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Right choice is (a) more ACCURATE and converges easily

Easy EXPLANATION: The realizable k-ε model and the RNG k-ε model have the same benefits and APPLICATIONS. But, the realizable model GIVES more accurate results and it is easy to CONVERGE when compared to the RNG k-ε model.

The CORRECT choice is (d) 1/s

The BEST explanation: TURBULENCE FREQUENCY has the same unit as the frequency (1/s). The dimension of ε is m^2/s^3. The dimension of kinetic energy is m^2/s^2. DIVIDING both, we get 1⁄s.

Correct answer is (d) TWO equations

Best explanation: The k-ω MODEL is a variation of the k-ε model. This ALSO adds two equations which are the TRANSPORT equations of k and ω to the RANS equations to overcome the linearity problem of the RANS equation.

Correct choice is (d) represented by random forcing FUNCTIONS

Explanation: In the Navier-Stokes equations, the EFFECTS of small-scale TURBULENCE are replaced by random forcing functions in the RNG k-ε MODEL. In the Large EDDY Simulation method, these are neglected.

The CORRECT option is (a) spatial FILTERING

To explain I would say: LES captures large eddies only. So, spatial filtering is used to separate the large and small eddies. A filtering function and the cut-off WIDTH above which the flow will be solved are selected before solving the flow.

Correct choice is (b) the FLOW has a high REYNOLDS number

The best explanation: Large Eddy Simulation (LES) method is useful to capture the large turbulent EDDIES. It is not as accurate as the DNS method and not computationally demanding. As high Reynolds number will have large eddies, it is PREFERRED when the flow has a high Reynolds number.

Correct ANSWER is (b) turbulent transport of MOMENTUM to turbulent transport of HEAT

The explanation is: Prandtl NUMBER is the ratio of transport of momentum to transport of heat. Turbulent Prandtl number is

Turbulent Prandtl number=\(\frac{Turbulent\, viscosity}{Turbulent\, DIFFUSIVITY}\).

Right answer is (d) m^2/sand kg/m s

For EXPLANATION: The UNITS of turbulent viscosities are the same as the viscosities GIVEN by Newton’s law. The unit of kinematic turbulent viscosity is m^2/s. The unit of dynamic viscosity is kg/m s.

The CORRECT choice is (b) Intermittency

The BEST explanation: Intermittency is the irregular alteration of phases. In turbulent flows, it is SEEN in the irregular alteration between the turbulent and non-turbulent region of jet flow. Intermittency REPRESENTS the burst of turbulent activity to the SURROUNDING region.

Correct option is (d) TURBULENT DIFFUSION

Explanation: Turbulence INCREASES the RATE at which conserved quantities are mixed. Here, different fluid PARCELS are brought into contact. As this mixing is accomplished by diffusion, the process is called turbulent diffusion.

Correct option is (C) Coherent turbulent structures

To EXPLAIN I would say: For a time-averaged statistic to be applicable, the turbulent STRUCTURE should have temporal COHERENCE. Though turbulent flows are chaotic, they should be resolved into coherent structures to APPLY these methods.

Right answer is (c) \(\rho\overline{\overline{u_i}u_j^{‘}} + \rho\overline{u_i^{‘}\overline{u_j}}\)

The best explanation: The cross-stresses AMONG the other SGS stresses OCCUR due to the INTERACTION between two VARIABLES. It can be given by the equation \(\rho\overline{\overline{u_i}u_j^{‘}} + \rho\overline{u_i^{‘}\overline{u_j}}\). The filtered and the unfiltered variables come together in each of these terms.

Right option is (b) one extra TRANSPORT equation

Easy EXPLANATION: Spalart-Allmaras is a turbulence MODEL to the RANS equations. This has an extra transport equation. This extra transport equation is used to overcome the non-linear problem of the RANS equations.

The correct answer is (d) \(\frac{\partial\overline{(\overline{\rho}u{‘}v{‘})}}{\partial y}\)

For EXPLANATION: The term \(\overline{(\overline{ρ}u’v’)}\) represents the TURBULENT shear STRESS (Reynolds stress) in the MOMENTUM equation. This leads to the turbulent or eddy viscosity in the turbulent models.

Correct answer is (c) the fluctuations

To explain I would say: TIME averaging is used only when the flow is steady and time-independent. The time INTERVAL TAKEN to average the fluctuations depend upon the time scale of the fluctuations itself. If this interval is large enough, the LOWER limit of the integral does not even MATTER.

The correct choice is (c) For PRECISE details

For explanation: The DNS method is used when we want the precise simulation with all the details in it. They are used for the DEVELOPMENT and validation of other turbulent models. The transport of any flow variable at any point can be precisely obtained USING this MODEL.

Right choice is (b) Reynolds ANALOGY

For explanation I would say: Reynolds analogy relates the turbulent momentum and heat transfer. It states that “both of these (turbulent momentum and heat transfer) are due to the same mechanism called turbulent eddies and hence the VALUES of turbulent VISCOSITY and diffusivity will be close to each other”.

The correct option is (B) WAVENUMBER

The best explanation: Kolmogorov spectral energy is, in general, a function of the wavenumber. The wavenumber is, in turn, a function of WAVELENGTH (λ) given by

κ=\(\frac{2\pi}{\lambda}\).

