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The correct answer is (c) Non-NEGATIVE k and ε values

The BEST explanation: The values of TURBULENCE quantities such as the turbulent kinetic energy (k) and the RATE of dissipation of the turbulent kinetic energy (ε) cannot be negative and must ALWAYS be constrained to have values above zero.

Correct choice is (b) the same as that of the k-ε model

The explanation is: The dynamic eddy VISCOSITY used in the RNG k-ε model is the same as that of the k-ε model. The EQUATION used is

μt=ρCμ\(\frac{k^2}{\varepsilon}\).

Correct answer is (c) the space-based integral of its mean component

Easy EXPLANATION: As the mean of the FLUCTUATING component is ZERO and the mean of the mean component is the mean component itself, the mean of the space-based integral of a flow variable is equal to the space-based integral of its mean component alone.

Correct option is (a) The RATIO of the distance in the CROSS-stream direction from the CENTRELINE and HALF-width at that cross section

Easiest explanation: The velocity at any point in the cross-stream direction at a PARTICULAR cross section depends on the ratio of the distance from the centreline and the half width of the cross-stream.

Correct answer is (a) Rate of dissipation of turbulent energy and fluid viscosity

Easiest EXPLANATION: KOLMOGOROV micro-scales can be expressed in TERMS of the rate of energy dissipation of the turbulent flow and the fluid viscosity. It USES the statement that the rate of production of turbulent energy and the rate of dissipation should be BALANCED.

Right answer is (d) μSGS=ρ(CΔ)^2\(\MID\overline{S}\mid \)

EASY EXPLANATION: The equation for SGS viscosity is obtained by the dimensional analysis. It is given by the equation μSGS=ρ(CΔ)^2\(\mid\overline{S}\mid \) . Where, C is the CONSTANT of SGS viscosity.

The correct choice is (C) stagnation

For EXPLANATION I would say: In the stagnation region, the VELOCITIES will be zero. So, there is no possibility of TURBULENCE there. The MODEL should be limited to prevent unrealistic turbulence in the stagnation region.

Right answer is (c) Numerical instability

The EXPLANATION: As the MODELLING equations vary from the converted k-ω model in the near-wall region to the standard k-ω model in the FAR away region, numerical instabilities MAY arise in the computed EDDY viscosities.

Right ANSWER is (c) 0.0845

Easy explanation: The value of Cμ is 0.0845. This is useful in finding the TURBULENT dynamic viscosity and hence the effective dynamic viscosity of the RNG k-ε model. This value is obtained by COMPARING to the EXISTING turbulence model DATA.

The correct answer is (c) vorticity

Best explanation: The RATE of production of the kinematic eddy viscosity PARAMETER is a term in the TRANSPORT EQUATION of the Spalart-Allmaras model. This is related to the local MEAN vorticity by means of the vorticity parameter.

Correct option is (d) the ratio of the kinematic eddy VISCOSITY parameter and the kinematic eddy viscosity

The explanation is: The first WALL damping FUNCTION is INTRODUCED in the dynamic eddy viscosity. The dynamic eddy viscosity divided by the density of the flow is the kinematic viscosity. So, the function is a function of the ratio of the kinematic eddy viscosity parameter and the kinematic eddy viscosity.

The correct choice is (a) goes above unity

To explain I would say: The value \(\FRAC{y}{b}\) going above 1 means that y CROSSES b and goes out of the TURBULENT region. So, the velocity GRADIENTS and its fluctuations also will become ZERO when the value \(\frac{y}{b}\) goes above 1.

The CORRECT choice is (a) 0.09 times the BOUNDARY LAYER thickness

For explanation: For a turbulent boundary layer problem, the MIXING length varies for different layers of the flow. For the 2-D case, the mixing length of the OUTER boundary layer is 0.09 times the boundary layer thickness.

