Engineering Questions with Answers - Multiple Choice Questions

# Computational Fluid Dynamics – Turbulence Modelling – Filtering

1 - Question

When is the LES filter commutative?
a) When the filter function is unity
b) When the filter function is quadratic
c) When the filter function is isotropic
d) When the filter function is uniform

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.

2 - Question

How many extra stress terms occur due to the LES filtering operation?
a) No extra terms
b) Four terms
c) Three terms
d) Two terms
Explanation: The LES filtering operation resolves the flow variables into two – the filtered one and the unresolved spatial variations. This resolution leads to three extra stress terms. They are collectively called as Sub-Grid-Scale stresses.

3 - Question

Identify Leonard stresses from the following.
a) ρui¯¯¯¯¯uj¯¯¯¯¯¯¯¯¯¯¯¯¯¯ρui¯¯¯¯¯uj¯¯¯¯¯
b) ρui¯¯¯¯¯uj¯¯¯¯¯¯¯¯¯¯¯¯¯¯
c) ρui¯¯¯¯¯uj¯¯¯¯¯
d) ρui¯¯¯¯¯uj¯¯¯¯¯¯¯¯¯¯¯¯¯¯ρui¯¯¯¯¯uj¯¯¯¯¯

Explanation: The term ρui¯¯¯¯¯uj¯¯¯¯¯¯¯¯¯¯¯¯¯¯ρui¯¯¯¯¯uj¯¯¯¯¯ is named Leonard stresses. It is named after an American Scientist A. Leonard who first identified an approximate method to compute them from the filtered flow.

4 - Question

The stress term ρuiuj¯¯¯¯¯¯¯¯¯is called as ____________
a) Filter Reynolds stress
b) LES Reynolds stress
c) Reynolds stress
d) Sub-Reynolds stress

Explanation: As the term resembles the Reynolds stress term, it is called the LES Reynolds stress term. This is modelled using Sub-Grid-Scale models, a special type of turbulence model used for these stresses.

5 - Question

Which of these terms corresponds to the cross stresses?
a) ρuiuj¯¯¯¯¯¯¯¯¯¯¯¯¯¯
b) ρui¯¯¯¯¯uj¯¯¯¯¯¯¯¯¯
c) ρui¯¯¯¯¯uj¯¯¯¯¯¯¯¯¯+ρuiuj¯¯¯¯¯¯¯¯¯¯¯¯¯¯
d) ρui¯¯¯¯¯uj¯¯¯¯¯¯¯¯¯ρuiuj¯¯¯¯¯¯¯¯¯¯¯¯¯¯

Explanation: The cross-stresses among the other SGS stresses occur due to the interaction between two variables. It can be given by the equation ρui¯¯¯¯¯uj¯¯¯¯¯¯¯¯¯+ρuiuj¯¯¯¯¯¯¯¯¯¯¯¯¯¯. The filtered and the unfiltered variables come together in each of these terms.

6 - Question

The SGS stresses are obtained from ___________
a) Reynolds stress term
b) Convection term
c) Source term
d) Diffusion term
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.

7 - Question

If a flow variable ϕ can be resolved by spatial LES filtering as Φ and Φ’. Expand the term ρuiuj¯¯¯¯¯¯¯¯¯.
a) ρui¯¯¯¯¯uj¯¯¯¯¯¯¯¯¯¯¯¯¯¯+ρui¯¯¯¯¯uj¯¯¯¯¯¯¯¯¯+ρuiuj¯¯¯¯¯¯¯¯¯¯¯¯¯¯
b) ρui¯¯¯¯¯uj¯¯¯¯¯¯¯¯¯¯¯¯¯¯+ρuiuj¯¯¯¯¯¯¯¯¯
c) ρui¯¯¯¯¯uj¯¯¯¯¯¯¯¯¯+ρuiuj¯¯¯¯¯¯¯¯¯¯¯¯¯¯
d) ρui¯¯¯¯¯uj¯¯¯¯¯¯¯¯¯¯¯¯¯¯+ρui¯¯¯¯¯uj¯¯¯¯¯¯¯¯¯+ρuiuj¯¯¯¯¯¯¯¯¯¯¯¯¯¯+ρuiuj¯¯¯¯¯¯¯¯¯

Explanation: The given term ρuiuj¯¯¯¯¯¯¯¯¯ represent the Reynolds stresses.
Resolving ui and uj, we get ui = ui¯¯¯¯¯+ui and uj=uj¯¯¯¯¯+uj. Therefore,
ρuiuj¯¯¯¯¯¯¯¯¯=ρ(ui¯¯¯¯¯+ui)(uj¯¯¯¯¯+uj)¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
ρuiuj¯¯¯¯¯¯¯¯¯=ρui¯¯¯¯¯uj¯¯¯¯¯¯¯¯¯¯¯¯¯¯+ρui¯¯¯¯¯uj¯¯¯¯¯¯¯¯¯+ρuiuj¯¯¯¯¯¯¯¯¯¯¯¯¯¯+ρuiuj¯¯¯¯¯¯¯¯¯
These terms are separated into the three components of SGS stresses

8 - Question

Leonard stresses are caused by ____________
a) The SGS eddies
b) The effects at the resolved scale
c) The effects of the unresolved variables
d) The combined effect of the SGS eddies and the resolved scale
Explanation: The Leonard stress terms occur because of the term ρui¯¯¯¯¯uj¯¯¯¯¯¯¯¯¯¯¯¯¯¯. These are both the resolved velocities. So, we can conclude that the cause for Leonard stresses is the effects at the resolved scale.

9 - Question

Cross-stresses are caused by ___________
a) Convection term
b) Resolved flow
c) SGS eddies
d) Interaction of SGS eddies and resolved flow
Explanation: The cross-stress terms are caused by the combination of the filtered function (Φ) and the eddy function (Φ’). They are given by ρui¯¯¯¯¯u‘j¯¯¯¯¯¯¯¯¯+ρu‘iuj¯¯¯¯¯¯¯¯¯¯¯¯¯¯. So, we can say that they are caused by the interaction of SGS eddies and resolved flow.

10 - Question

LES Reynolds stresses are caused by ____________
a) Source term
b) Resolved flow
c) SGS eddies
d) Diffusion term