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The CORRECT choice is (b) DES model

The best I can EXPLAIN: DES model is a hybrid of LES and RANS model and makes use of advantages of both. For treating near –wall REGIONS, DES works like the RANS model and for rest of the region, it works as the LES model.

The correct choice is (a) Rex^–\(\frac {1}{5}\)

The EXPLANATION is: The turbulent BOUNDARY layer thickness in an incompressible FLOW is GIVEN by:

δ = \(\frac {0.37x}{Re_x^{-1/5}}\)

Thus the turbulent boundary layer thickness VARIES as Rex^-1/5 whereas in case of laminar flow, it varies as Rex^-1/4.

Right answer is (a) 2.72 × 10^-3

Easy explanation: GIVEN, Rec = 1.5 × 10^7

The skin friction drag over a flat plate for an incompressible turbulent FLOW is given by:

CF = \(\frac {0.074}{Re_c^{1/5}}\)

Substituting the VALUES,

Cf = \(\frac {0.074}{1.5 \TIMES 10^{7^{1/5}}}= \frac {0.074}{27.24}\) = 2.72 × 10^-3

Correct answer is (b) δ^* = \(\int_0^∞ \frac {u}{U_e} \big [ \)1 – \(\frac {u}{U_e}\big ] \)dy

The explanation: WITHIN the boundary layer, momentum thickness is DESCRIBED in RELATION to the momentum flow rate. This rate is lower than that which would occur if there were no boundary layer, when the velocity would be equal to the mainstream velocity UE in the vicinity of the surface considered at the station.

It is given by:

δ^* = \(\int_0^∞ \frac {u}{U_e}\big [ \)1 – \(\frac {u}{U_e} \big ] \)dy

Where, u is velocity at some point x on the plate

Ue is the freestream velocity.

Correct CHOICE is (d) K – EPSILON model

Best explanation: K – epsilon model is a two – equation model which includes two transport equations REPRESENTING the turbulent flow PROPERTIES. The first transport equation is solved is the turbulent kinetic energy, and the second one is the turbulent dissipation rate.

Right answer is (a) True

The best explanation: Displacement thickness is one of the properties of boundary layer which is the DISTANCE by which the external streamline gets displaced due to the PRESENCE of the boundary layer.

Without the presence of boundary layer, which is the case of inviscid flow, the streamline would be straight and parallel to the FLAT surface. But due to the presence of boundary layer in real life scenario having viscous flow, the streamline is displaced.

The formula for the displacement thickness δ^* is given by:

δ^* = \(\INT _0^{y1}\)(1 – \(\frac {ρu}{ρ_e u_e}\))dy

The CORRECT OPTION is (d) δturbulent > δlaminar

To explain: In case of turbulent flow, there is a high energy and momentum exchange compared to the laminar flow DUE to the PRESENCE of eddies. This leads to the thermal and velocity boundary layer THICKNESS of the turbulent flow to be higher than that of the laminar flow. Thus, δturbulent > δlaminar and δTturbulent > δTlaminar.

Right ANSWER is (a) True

To explain I would say: When a flat plate is kept in the freestream flow, there’s a FORMATION of a laminar boundary LAYER at the leading edge. This boundary layer THICKNESS grows to a point where a transition point is reached. Beyond that point, there’s turbulence due to the PRESENCE of eddies and there’s turbulent boundary layer formation whose thickness keeps on increasing.

Right option is (d) Thermal boundary layer is EQUAL to velocity boundary layer

The EXPLANATION is: When there’s a viscous flow over a flat plate, there’s a boundary layer formation which has certain properties. On the surface, there’s a no slip CONDITION. Apart from this the temperature of the fluid which is immediately at the surface has the same temperature as the surface which is known as the wall temperature. The velocity profile inside a boundary layer increases along the y – direction until it BECOMES equal to the freestream velocity. The only property that is incorrect is that the thermal boundary layer is equal to the velocity boundary layer.

