Explore topic-wise InterviewSolutions in .

The correct answer is (d) The Reynolds stress model needs 7 EXTRA transport equations

Explanation: The most common RANS turbulence MODELS are classified on the basis of the number of extra transport equations they NEED. These models form the basis of the CURRENT procedures for turbulence problems in CFD packages. The Reynolds stress model needs seven more equations.

Correct choice is (c) 1

The explanation is: Reynolds analogy STATES that “because of eddy MIXING, the values of TURBULENT viscosity and turbulent diffusivity will be FAIRLY close to each other”. So, dividing both we will get UNITY. Therefore, turbulent Schmidt or Prandtl number becomes unity.

Correct CHOICE is (a) REALIZABLE k-ε MODEL

Explanation: The realizable k-ε model is a variant of the k-ε model. The realizable k-ε model is DIFFERENT from its parent that a new turbulent viscosity is formulated. ANOTHER variation is that a new transport equation for the dissipation rate is formed.

Correct answer is (c) DNS

Easiest explanation: The models k-ε, k-ω and SST are all models which include turbulent viscosity. DNS stands for Direct NUMERICAL Simulation which is the basic MODEL to solve turbulent FLOWS. It does not involve turbulent viscosities.

The CORRECT choice is (c) proportional to the PRODUCT of turbulent length and velocity scales

Explanation: By using dimensional analysis, the relationship between KINEMATIC turbulent VISCOSITY, turbulent length and TIME scales can be established using the dimensional analysis. It can be expressed as

νt∝vl

Where,

νt →Kinematic turbulent viscosity.

v →Turbulent velocity scale.

l →Turbulent length scale.

The CORRECT ANSWER is (b) Dissipation

For explanation I would say: HIGH wavenumbers represent small eddies. Dissipation is associated with small eddies and kinetic energy is associated with large eddies. This is given by the RELATION between energy and WAVENUMBER.

Right CHOICE is (d) The RATES of change of the flow VARIABLES in the flow DIRECTION are smaller than that of the cross-sectional direction

The explanation: Considering turbulence in thin shear LAYERS, large variations are concentrated in thin regions. The variables do not change much in the flow direction. But, the rates of change in the cross-sectional direction are more.

Correct choice is (b) RATE of DISSIPATION of turbulent energy

The best explanation: Kolmogorov STATED that the structure spectral energy of the smallest eddies depends only on the rate of dissipation of turbulent energy. But later studies revealed that only the spectral energy of the smallest eddies depends only on the rate of dissipation of turbulent energy and not their structure.

Right choice is (c) three-dimensional and ANISOTROPIC

Best EXPLANATION: TURBULENT flows are characterized by their three-dimensional fluctuation. So, the large eddies are ALSO three-dimensional. The flow variables highly vary in all three directions. This leads to an anisotropic NATURE. Especially, large eddies are highly anisotropic.

Correct option is (a) REYNOLDS STRESS term

Best explanation: Reynolds stress term comes from the Reynolds-Averaged Navier-Stokes (RANS) equations. When this term is again averaged, but based on spatial coordinate this TIME, the SGS STRESSES occur.

Right choice is (b) K=\(\frac{1}{2}T_i^2(\vec{v}.\vec{v})\)

To explain I WOULD say: To find the turbulent kinetic energy k using the turbulence intensity value, the following FORMULA is used.

k=\(\frac{1}{2}T_i^2(\vec{v}.\vec{v})\)

Where,

\(\vec{v}\) → Velocity vector.

The CORRECT option is (a) y^+ is dimensionless

The explanation is: y^+ is dimensionless length. It does not have any dimensions. This can be again proved from the equation

y^+ (unitless and dimensionless)= \(y(m)u_t(\FRAC{m}{s})⁄ν(\frac{m^2}{s})\).

Right option is (b) ρ k/ω

The best explanation: The turbulent dynamic VISCOSITY is

μt = ρΘl

Where,

ρ → Density of the flow

ϑ → LENGTH scale of the large eddies

l → Length scale of the small eddies

Replacing with the k and ω equivalents,

\(μ_t=\rho×\SQRT{k}×\frac{\sqrt{k}}{\omega}\)

\(μ_t=\rho×\frac{k}{\omega}\).

Right answer is (b) k^3/2/ε

The explanation: The length scale of the large EDDIES can be given as k^3/2/ε. The SMALL scale dissipation rate of the turbulent kinetic energy can be USED to represent the large scale length as the rate at which the large eddies extract energy from the mean flow is matched with the rate of energy transfer to small eddies.

Correct answer is (a) position

Easy EXPLANATION: The mixing length MODEL is a variation of the RANS model. It does not need any ADDITIONAL transport equations. It describes the stresses in terms of a simple algebraic formula for the turbulent dynamic viscosity as a function of position.

Correct answer is (B) Runge-Kutta method

Explanation: Runge-Kutta method is generally USED to advance in time in the DNS method. They need more computation time per UNIT step. In SPITE of this disadvantage, they are PREFERRED because of their accuracy.

The correct CHOICE is (b) 0
Explanation: This is the layer which is in immediate contact with the SMOOTH wall. It obeys NEWTON’s law of viscosity. The SHEAR stress in this layer is constant and approximately equal to that of the wall. It extends from the wall till y^+ REACHES 5.