The correct OPTION is (d) Interaction of SGS eddies and resolved FLOW

For EXPLANATION: The cross-stress terms are caused by the combination of the FILTERED function (Φ) and the eddy function (Φ’). They are GIVEN by \(\rho\overline{\overline{u_i}u_j^{‘}} + \rho\overline{u_i^{‘}\overline{u_j}}\). So, we can say that they are caused by the interaction of SGS eddies and resolved flow.

Right OPTION is (c) spreading of jets

Best explanation: The REALIZABLE k-ε model more accurately predicts the spreading of jets, be it planar or round jets. It performs better than the other models for complex problems involving RECIRCULATION and FLOW SEPARATION.

Right choice is (a) TWO-equation MODEL

Explanation: The RNG k-ε model is a variation of the k-ε model. So, the RNG k-ε model also has two extra transport equations like the k-ε model. It comes under the two-equation TURBULENCE models.

The correct answer is (b) Easier to integrate

Easiest explanation: The greatest ADVANTAGE of replacing the ε VALUE with the ω value is that this ω value is easier to integrate. It does not need additional damping FUNCTIONS to integrate. The k-ω model also depends on the ε value for the ω value. Both can be applied for TURBULENT boundary layers. Both has two extra equations.

Right choice is (c) Vortex stretching

The BEST I can explain: Vortex stretching is the lengthening of vortices with a corresponding increase in the component of VORTICITY in the stretching direction. This vortex stretching is RESPONSIBLE for the LARGEST turbulent eddies to interact with the mean flow and extract energy from them.

Correct option is (b) LEONARD filter

The EXPLANATION is: The LES method uses a filter function to spatially filter and get the LARGER eddies of interest. The most common three-dimensional filters are Top-hat filter, GAUSSIAN filter and Spectral cut-off filters.

The correct answer is (d) \(lim_{T→∞}⁡\frac{1}{T}\int_t^{t+T}\phi DT\)

Best EXPLANATION: Time averaging represents the average of the flow variable BASED on a time interval ‘T’. It USES INTEGRATION to sum up the flow variables at different times and then divides by the time interval \(lim_{T→∞}⁡\frac{1}{T}\int_t^{t+T}\phi dt\).

The CORRECT option is (B) 5 < y^+ < 30

For explanation I would say: Buffer layer has the TURBULENT FORCES and the viscous forces in equal magnitude. In this layer, the range of y^+ is5 < y^+<30. 0 < y^+ < 5 is for the linear or viscous sub-layer. The buffer layer lies just above the viscous sub-layer.

The correct answer is (d) the QUADRATIC tensor products of strain rate and vorticity

For explanation I would say: The Reynolds stresses in the non-linear k-ε MODELS RELATE the Reynolds stresses to the quadratic product of LOCAL vorticity and strain rates. These two quantities are tensors. The method sensitizes the Reynolds stresses.

Correct answer is (a) the addition of molecular dynamic viscosity and dynamic eddy viscosity

Explanation: The SMALL SCALES of motion in the governing equations are REPLACED by the larger scale MOTIONS and MODIFIED viscosity. This modified effective viscosity is the addition of molecular dynamic viscosity and dynamic eddy viscosity.

The CORRECT answer is (a) REYNOLDS stresses and turbulent scalar flux

Easy explanation: While the conservation EQUATIONS are Reynolds averaged, they get ADDITIONAL terms due to the decomposition of the flow variables. These additional terms INCLUDE Reynolds stresses and turbulent scalar fluxes. This occurs because of the mean of the product of the fluctuating components.

Correct choice is (a) Sub-grid-scale STRESS

Easy explanation: During spatial filtering, the information about the small EDDIES will be lost. The INTERACTION between large eddies and small eddies LEADS to this SGS stress. It stands for sub-grid-scale stress.

Correct CHOICE is (a) 100

Best explanation: The number of time steps depends on the ratio of the largest to the SMALLEST time scales. This ratio depends on the REYNOLDS number. The times steps needed is Re^1/2. Here, it is (10^4)^1/2, which is equal to 100. 100-time steps are needed to SOLVE this problem.