The boundary of thermal layer is defined as the layer where the outer EDGE temperature becomes equal to the freestream temperature. Similarly, at the velocity boundary layer, the outer edge velocity is equal to the freestream velocity.

Correct ANSWER is (b) False

For explanation: One equation turbulence model only solves one TURBULENT TRANSPORT equation mostly the kinetic energy. It is the two equation turbulent model that ACCOUNTS for the history EFFECTS such as turbulent energy, diffusion and convection.

Correct answer is (c) T = 0.99Te

To elaborate: The FLOW temperature just like velocity varies within the BOUNDARY layer. It is a function of y – direction. The temperature ranges from TW which is the temperature at the wall (y = 0) to T = 0.99Te at y = δt, where δt is the thermal boundary layer thickness. This VARIATION of temperature is known as temperature PROFILE.

Right answer is (b) PR = 1

For explanation I would say: In most of the CASES the two thermal and velocity BOUNDARY layers are not same except in one exceptional case when the Prandtl number=1, in which case δt = δ. When Prandtl number is greater than 1, δt < δ and when Prandtl number is LESS than 1, δt > δ. In real life scenario, the Prandtl number is equal to 0.71 thus the thermal boundary layer thickness is greater than the velocity boundary layer thickness.

Right choice is (a) U = 0.99ue

Best explanation: Inside the BOUNDARY layer, the velocity INCREASES along the y – direction until it becomes equal to the freestream velocity. The thickness of boundary layer δ is defined as the POINT from the surface where the velocity is 0.99 times the free stream velocity.

Correct choice is (b) LES

For explanation I would say: In Large Eddy simulation, large EDDIES are computed by resolving large time and length SCALES. In LES, the smaller length scales are IGNORED making it an economical and LESS time consuming than DNS.

Correct option is (a) True

Best EXPLANATION: Turbulent boundary layer consists of inner and outer layers. There is a VISCOUS – dependent part of the PROFILE very close to the surface and different LENGTH scaling parameters are needed for the REMAINING Reynolds – stress – dependent part of the profile.

Correct option is (a) Possible for low Reynolds number

Explanation: The DNS solves the time – DEPENDENT NAVIER’s Stokes equation by resolving eddies of all scales for a SUFFICIENT time before reaching STATISTICAL equilibrium. The only shortcoming is that DNS is only applicable for low Reynolds number flow which has simple GEOMETRY.

Right ANSWER is (a) Define reynolds stress for closure problems

For explanation: While solving Navier’s Stokes equation for turbulent flow which governs the velocity, pressure of the fluid, the quantity is decomposed into mean and fluctuating components. While solving these using RANS equation, we get a reynolds stress term that needs to be closed in order to SOLVE it. HENCE we make use of TURBULENCE modeling which defines these reynolds stresses in terms of the known averaged quantities.

Correct choice is (C) Remains constant

To elaborate: The y – momentum equation for a boundary LAYER is given by:

\(\frac {∂p}{∂y}\) = 0

According to the FORMULA, at any x POINT in the boundary layer, pressure remains constant in the direction normal to the SURFACE.

Correct answer is (b) Viscosity

For explanation: There is shear stress between the ADJACENT layers of fluid in both laminar and turbulent FLOW inside the boundary LAYER. This is due to the viscosity and it is given by the relation:

τ = μ\(\frac {∂u}{∂y}\)

Where, \(\frac {∂u}{∂y}\) is the transverse VICTORY gradient.

Correct option is (a) K – omega MODEL

Easy explanation: K – omega is ONE of the POPULAR turbulence model. It is a TWO-equation model which solves two transport equations –turbulent kinetic energy and specific dissipation. Turbulent kinetic energy determines the energy whereas the specific dissipation determines the turbulence scale.

The correct ANSWER is (b) Approaches zero

Explanation: As the Reynolds number INCREASES, the boundary LAYER thickness decreases when compared to the length of the body. Usually for very large AIRCRAFTS, the value of \(\frac {δ}{L}\) is AROUND 0.01 which is a very small value. So hypothetically, as Re ➔ ∞, δ ➔ 0.