The correct answer is (C) The ratio of small and large SCALE eddies

Explanation: The TIME-scale ratio is the ratio between small-scale time (of small-scale eddies) and large-scale time (of small-scale eddies). SIMILARLY, the length and velocity-scale ratios are also the ratios between small and large-scale lengths and VELOCITIES.

Right option is (c) Kolmogorov micro-scales

The explanation is: The smallest eddies with dominating VISCOSITY are called Kolmogorov micro-scales. It is named after the Russian scientist Andrey Kolmogorov who CARRIED out WORKS on the structure of TURBULENCE in the 1940S.

Right choice is (d) When the filter function is UNIFORM

The BEST explanation: The LES filter function is always linear. If a uniform filter function is used, the order of filtering and differentiation can be swapped with respect to TIME and space coordinates. Thus, the function will be COMMUTATIVE.

Correct choice is (d) viscous sub-LAYER

The explanation is: It is difficult to MODEL the flow in the buffer layer. So, the low Reynolds NUMBER models place the first INTERNAL grid POINT in the viscous sub-layer and the high Reynolds number models place it in the inertial sub-layer skipping the buffer layer.

Right answer is (d) \(-\rho \overline{u_{i}^{‘} u_{J}^{‘}}\)<0

Easiest explanation: ACCORDING to the realizability CONDITIONS, the PROPERTIES which are physically non-negative must be numerically non-negative too. So,\(-\rho \overline{u_{i}^{‘} u_{j}^{‘}}\)>0. Therefore, \(-\rho \overline{u_{i}^{‘} u_{j}^{‘}}\) should be less than zero.

Correct CHOICE is (b) Neither the STANDARD k-ε model nor the RNG k-ε model is REALIZABLE

Easy explanation: Both the standard k-ε model and the RNG k-ε model are not realizable. They do not satisfy the MATHEMATICAL condition of REALIZABILITY. Only the realizable k-ε model is realizable.

Correct option is (d) effects of small-scale turbulence

For EXPLANATION I would say: The EFFECT of small-scale turbulence is used while representing the DIFFUSION of turbulent kinetic energy in its transport equation as αk. In a similar way, the transport equation for the rate of dissipation of the turbulent kinetic energy contains αε.

Right option is (B) Adverse pressure GRADIENTS in TURBULENT flows

To elaborate: For free-shear flows, k-ε models are well suited. But, it cannot model adverse pressure gradients in the turbulent flows. This problem can be overcome by the k-ω model.

The CORRECT choice is (c) Turbulence models

To explain I would say: It is impossible to derive a closed set of RANS equations. So, some approximations in the flow MODEL are done. These approximations are called the turbulence model. This USUALLY means PRESCRIBING the Reynolds stresses and TURBULENT scalar flux in terms of the mean flow quantities.

The correct CHOICE is (d) \(lim_{N→∞}\FRAC{⁡1}{N} \sum_{i=1}^N\phi_i \)

Explanation: Ensemble AVERAGING is based on IDENTICAL flow variables. It sums up the identical variables and then takes the average. The equation is \(lim_{N→∞}\frac{⁡1}{N} \sum_{i=1}^N\phi_i \).

Right ANSWER is (b) equal to the mean COMPONENT itself

The explanation is: The mean component is already FOUND by taking the arithmetic mean (average) of the flow VARIABLES. So, if the average of only the mean component is TAKEN, it will again be the same mean component itself.

The correct choice is (C) moments of different PAIRS of variables

To EXPLAIN I would say: Turbulent flows have COMPLEX rotating three-dimensional fluctuations. Details about the structure of these fluctuations are contained in moments constructed from pairs of different variables.

The correct choice is (b) Fluctuating velocity and pressure are not equal everywhere

Easiest explanation: Turbulent flow structures are HIGHLY ANISOTROPIC. The flow VARIABLES are not the same in a particular DIRECTION. Therefore, the fluctuating velocities are also not the same everywhere. Instead, they SHOW continuous variation.

Correct answer is (d) jets and wakes

The explanation is: For turbulent FLOWS at jets and wakes, the sign must CHANGE at the symmetry LINE. The symmetry line is the centreline here. For the sign change to be possible, the velocity gradients should reach zero at this line.

The correct OPTION is (d) The square root of the SGS TURBULENT KINETIC energy

The best explanation: The major difference between the Smagorinsky-Lilly SGS model and the higher-order SGS models is the velocity scale used. The higher order models use velocity scale which is equal to the square root of the SGS turbulent kinetic energy.

Right choice is (a) Kronecker delta

The best I can explain: The rate of dissipation of the turbulent kinetic ENERGY in DIFFERENT directions are GIVEN by the equation εij = ^2⁄3 ρδij. Here, the term δij is the Kronecker delta. This value becomes ZERO if i≠j. If i=j, it becomes 1.

Correct option is (b) the DISTANCE from the WALL and von Karman’s constant and dimensionless distance

Easiest EXPLANATION: The mixing LENGTH for a 2-D turbulent boundary LAYER is given by κy[1-exp⁡(y^+/26)]. Where, κ is the von Karman’s constant which is equal to 0.41. y is the distance from the wall. y^+ is the dimensionless distance.

The correct answer is (a) DIV \(\VEC{A}\)

To explain: From the given PROBLEM,

\(\overline{div \,\vec{a}}=div\overline{\vec{a}}=div\overline{\vec{A}+\vec{a’}} = div\overline{\vec{A}}=div\vec{A}\).