Right option is (a) INERTIA forces dominate in the FLOW far from the wall

To explain: As the flow of a fluid near the wall moves away from the wall, the REYNOLDS NUMBER of the flow increases accounting to the increase in the distance. This leads to high inertial forces and low VISCOUS forces.

The correct option is (b) It is dimensionless

Explanation: Both viscosity and diffusivity are in the same UNITS. As the turbulent Schmidt or PRANDTL NUMBER is the ratio of viscosity to CONDUCTIVITY, the number BECOMES dimensionless. So, it does not have units.

The correct choice is (c) Decrease in the magnitude of the VELOCITY gradients in the FLOW direction

For explanation: Because of the entrainment of the SURROUNDING fluid, the velocity gradients decrease in magnitude in the flow direction. This ALSO decreases the difference between the speed of the wake fluid and its SURROUNDINGS.

Correct choice is (a) ENERGY cascade

The BEST explanation: Smaller eddies are stretched STRONGLY by large eddies. THEREBY, KINETIC energy is transferred from larger eddies to smaller and smaller eddies. This is called energy cascade.

Correct choice is (c) modulate heat transfer results

For EXPLANATION: Prandtl number relates MOMENTUM transfer and heat transfer in a turbulent FLOW. So, it is used in turbulent flows with heat transfer. In general CFD problems, it is used to tune the heat transfer results.

Correct answer is (a) Turbulent EDDIES

The EXPLANATION: The turbulent fluctuation has a three-dimensional spatial character. Visualizations of turbulent flows show that they have a highly rotational flow STRUCTURE. These rotational flow STRUCTURES are called Turbulent eddies.

Right choice is (a) KINETIC, internal

The best explanation: Viscous effects reduce the velocity GRADIENTS and hence the kinetic energy of the flow. THUS, mixing is dissipative. This lost energy is CONVERTED into THERMAL internal energy of the flow. Thus, kinetic energy is converted into internal energy.

Right option is (d) Low VISCOSITY and angular momentum are conserved

For explanation I would say: Vortex stretching leads to CONSERVATION of angular momentum. As the large EDDIES are associated with vortex stretching, here angular momentum is conserved. They have a HIGH Reynolds number which directly tells that they are RELATIVELY inviscid.

Right answer is (b) mass

Best explanation: The averaging in FANS method is a WEIGHTED average method which uses mass as the weight for it. Here, mass decides the IMPORTANCE of the TERMS and WHETHER it can be filtered or not.

The correct option is (C) Sub-grid scale MODELS are USED for small turbulent scales

The explanation: Large scale turbulent structures are directly simulated and the small scales are simulated using sub-grid models. A spatial STATISTICAL filter is used to filter the Navier-Stokes equation to determine which scale to keep and which to discard.

The CORRECT OPTION is (b) Statistical analyses

To EXPLAIN: Statistical analysis is used to SIMPLIFY the resolution of turbulent flows. Statistical time averaging is used to reduce the random fluctuations in the time-dependent NATURE of turbulence flows.

Correct choice is (a) Time-independent

Easiest EXPLANATION: Turbulent FLOWS are CHAOTIC, diffusive CAUSING rapid mixing, time-dependent as they are unsteady, and involve vorticity fluctuation in all three-dimensions. Turbulence develops an INSTABILITY in flows.

Right option is (a) STRESS due to VELOCITY fluctuations

Explanation: Turbulent FLOWS are highly chaotic and unstable. The high fluctuation in the turbulent flows creates highly varying velocities. These velocities create additional STRESSES called REYNOLDS stress.

Correct answer is (c) Computationally demanding

For EXPLANATION: The time-step sizes in DNS technique is limited by COURANT number. So, it involves many steps to reach the actual interval NEEDED to be CROSSED. This MAKES the technique computationally demanding. This is the disadvantage of DNS technique.

The correct option is (a) HIGH diffusion coefficients

Explanation: Because of the eddying motion of the TURBULENT flows, heat, mass and MOMENTUM are effectively exchanged. So, the VALUES of diffusion coefficients of heat, mass and momentum are high.

Right choice is (b) SIMPLE

To explain: The SIMPLE algorithm is a WIDELY used iterative solution technique for Navier-Stokes EQUATIONS for PRESSURE linked systems. It is not used to solve turbulent models. The other techniques – RANS, DNS and LES – are all used to solve turbulent flows.

The correct option is (B) Steady velocity + FLUCTUATING component of velocity

Best explanation: Reynolds decomposition separates the steady mean component and some statistical PROPERTIES of their fluctuations. TOTAL velocity = Steady velocity + Fluctuating component of velocity.

Correct option is (a) DNS

The explanation: DNS is the first METHOD USED to solve the TURBULENT flow models. DNS stands for Direct Numerical Simulation. It uses the energy CASCADE concept developed by Kolmogorov. Its time-steps are limited by Courant number.

Correct choice is (d) LES

The EXPLANATION: The LES METHOD is USED to overcome the disadvantages of the DNS technique. LES stands for Large Eddy Simulation. This filters the Navier-Stokes equations to discard some SCALES and keep the rest.