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MECH4620: COMPUTATIONAL FLUID DYNAMICS
创建日期：2024-05-05 17:49:17
标签： MECH4620
COMPUTATIONAL FLUID DYNAMICS
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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]
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MGMTMFE 405 25579 1ECE 273 M122 COMP4434 1ELEC ELEC5620M STAT0010 BFF2401 MXB361 MATH3811 CS330 CMT307 FIT1033 CptS 583 UP 431 MATH6005 AF5343 CS2435 ECOM30002 ES50061 CS 2506 ECMT6002 CODE 00099F MT4539 ESSAY ICM317 MATH1231 MFIT5010 BMA547 MATH334 CIVL2201 MATH39032 T-04 CIVE97119 EMESTER CAB302 CAB301 59PM STAT802 ISYS3412 RM3 COSC 2123 AcF 311 MATH2022 1FINAL 4CCS1PHC ICM 142 ENVS3023 Math 4023 I1 ACSE8 FIN B385F CS-275 STA 4109-01 A31021 EE140 MT1 EE124 ECO-6004B Inf2-IADS CS126 IS2184 UL18 MATH5092 ECOM009 COMP 6211 ELEC202 MKT3019 IAB230 FIT5046 584-S21 COMP3210 CO250 A29401 MATH 136 MGT6174 ECMT6007 DATA2001 MAT 443 MATH10222 PHDE0071 ELE00123M COSC1295 MAT00045H MATH32032 1004GRC MAS223 COMP10001 DATA3404 CIVL2110 STAT2008 FNCE10002 EEE6431 COM6515 COMP9120 NBS8185 ECTE942 ECON 405 MATH314301 STAT 2011 COMPSCI 350 COMP20007 CMPSC-132 ECON5002 STA 35 MTH6108 FIT5147 MTH6150 100C FINA 5260 DESC9115 ECON4998 NBS8257 GMM ECON 6070 BSA2 ECE599 STATS 102B STA120 INFS601 BFC3241 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MOEC0021 STA 106 ENGG 1300A ENGG 1300 OLET1139 STAT 3503 STAT 206 FEM11149 ELEN 4720 COMP20003 SOLA1070 CS574 C11CS LINB29H3 MAST90083 ECON7200 STAT 610 LINB29 DSM-5 COMP3161 EEEN40010 MATH 4431 K353 STA 3386 IERG4300 COMS W4167 ENG5298 AMME 2302 CS3910 COMPSCI 320 STATS 369 GR5242 COSC 328 CSCI435 MGTS1301 INFS2200 COMP3900 CIS 375 Module AE03 COMP3121 CS260 HAM503 MGMT5050 INT3075 COSC 285 GEOL0029 GEGE2X01 STAT1201 MATH1061 MMF1941H STAT 5060 CS 520 COMP 4320 MSIN0104 000T FINS3648 ECMT2160 ECON4003 Phys 129L CSE 142 CS 3130 MGEB01 EECS 340 Finance (20443/20444) ECMM149 COMP5310 EEEN60180 CSC 111 AT2 CSCI 4430 STAB57 MA/CSC 427 MATH322 D100 CSCI544 CITS3004 CI6227 CSE 565 APCO 1P01 852L1 ELEC S411F COMP3207 STATS330 ECON7530 FIT5149 CSI4104 CMPT 371 COMP201 SEHS4696 FI4003 MATH6182 CG1 WS MATH401 MGT 205 QTM 110 COMP 0137 MACE12201 FIT5210 ECE 544 BISM7206 HUDM 6055 ECON3203 STATS 210 MSCI 570 MATH6173 COMPSCI4039 Accounting COM3503 AOE2024 ECON213 PSYC10004 Control Data 100/200A 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COMP2013 IB9X60 INVP001 EMATM0051 COMP220 BLAW1002 E20 TCP8001 ECON61001 EART40005 ECONM1022 MATH 365 MATH 367 ELEC6218 COMP 5812M EDUC 5061M ELEC ENG 1101 equation MATH6174 ST334 C4 EC9570 A33648 EBUS603 ECON47815 stata WFMS0001 PEM102 INF6060 ionically ELECTRICAL MATH 375 MMW 12 MKTG860 ECON60401 ALY6010 SOST20131 Introduction COM3524 MME2 GGR305 JNB 538 EECS101 COMM5030 IEOR E4601 2B CSC336 EN2315 LAW 432 CSC263 MATH2001 OLET1143 CSCB63 SIT772 COMM1170 STAT 441 MS930 INFT3050 GLBH0030 Stat 120B MAST10007 MGEC61 Machine GGR 252H1S ECON7030 Financial Marketing MGMT30019 ECON5120 SDSC 8009 CSC165H1S DSCI 551 3081W ACM41000 ECA 5304 MATH 1064 ECSE444 DATA 604 COMP7105 MIE1615 ECON4004 ENV200H1S EC481 MKT 306 EC1B1 MATH08051 ALY6140 CS260C CSE30 MSIN0226 CS4103 CSC3064 AM16 COMP11212 CSE4101 PSTAT 174 Math 380W CNT 5106C STAT 310 FIN2028 CS5014 STAT 425 COMP 4102A ELEC2140 MANF9544 QRM 9 QRM 8 ECON 457 COMPSCI 4091 MATH 523 DNSC-4211 PEAS 6000 MSIN0180 COMP2119 A2A HT 2022 IB93F0 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