JNTU
JNTU B.Tech IV COMPUTATIONAL FLUID DYNAMICS Previous Question Paper (January/February - 2023 - R18)
Note: i) Question paper consists of Part A, Part B. ii) Part A is compulsory, which carries 25 marks. In Part A, Answer all questions. iii) In Part B, Answer any one question from each unit. Each question carries 10 marks and may have a, b as sub questions.
Part A
What steps are involved in solving a typical CFD problem?
Answer
- Problem definition and geometry creation.
- Grid generation (discretization).
- Selection of physical models and boundary conditions.
- Numerical solution of governing equations.
- Post-processing and result analysis.
Write down continuity equations for conservative and non-conservative flows. Explain the terms involved in them.
Answer
Conservative form: ∂ρ/∂t + ∇·(ρu) = 0. Non-conservative form: Dρ/Dt + ρ(∇·u) = 0. Here, ρ is density, u is velocity vector, and t is time. The conservative form accounts for mass flux across control volume boundaries, while the non-conservative form follows a fluid particle.
Laplace equation in two dimensions is of elliptic type partial differential equation. Justify the statement.
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Define the terms Truncation Error, Consistency, Order of Approximation.
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Give the mathematical form of linear parabolic differential equation along with physical examples.
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Differentiate between explicit and implicit methods using suitable examples.
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List the various numerical methods to solve hyperbolic problems.
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Obtain the Poisson equation from vorticity and stream function.
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What is meant by staggered grid?
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What is false diffusion?
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Part B
Discuss the relative merits and demerits of finite difference, finite volume, finite element methods with reference to fluid flow problems.
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Derive the integral form of conservation of linear momentum equation for fixed control volume.
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What is meant by the ill-conditioning of a matrix? List the indicators of ill-conditioning for a linear system.
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Use the Gauss – Jordan method to solve [A]{X} = {B}. Also find the inverse of A.
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Obtain a 5-point centre-difference scheme for second order partial derivative of phi with respect to x at a grid point i assuming constant grid space. Also find truncation error.
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Why boundary conditions are needed? List common thermal and flow boundary conditions used in CFD.
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Consider the function f(x) = 2e^x. Using a mesh size delta x = 0.1, determine f(x) at x = 2 with the forward formula equation and the central difference formula and compare the results with the exact value.
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Consider the one-dimensional heat equation, where u is a known function of x and t and a is a constant coefficient. Assume that the computational grid is uniform. Develop a finite difference scheme with explicit scheme of the first order in time and second order in space. Use central differences for the space derivatives. Enumerate the methods to solve these equations.
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Discretize the first order wave using Forward Time Forward Space (FTFS) finite difference scheme. Using von Neumann stability analysis, find the criteria for the stability of the discretized equation.
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Explain the various steps involved in Lax-Wendroff scheme. Draw the schematic diagram of the evolution scheme.
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Bring out the major differences between the incompressible and the compressible Navier-Stokes formulations along with the corresponding equations.
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Derive the expression for vorticity at the wall in terms of stream function. The expression should contain the interior points only. Use no-slip velocity boundary condition at the wall in deriving the expression.
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Explain the Mac-Cormack’s scheme for solving Navier-Stokes equations.
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Give the general form of one-dimensional Burgers’ equation and explain the terms involved in it. Develop finite difference formulation for this equation using up-wind conservative and non-conservative schemes. Why an up-wind conservative is preferred?
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Describe the node-Centered and vertex-centered finite volume schemes with suitable sketches.
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