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# Computational Fluid Dynamics – Incompressible Flows – Special Features of Navier Stokes Equation

1 - Question

Which of these statements is correct?

a) Body force term in the momentum equation is non-linear

b) Rate of change term in the momentum equation is non-linear

c) Convective term in the momentum equation is linear

d) Convective term in the momentum equation is non-linear

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Answer: dExplanation: The convective term in the momentum equation is given by ∂(ρuiuj)∂xj. Where, ρ and u are density and velocity respectively. This term is a non-linear term. The rate of change and the body force terms are linear.

2 - Question

For the incompressible flows, which of these terms will be zero?

a) Pressure force

b) Body force

c) Bulk viscosity

d) Shear force

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Answer: cExplanation: A part of the viscous terms in the momentum equation is present in the diffusive term. Among these comes the bulk viscosity terms. These terms will be non-zero only for the compressible flows.

3 - Question

In which of these approaches is the pressure force treated as a body force?

a) Finite volume method – non-conservative approach

b) Finite volume method – conservative approach

c) Finite difference method – conservative approach

d) Finite difference method – non-conservative approach

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Answer: bExplanation: In the general integral form of the conservation equations, the pressure force is taken as a volume integral. While using the finite volume method, this is changed into a surface force by using the Gauss-Divergence theorem.

4 - Question

If the pressure force is not treated as a surface force in the finite volume method, what will happen?

a) Non-conservative error

b) Stability issues

c) Boundedness problems

d) Convergence issues

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Answer: aExplanation: Without using the Gauss-Divergence theorem, the pressure force can be treated as a volume integral itself. But, this will lead to a non-conservative form of equations which, in turn, will result in non-conservative errors.

5 - Question

The difference between the conservative and the non-conservative approaches occurs in the ___________

a) finite difference method

b) finite volume method

c) finite element method

d) spectral element method

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Answer: bExplanation: The conservative and non-conservative approaches gives rise to a considerable difference only in the finite volume method. In the finite difference approach, they do not result in any variation.

6 - Question

Which of these is correct for extra viscous terms in cylindrical coordinates?

a) The implicit and explicit treatments do not depend on the sign of the coefficients

b) It is treated implicitly when its contribution to the coefficient of the central node is negative

c) It is treated implicitly when its contribution to the coefficient of the central node is positive

d) It is treated explicitly when its contribution to the coefficient of the central node is positive

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Answer: cExplanation: While using the non-Cartesian coordinate systems, extra terms occur such as that of the extra viscous term in the momentum equation. This term is treated implicitly when it leads to a positive coefficient for the central node. Otherwise, it is treated explicitly.

7 - Question

Which of these changes do not contribute to a change in momentum in the momentum equation?

a) Surface fluxes

b) Surface forces

c) Body forces

d) Rate of change term

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Answer: dExplanation: The rate of change term represents the change in momentum in the momentum equations. This change is affected by any changes in the surface fluxes, surface forces and body forces acting on the element.

8 - Question

In which of these flows is the kinetic energy important?

a) Compressible flows

b) Compressible isothermal flows

c) Incompressible isothermal flows

d) Incompressible flows

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Answer: cExplanation: When the flow is not isothermal, thermal energies play an important role in energy conservation. When the flow is compressible, internal energies play an important role. Only when the flow is incompressible and isothermal, kinetic energies become significant.

9 - Question

An equation for the conservation of kinetic energy can be obtained by ___________

a) the product of momentum equations and mass

b) the product of momentum equations and velocities

c) the product of continuity equations and velocities

d) the product of continuity equations and mass

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Answer: bExplanation: Momentum is the product of mass and velocity. Kinetic energy is half of the product of mass and the square of velocities. Therefore, by multiplying the momentum equation with the velocity and further simplifying the resultant equations, we can get the conservation equations of kinetic energy.

10 - Question

For incompressible flows with no body forces, the volume integral term is ____________

a) viscous terms

b) pressure forces

c) body forces

d) flux terms

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Answer: aExplanation: Pressure forces and body forces are not present as the flow is incompressible and has no body forces. The flux terms are usually treated with the Gauss-Divergence theorem and converted into surface integrals. Therefore, the viscous terms remain as volume integrals here.