Miss

COMPUTATIONAL FLUID DYNAMICS (MKM411)
Dr. M. Sharifpur [e-mail]

April 2nd
Department of Mechanical and Aeronautical Engineering

University of Pretoria

2013

Test 1 Perusal Friday April 5th 12:00 to 14:00
CFD Training Courses The schedule is already posted on clickUP (find your group in the clickUP)
ANSYS-FLUENT (Group1) FLoEFD ANSYS-FLUENT (Group2) STAR CCM+ (Group 1) STAR CCM+ (Group 2) April 3rd 9:00-17:00 April 10th 9:00-17:00 April 11th 8:00-10:15 and then
11:30 -17:00

April 17th 9:00-17:00 April 24th 9:00-17:00

Finite Difference Method (FDM)
Computational Solution

   

Finding; - Governing (Differential) Equations - Initial & Boundary Conditions

Discretization of the Domain

Changing Differential Eqs. to Algebraic Eqs.

Internal Nodes and Boundary Nodes

Solving the system of Algebraic equations

Example:

Example: A chimney
Inside: Convection Ti  300 oC , hi  70 W/m 2 .o C Outside: Convection + Radiation TO  20 oC , hO  21 W/m 2 .o C

TO , hO Tsky

Tsky  260 K Inside Flow Section: 20 cm x 20 cm
Wall Thickness: 20 cm

TO , hO Tsky

Ti , hi

TO , hO Tsky

if x  y  10 cm k  1.4 W/m. o C and   0.9
Using the advantage of symmetry to find:

TO , hO Tsky

Temp. at all Nodes by FDM

In the Representative Section: How many internal nodes do we have? Only one; Node 4 It can change to 3; Nodes 3,4 & 5 How many nodes do they have the same conditions ? Only Two; Nodes 7 and

8

Node 1


All sides

Q  eVelement  0

Taking x  y  l

Node 2


All sides

Q  eVelement  0

Taking x  y  l

Nodes 3,4 and 5 (Interior nodes)

Node 4 : T3  T5  T7  T2  4T4  0 Node 3 : T4  T4  T1  T6  4T3  0 Node 3 : 2T4  T1  T6  4T3  0 Node 5 : T4  T8  T4  T8  4T5  0 Node 5 : 2T8  2T4  4T5  0

Node 6


All sides

Q  eVelement  0

Taking x  y  l

Nonlinear equation

(T6  273) 4

Node 7


All sides

Q 