Correct answer is (a) turbulent VISCOSITY to turbulent diffusivity

Explanation: Turbulent Schmidt number gives the ratio of turbulent transfer of momentum to the turbulent transfer of MASS. It is GIVEN by

Turbulent Schmidt number=\(\FRAC{Turbulent\, viscosity}{Turbulent\, diffusivity}\).

Right choice is (b) To get the mean COMPONENT of the flow variable

For explanation I would SAY: By REYNOLDS decomposition, the flow variables are decomposed into mean and fluctuating COMPONENTS. These methods of averaging are USED to get the mean component during this decomposition.

Right answer is (B) Entrainment

Easiest explanation: While turbulent flows BURST out of its region, fluid from the SURROUNDING is DRAWN into the turbulent region. This is the process of entrainment. This is the cause of spreading of turbulent flows in the flow direction.

The correct option is (d) VELOCITY and length SCALES

Explanation: Velocity and length of the large EDDIES will be large. The variation of flow with time is not MUCH. Thus, they are not dependent much on the time scales. Instead, they are dependent on the velocity and length scales.

Right option is (a) 0.1

Best EXPLANATION: The smallest scales of motion in the turbulent flows are dominated by VISCOUS flows. They are associated with a Reynolds NUMBER 1. The smallest scales are those for which inertia and viscous flows are the same.

The correct option is (B) The effects at the resolved SCALE

Easy explanation: The Leonard stress terms occur because of the term \(\rho\overline{\overline{u_i}\overline{u_j}}\). These are both the resolved VELOCITIES. So, we can CONCLUDE that the cause for Leonard stresses is the effects at the resolved scale.

Right answer is (b) Law of the WAKE

Easiest EXPLANATION: All these LAWS are used in MODELLING turbulent boundary layers. The law of the wake depends on the function of the distance from the wall and the boundary layer THICKNESS. It does not depend on the y^+ value.

The CORRECT choice is (d) TURBULENCE Reynolds number, the ratio of turbulence and distance from the wall

For explanation: The BLENDING FUNCTION is a function of lt/y and Rey. Where,

lt→ Ratio of turbulence.

y→ Distance from the wall.

Rey→ Reynolds number based on the y-distance.

Right OPTION is (b) Renormalization group

To EXPLAIN I would SAY: The RNG in the RNG k-ε model means renormalization group. This method was invented by Yakhot and Orszag of Princeton University. This is invented to overcome the DISADVANTAGES of the k-ε model.

Correct choice is (a) ω=ε/k

Easiest explanation: TURBULENCE frequency is the ratio of the RATE of DISSIPATION of the turbulent KINETIC energy to the turbulent kinetic energy. It is given by ω=ε/k. The values of ω are easier to ASSUME than the ε values.

The CORRECT option is (a) ρCμk^2/ε

Explanation: USING dimensional analysis, the turbulent dynamic viscosity can be given as

μt = Cμ ρ&vartheta;l

Where,

&vartheta; → Velocity scale of large eddies

l → Length scale of large eddies

Substituting these two in K and ε terms, we get

μt = Cμ ρ\(\frac{k^2}{\varepsilon}\)

Where, Cμ is a dimensionless constant which is ADJUSTABLE. The STANDARD k-ε model uses Cμ=0.09.

The correct OPTION is (d) TURBULENT flows with separation

Best explanation: Mixing length model is ideal for predictions of THIN turbulent shear flows such as turbulent JETS, wakes, boundary layers and mixing lengths. But, they will not be able to PREDICT flows with separation or even recirculation.

Correct choice is (a) Ensemble averaging

Explanation: Ensemble averaging is a METHOD used in statistical mechanics. Here, it is used as one of the methods of averaging. This is SUITABLE for any type of TURBULENT FLOWS including unsteady turbulent flows.