Computational Fluid Dynamics Questions and Answers – Incompressible Flows – Special Features of Navier Stokes Equation

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This set of Computational Fluid Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Incompressible Flows – Special Features of Navier Stokes Equation”.

1. 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

Explanation: The convective term in the momentum equation is given by $$\frac{\partial(\rho u_i u_j)}{\partial x_j}$$. 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. For the incompressible flows, which of these terms will be zero?
a) Pressure force
b) Body force
c) Bulk viscosity
d) Shear force

Explanation: 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. 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

Explanation: 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. 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

Explanation: 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. 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

Explanation: 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. 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

Explanation: 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. 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

Explanation: 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. In which of these flows is the kinetic energy important?
a) Compressible flows
b) Compressible isothermal flows
c) Incompressible isothermal flows
d) Incompressible flows

Explanation: 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. 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

Explanation: 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. For incompressible flows with no body forces, the volume integral term is ____________
a) viscous terms
b) pressure forces
c) body forces
d) flux terms