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Indian Institute of Space Science and Technology
AE721/AE480 Boundary Layer Theory

Quiz-I
(February 17, 2023)
Duration: 60 min Total marks: 30
General Instructions:
" Draw schematic diagram wherever possible and label clearly
" State the assumptions clearly wherever required
" Assume suitable value for parameter if required and mention it clearly with units
Questions:
1. Using tensor indicial notation, prove the following: (a xb) xc = (a-c)b (b-c)a [4]
2. Derive the rate of change of entropy of a material element and explain each term. Also, [6]
explain how thermodynamic II law is imposed in the fluid flow. T7s= 7h
3. Write the following terms in symbolic notation and explain the physical meaning [10]
o (a) d¡ij
dxj
dui
(b) ijdx;
(c) d(oju:)
dxj
(a) dui
dx;
dp dx;
(e) eijkdxy dp
4. The non-dimensional velocity field with respective to the stationary frame is given by [10]
U=3xx e1 + 2xzez (ej and ez are unit vectors in xË and x> direction). Calculate the
following at point A = (1, 1)
(a) the components of the velocity gradient , the rate of linear strain, the rate of
shear strain, and vorticity at A,
(b) What will be the linear strain rate, shear strain rate and vorticity at point Awith
respect to a person who rotates with angular velocity (non-dimensional) of 10 e.
* End of Paper *
Indian Institute of Space Science and Technology
AE721/AE480 Boundary Layer Theory
End Semester
(May 09,2023)
Total marks: 100
Duration: 180min
General Instructions:
" Draw schematic diagram wherever p0ssible and label clearly

" State the assumptions clearly wherever required
clearly with units
" Assume suitable value for parameter if required and mention it
Questions: Low of mgtiary

1. Write brief answer
[3]
(a) What is Galilean invariance and Objectivity. Give examples.
brau ind fens Dono deperel [3]
(3) State Helmholtz voriticity theorem, (3]
(c) What is barotropic flow? Give two examples.
(d) What is self-similar flow and its advantages. [3]
an incom [3]
(e) Write the velocity dependence of pressure drag and friction drag in
pressible laminar boundary layer.
(3]
() What is aerodynamic heating and adiabatic heating?
(3]
(g) What is natural transition and forced transition of boundary layer?
(h) Relation between Reynolds shear stress and turbulent kinetic energy.
[3]
(i) What is RANS, LES and DNS?
[3]
in the
(i) Plot vorticity profile as well as total pressure profile (along y- direction) [3]
laminar incompressible boundary layer over a flat plate.
direction)
(k) Static pressure distribution across the flat plate boundary layer (along y- [3]
flow and (ii) incompressible turbulent flow.
(ons laminar
for (i) incompressible an
(1) What is reference temperature method in compressible boundary layer? and its [3]
merits.
(m) What is stationary and non-stationary in turbulent flow? (3]

(n) What is shear production term and its role in turbulent mean kinetic energy equa 3]
tion as wellas in turbulent kinetic energy equation.
(o) What is viscous sublayer in incompressible turbulent boundary layer and corre [3]
sponding equation for this layer.
that non-linearity generates new scales using the following equation
Jhow du
[6]
=0; u(x, to) = Acos(ky*)Tay'or Se u

where k, denotes wave number in x- direction.
3. Derive kinetic energy thickness for compressible flow. [6]
4. Derive the relation between material line and vorticity line and using this explain vor [10]
ticity stretching and tilting.
5. Explain the following [10]
(a) Explain the effect of favorable and adverse pressure gradient laminar incompress
ible boundary layer.
(b) Explain the effect of shear gradient on laminar incompressible boundary layer.
(c) Why laminar incompresible boundary layer is not separating immediately after
experiencing the adverse pressure gradient?
[12]
6. Derive the Reynolds averaged Navier-Stokes equation (RANS) for an incompressible
flow and discuss its implications. Also explain the Boussinesq turbulent viscosity hy
pothesis.
non-dimensional [11]
7. Calculate the displacement thickness (6*), momentum thickness (0) and
shear stress coefficient (cp) of the laminar incompressible boundary layer over a flat
plate using Thwaites method.
6 due 0.45
He dr
) We
=0
0.56 A2
H(A) = 2.61 4.1A+ 14 13+
(A +0.18)2
0.072 A2
T(A)= 0.220 + 1.52 A- 51 - A+0.18)2
* End of Paper *

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Indian Institute of Space Science and Technology

AE721/AE480 Boundary Layer Theory

" Draw schematic diagram wherever p0ssible and label clearly

Questions: Low of mgtiary

(m) What is stationary and non-stationary in turbulent flow? (3]

=0; u(x, to) = Acos(ky*)Tay'or Se u

3. Derive kinetic energy thickness for compressible flow. [6]

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