equations for 4 4 grid. c) Explain any numerical method to obtain solution for temperatures. OR Q8) Explain following with merits and demerits. a) Explicit method. b) c) [16] Implicit method. Semi-implicit method. Unit - V Q9) Describe the MacCormak s technique for evaluatory the density at time step. (t + t ) . [16] OR Q10)a) Obtain following relation for nozzle flow- ( ) t b) [3764]-145 + ( V ) x [8] = 0. For the quasi one dimensional, steady, isentropic flow through a converging diverging nozzle, write down the governing equations. [8] 2 Unit - VI Q11)Outline the Mac algorithm and show how the incompressible flow field is obtained. [18] OR Q12)a) b) Describe the important features of finite volume method. Write down step by step procedure for SIMPLE algorithm. Y [3764]-145 3 [8] [10]

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Additional Info : 2003 Course
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