This set of Computational Fluid Dynamics Multiple Choice Questions & Answers (MCQs) focuses on “Compressible Flows – Conservation Equation”.

1. Which of these equations are needed for compressible flows?

a) Mass, momentum and energy conservations and equation of state

b) Mass and momentum conservations and equation of state

c) Momentum and energy conservations and equation of state

d) Mass, momentum and energy conservations

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Explanation: For the compressible flows, the basic governing equations – the mass, momentum and energy conservations are solved first. From these known values, to find the unknowns, an extra governing equation – the equation of state is also used.

2. Which of these differences occur in the momentum equation of the compressible flows when compared to that of the incompressible flows?

a) Temperature term

b) Source term

c) Bulk viscosity

d) Bulk modulus

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Explanation: In the incompressible flows, the bulk viscosity term is omitted as the density is constant. But, in the compressible flows, this cannot be omitted. This is an additional term in the momentum equation of the compressible flows.

3. Which of these terms is newly interpolated for the compressible flows?

a) Temperature

b) Density

c) Pressure

d) Mass

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Explanation: In the incompressible flows, the density was constant everywhere. But pressure values were calculated. But, for the compressible flows, the density values vary at different points. So, at the interfaces, they should be interpolated.

4. Which of these methods is used in the compressible flows to find the densities at the faces?

a) Central difference

b) Upwind difference

c) Rhie-chow interpolation

d) Weighted average

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Explanation: The central difference scheme (or linear interpolation profile) produces oscillations at high speeds. So, a bounded upwind first or higher-order equation is used to get the density values at the interfaces.

5. The bulk viscosity term in the compressible flows are discretized as ___________

a) summation of bulk viscosity and area at the faces

b) product of bulk viscosity and volume at the cell centre

c) product of bulk viscosity and area at the faces

d) summation of fluxes over the faces

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Explanation: The bulk viscosity term in the momentum equation is a volume integral. This is converted into a surface integral. This surface integral is then discretized as the summation of fluxes over the faces of the control volume.

6. The extra term in the pressure-correction equation of the compressible flows ___________

a) density-correction field

b) pressure-correction field

c) velocity-correction field

d) viscosity-correction field

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Explanation: The variable nature of the density in the compressible flows adds an extra term to the pressure-correction equation. Density-correction is that extra term. It is obtained using the pressure-density relation.

7. The pressure-correction equation of the compressible flows is ___________

a) a hyperbolic equation

b) an elliptic equation

c) a combined elliptic and hyperbolic equation

d) a parabolic equation

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Explanation: The pressure-correction equation in the incompressible flows is an elliptic equation. This is transformed into a hyperbolic equation in the compressible flows which is capable of resolving shock waves.

8. In the mass flow rate correction term at low Mach numbers, which of these terms dominate?

a) The density correction

b) The gradient of density correction

c) The pressure correction

d) The gradient of pressure correction

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Explanation: There are two terms involved in the mass flow rate correction. When the Mach number is low, the gradient of pressure correction term dominates the flow and makes the equation elliptic.

9. An extra term in the energy equation of the compressible flows is ___________

a) convection term

b) viscous dissipation term

c) diffusion term

d) unsteady term

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Explanation: The viscous dissipation term is an additional term in the energy conservation equation of the compressible flows like the bulk viscosity term of the momentum equation. The discretization procedure is the same as that of the bulk viscosity term.

10. Which of these properties of the SIMPLE scheme matches with the energy equation of the compressible flows?

a) Instability

b) Overshoots

c) Extra equation

d) Under-relaxation term

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Explanation: Like the SIMPLE scheme, the energy equation of the compressible flows also needs an under-relaxation term. The overall solution of the compressible flows follows the SIMPLE family of algorithms.

**Sanfoundry Global Education & Learning Series – Computational Fluid Dynamics.**

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