JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III COMPUTATIONAL AERODYNAMICS Previous Question Paper (April - 2018 - R15)
Note: This question paper contains two parts A and B. Part A is compulsory which carries 25 marks. Answer all questions in Part A. Part B consists of 5 Units. Answer any one full question from each unit. Each question carries 10 marks and may have a, b, c as sub questions.
PART - A
What are some of the advantages of using CFD?
Answer
Computational Fluid Dynamics (CFD) offers several significant advantages over traditional experimental methods. First, it provides a comprehensive flow field visualization, allowing for the detailed analysis of velocity, pressure, and temperature distributions at every point in the domain, which is often impossible to measure physically. Second, it is highly cost-effective and time-efficient, as it enables rapid iterative design changes and parametric studies without the need for expensive wind tunnel models or complex test rigs.
Explain the physical meaning of Divergence of Velocity.
Answer
The divergence of velocity, denoted as ∇ · V, represents the time rate of change of the volume of a fluid element per unit volume as it moves with the flow. Physically, it measures the net volumetric expansion or contraction of a fluid element at a specific point.
In the context of fluid dynamics, if ∇ · V > 0, the fluid element is expanding (diverging); if ∇ · V < 0, the element is contracting (converging). For an incompressible flow, the divergence of velocity is zero, meaning the volume of the fluid element remains constant as it moves through the flow field.
Define well-posed problems.
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Explain with a sketch the concepts of domain of dependence and range of influence for hyperbolic partial differential equations.
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Define consistency and stability relating to numerical solution of CFD problems
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Explain stretched and adaptive grids used in CFD
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Is the finite-volume method more suited for structured or for unstructured mesh geometries? Why?
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What are the constraints to be satisfied on the choice of sub-domains for a consistent finite volume method?
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What is the difference between a direct method and an iterative method for solving the discretized equations in CFD?
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Explain the difference between SIMPLE and SIMPLEC pressure correction algorithms.
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PART - B
Derive the momentum equation of fluid mechanics in component form assuming a flow model of infinitesimally small fluid element moving with the flow
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Discuss the relative merits and demerits of theoretical fluid dynamics, experimental fluid dynamics and computational fluid dynamics.
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Explain the importance of conservation form of governing equations in computational fluid dynamics.
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Explain the general method of classification of a system of quasi-linear partial differential equations using Cramer’s rule
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Classify the following equations (elliptic / parabolic/ hyperbolic):
b) Velocity potential equation: (1-M²) ∂²φ/∂x² + ∂²φ/∂y² = 0 for Mach number M>0, M=0 and M<0
c) Second-order wave equation: ∂²u/∂t² = c² ∂²u/∂x²
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Explain Von Neumann stability analysis method using the example of one-dimensional heat conduction equation (∂T/∂t) = α (∂²T/∂x²), where ‘T’ is temperature and ‘α’ is diffusivity.
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What are structured grids? Describe different types of structured grids with sketches.
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Describe the basic procedure of finite volume discretization and discuss the interesting features which distinguish the interpretation of finite volume methods from the finite difference approach.
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Explain the practical implementation of two-dimensional finite volume method on a Cartesian grid.
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Describe alternating-direction-implicit scheme (ADI) using unsteady, two-dimensional heat conduction equation.
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Explain relaxation technique to solve inviscid, incompressible, two-dimensional irrotational flow governed by Laplace equation for velocity potential ∂²Φ / ∂x² + ∂²Φ / ∂y² = 0
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