B.E/B.TECH DEGREE EXAMINATION, NOV/DEC 2011

SEVENTH SEMESTER

AERONAUTICAL ENGINEERING

AE2402 --- COMPUTATIONAL FLUID DYNAMICS

(Regulation 2008)

Answer ALL questions

PART-A (10 X 2 = 20 marks)

1. What is the physical significance/meaning of the various terms in conservation form

of momentum equation?

2. What are limitations of panel methods?

3. Define (a) Convergence and (b) Lax equivalence theorem

4. Name the important errors that commonly occur in numerical solution.

5. Transform the steady, incompressible continuity equation from x, y physical plane to

the ξ , η computational plane.

6. What is the importance of CFL condition?

7. Compare implicit and explicit methods.

8. What are the different categories of boundary conditions? Give example for each

category.

9. What is the necessity for staggered grid in control volume method?

10. Define peclet number and state its importance?

PART – B (5X 16 = 80)

11. (a) (i) What is the need for classification of PDE and how do you classify second

order PDE? [8]

(ii) What are the discretization techniques and how do you discretize the

equations for subsonic and supersonic flows? [8]

Or

(b) Write down the procedure for the calculation of pressure coefficient

distribution around a circular cylinder using the source panel technique.

12. (a) (i) How is conformal mapping of a polygon carried out by Schwarz-Christoffel

transformation? [8]

(ii) Illustrate the basic ideas of algebraic transformations of two dimensional,

steady, boundary layer flow over flat plate with suitable transformation

relations. [8]

Or

(b) (i) What is the need for grid generation? Mention the different grid generation

technique and list down their relative merits and demerits. [6]

(ii) Explain how grid generation is achieved by numerical solution of elliptic

Poison‟s equations. [10]

13. (a) (i) What is meant by “wiggles” in the numerical solution? Describe with an

example. [6]

(ii) Consider steady 1-D convection diffusion equation of a property φ

d/dx (ρu φ) = d/dx {Γ d φ/dx}

using control volume approach discretize the above equation and obtain the

neighboring coefficients by

(1) Central difference scheme

(2) Upwind difference scheme [10]

Or

(b) What is meant by hierarchy of boundary layer equations? Derive Zeroth, first

and second order boundary layer equations?

14. (a) Write short notes on the following :

(i) Strong formulation

(ii) Weighted Residual formulation

(iii) Galerkin Formulation

(iv) Weak formulation (4 X 4 = 16)

Or

(b) Consider a cylindrical fin with uniform cross-sectional area A. the base is at a

temperature of 1000C (TB) and the end is insulated. The fin is exposed to an

ambient temperature of 200C. One-dimensional heat transfer in this situation is

governed by

d/dx {kA (dT/dx)}-hP(T-T∞) = 0

where „h‟ is the convective heat transfer coefficient, „P‟ the perimeter, k the

thermal conductivity of the material and T∞ the ambient temperature. Calculate

the temperature distribution along the fin using five equally placed control

volumes. Take hp / (kA)=25m2 (note: kA is constant)

15. (a) (i) Explain explicit Lax-Wendroff scheme of time dependent methods. [8]

(ii) Discuss cell centered formulation in Finite Volume Techniques. [8]

Or

(b) Draw a flow chart and describe SIMPLE algorithm for two-dimensional laminar

steady flow equations in Cartesian co-ordinates.