Download GTU BE/B.Tech 2019 Summer 4th Sem New 2140107 Computational Fluid Dynamics I Question Paper

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Subject Code: 2140107

GUJARAT TECHNOLOGICAL UNIVERSITY

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SEMESTER-IV(NEW) — EXAMINATION — SUMMER 2019

Subject Name: Computational Fluid Dynamics I

Time: 02:30 PM TO 05:00 PM

Date: 15/05/2019

Total Marks: 70

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Instructions:

1. Attempt all questions.
2. Make suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.

1. 1. Define CFD? Why is it widely used as a research tool nowadays? (03 MARKS)

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   2. State applications of CFD in various fields. (04 MARKS)
   3. Derive the Continuity equation for any model of finite control volume fixed in space. (07 MARKS)
2. 1. Define Substantial derivative. (03 MARKS)
   2. What are the three approaches used to study fluid flow problems? Explain in detail. (04 MARKS)

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   3. Define Discretization. Explain different discretization methods. (07 MARKS)

   OR

   1. Using Taylor’s series expansion, derive 1^st order forward, backward, and 2^nd order central difference formulas. (03 MARKS)
   2. What is the physical significance of the CFL number? (04 MARKS)
   3. Explain the Eigenvalue method for determining the classification of PDEs. (07 MARKS)

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3. 1. Explain the Finite Volume Method for a 1-D diffusion problem. (07 MARKS)

   OR

   1. Define:
      • Truncation error
      • Round-off error

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      (03 MARKS)
   2. What do you mean by order of accuracy? Explain with an example. (04 MARKS)
   3. Using Taylor’s series expansion derive:
      • Second-order central second difference w.r.t x & y
      • Second-order central second difference for mixed derivative
      (07 MARKS)

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4. 1. What are the factors affecting the grid? (03 MARKS)
   2. Write a note on Structured and Unstructured grids. (04 MARKS)
   3. What is Grid Transformation? Explain with an example. (07 MARKS)

   OR

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   1. What is a Boundary Condition? State its importance in solving fluid flow problems. (03 MARKS)
   2. Explain Predictor and Corrector steps of the Mac-Cormack technique. (04 MARKS)
   3. Derive expressions to transform first derivatives w.r.t x, y & t to ξ & η. (07 MARKS)
5. 1. Truncation error can be reduced by considering more number of grid points. True or False? How? (03 MARKS)

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   2. Discuss: Explicit vs. Implicit approach. (04 MARKS)
   3. Write a short note on the ADI scheme. (07 MARKS)

   OR

   1. What are the three basic principles of fluid dynamics? (03 MARKS)
   2. Write a note on the stretched grid. (04 MARKS)

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   3. Write a note on the Lax-Wendroff technique. (07 MARKS)

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