A

QUESTION BANK

ON

COMPUTATIONAL FLUID DYNAMICS

(AE-2402)

Prepared for Anna University syllabus (2012)

By

Surendra Bogadi Asst. Professor

Department of Aeronautical Engineering Rajalakshmi Engineering College, Thandalam, Chennai - 602105

PART-A QUESTIONS

(2 MARKS)

1. What are the important applications of CFD in engineering?

2. Distinguish between conservation and non-conservation forms of fluid flow.

3. Write down the conservative form of the continuity equation and explain the terms

involved.

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

of momentum equation?

5. Write down an expression for substantial derivative in Cartesian coordinates.

6. List out advantaged of panel method.

7. Explain the difficulties of evaluating the influences of a panel at its own control point.

8. What are limitations of panel methods?

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

10. Elaborate the basic aspects of the finite difference equations.

11. Write down the significance of Taylor series expansion.

12. Write down the second order central mixed finite difference expression for yx

u

2

13. Explain cell-centered method.

14. Define stability in numerical solution of fluid flow governing equations.

15. Define convergence in numerical solution of fluid flow governing equations.

16. Write down the second order central mixed finite difference expression for 1D heat

conduction equation.

17. Discuss the need of upwind type discretization.

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

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

the ξ , η computational plane.

20. What is the importance of CFL condition?

21. Compare implicit and explicit methods.

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

category.

23. Differentiate between structured and unstructured grids.

24. Differentiate between surface fitted and body fitted coordinate systems.

25. What are the methods available for grid generation?

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

27. List out differences between finite volume and finite difference methods.

28. Define peclet number and state its importance?

29. What is the necessity of strong and weak formulations in boundary value problems?

30. What types of grids are generally used in Finite Volume Method?

PART-B QUESTIONS

(16 MARKS)

1. (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]

2. Write down the elliptic, parabolic and hyperbolic partial differential equations as

applicable to computational fluid dynamics.

3. (a) Derive the continuity equation in differential form for in compressible flow. [10]

(b) Define & develop expression for substantial derivative. [6]

4. Derive the continuity equation for a inviscid flow in partial differential non-

conservation form.

5. Derive the energy equation for a viscous flow in partial differential non-conservation

form.

6. Discuss the source panel method for the flow past an oscillating cylinder.

7. Write down the procedure for the calculation of pressure coefficient distribution

around a circular cylinder using the source panel technique.

8. Discuss the vortex panel method applied to lifting flows over a flat plate.

9. Obtain the 2D compressible continuity equation in transformed coordinates for

transformation )1ln(, yx .

10. (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]

11. Explain the grid generation techniques based on PDE and summarize the advantages

of the elliptic grid generation method.

12. (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. (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]

14. What is meant by hierarchy of boundary layer equations? Derive Zeroth, first and

second order boundary layer equations?

15. Explain the description of Prandtl boundary layer equation and its solution

methodology.

16. Write short notes on the following :

(i) Strong formulation

(ii) Weighted Residual formulation

(iii) Galerkin Formulation

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

17. 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)

18. State and explain the difference between explicit and implicit methods with suitable

examples.

19. How do you determine the accuracy of the discretization process? What are the uses

and difficulties of approximating the derivatives with higher order finite difference

schemes? How do you overcome these difficulties?

20. Study the stability behaviour of second order wave equation by Von-Neuman stability

method.

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

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

22. What are quadrilateral Lagrange elements and isoparametric elements in FEM?

23. Draw a flow chart and describe SIMPLE algorithm for two-dimensional laminar

steady flow equations in Cartesian co-ordinates.

24. Solve the simplified Sturn-Lioville equation:

Fy

x

y

2

2

With boundary conditions y(0) = 0 and 01

x

y

; using Galerkin finite

element method.

25. What is strong formulation? Explain with the help of one dimensional boundary value

problem.

26. Explain Runge-Kutta and multi-stage time stepping.

27. Discuss the properties of discretization schemes and explain upwind discretization

applied to FVM.

28. What is cell centered formulation? Explain with the help of using control volume,

semi discretization equation, .0./ ndsFtUij

29. State and explain the spurious modes for Runge-Kutta cell vertex formulation in

FVM.

30. What is cell centered formulation? Explain with the use of control volume and semi

discretization equation.

31. Derive an expression for energy equation for infinitesimally small, moving fluid

element.

32. List the full procedure for the solution of Blasius equation using shooting method.

33. How characteristics lines are related to Courant number from stability view? Explain.

34. (a) Derive

)(254

2

2

,,1,2,3

,

2

2

xOx

uuuu

x

u jijijiji

ji

[8]

(b) Write short notes on

(i) Consistency (ii) Convergence (iii) Stability [8]

35. (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 Ist order wave equation. [8]

35. For the following equation:

2

2

x

T

t

T

(a) Obtain discretized 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. [16]

36. Explain the following with merits and demerits.

a) Explicit method

b) Implicit method

c) Semi-implicit method [16]

37. Describe the MacCormak‟s technique for evaluating the density at time step (t + Δt).