UNSWSydney
SEMESTER 1 2017 EXAMINATIONS
MECH4620: COMPUTATIONAL FLUID DYNAMICS
1. TIME ALLOWED-2 hours
2. READING TIME-10 minutes
3. THIS EXAMINATION PAPER HAS 4 PAGES
4. TOTAL NUMBER OF QUESTIONS-2
5. TOTAL MARKS AVAILABLE-100
6. MARKS AVAILABLE FOR EACH QUESTION ARE SHOWN IN THE EXAMINATION PAPER
7. ALL ANSWERS MUST BE WRITTEN IN INK. EXCEPT WHERE THEY ARE EXPRESSLY REQUIRED, PENCILS MAY BE
USED ONLY FOR DRAWING, SKETCHING OR GRAPHICAL WORK
8. THIS PAPER MAY BE RETAINED BY CANDIDATE
9. CANDIDATES MAY BRING UNIVERSITY APPROVED CALCULATOR WITH THE UNSW TAMPER-PROOF STICKER
ON IT TO THE EXAMINATION
10. ANSWER EACH QUESTION IN SEPARATE BOOK
11. USEFUL FORMULAE
Von Neumann Stability Analysis:
1
QUESTION 1 [SO Marks]
(a} The instantaneous time-averaged equation governing the three-dimensional inviscid
conservation of momentum for the u component can be written as
a(pu) a(puu) a(puv) a(puw) ap
--+---+---+---=--at ax 8y az ax (1}
Applying the Reynolds averaging rule such as a= a ; a+ f3 =ii+ p ; ii/3 = ap ;
- - - aa aa
a/J = ii/3 + a'/J'; and - = - , derive the Reynolds-Averaged Navier-Stokes (RANS}as as
form of the above Equation (1).
[10 Marks]
If a mean property rjJ can be defined as <} = P!_ , derive the Favred-Averaged Navier­
p
Stokes (FANS} form of the above Equation (1).
[10 Marks]
Assuming the fluid flow is incompressible, comment on the difference between the
RANS and FANS equations.
[4 Marks]
Based on the above RANS and FANS forms of the governing equation for the u
component, additional terms are introduced through the time-averaging process. What
are these additional terms known as and how are these terms resolved through the
two-equation turbulence framework?
[6 Marks]
(b} What are the commonly applied two-equation turbulence models utilised in CFO? Describe
the main differences between these models. The standard two-equation turbulence
model is commonly used but is limited to predict specific types of flow cases. What are
these flow cases?
(c} Identify the different approaches in resolving wall-bounded turbulence flows.
2
[8 Marks]
[6 Marks]
(d) Describe the different features of Direct Numerical Simulation (DNS), Large Eddy
Simulation (LES) and RANS or FANS for turbulence closure.
[6 Marks]
QUESTION 2 [SO Marks]
PART A
(a) For the stress tensor n = 8.8 .(-p)8 .. +,;, describe the physical meaning of the terms
Z l j ij Z
on the right hand side of Equation.
(b) What would be the simplification for a fluid in static equilibrium?
[S Marks]
[3 Marks]
(c) It can then be shown that 't
ii
= ).,'f:,
ii
ekk + µ( eii +eji ) where the deformation tensor
eii =½(Bu
j + Bui ) , µ is the first coefficient viscosity and A is the second coefficient
Bxi Bxj
viscosity.
Calculate the tensori;
ii
if grad V is given by:
µ=2xl0-1 kg/ms, ).,=10-3 kg/ms
[15 Marks]
Indicate if this fluid is incompressible or compressible.
[2 Marks]
3
PARTB
Consider advection only transport equation in one dimension:
(2)
(a) Write the Finite Difference Approximation (FDA) of Equation (2) using forward
differences in time and upwind differences in space (u < O) for the advection term using
explicit formulation.
(b) Apply Von Neumann stability analysis to FDA written in (a).
[S Marks]
[15 Marks]
(c) Is the scheme unstable, stable or unconditionally stable? Give reasons for your answer
based on your analysis in (b) and specify the stability criterion.
[S Marks]
End of exam paper
4