An Introduction to My CFD Code (2D Version)

Jiannan(Jay) Tan

Highlights• 1. Based on MATLAB.• 2. Aiming on 2D, Steady, Laminar, viscous flow.• 3. Using unstructured, arbitrary-shape,

collocated grids.• 4. Navier-Stokes equations are solved and

velocity and pressure are calculated.• 5. Results are compared with those results

from FLUENT.• 6. A few benchmarking cases are tested.

How does the code work

2D Code

Part 1: Mesh reader Part 2: N-S Equation Solver

Files in certain format that contains the mesh information. For example, the FLUENT *.msh file.

Velocity filed U, V and Pressure P.

Part 3: Post-processing sub-programs

Visualized vector plots and contours.

The Data structure of Mesh

U,V,P

B(xb, yb)

A(xa, ya)

C(xc, yc)

4.Face normal

Cell ID = P

1. Point ID (x, y)2. Face ID (A, B, P, nb, property )3. Cell ID (3, face1, face2, face3)

3 elemental data groups which decide the whole mesh:

1.Flow flux

3.Face area

6.Volume

7.Presssure gradient

2.Face velocity components

5.Face velocity components’ gradient

7 important variables:

The N-S Euqation Solver

( ) ( ( ))U Pt

��������������

( ) 0U ��������������

Momentum equation:

Continuity equation:

1. Discretization: Gauss Theorem

2. Face Mass Flux and Face Scalar

3. SIMPLE Method

4. Least Square Method

5. Pressure-Correction Equation

6. Convergence Criteria

Steady flow

Methodology-SIMPLE MethodInitial guess of u, v and p

Solving the dicretized momentum equations and get interim velocity u, v

Calculating the face mass flux using momentum interpolation method

Solving the discretized continuity equation and geting the pressure

correction p’

Correcting the cell-central pressure and velocity

Convergence reached?

Post-processing

Resuming iteration with

new u, v and p

Discretizing Momentum Equations Using Gauss Theorem

ˆ ˆ( ) ( ( ))U n ds n ds P V ��������������

( ) ( ( ))U dv dv P dv ��������������( ) ( ( ))U P

��������������

. .

( ) [ ( ) ]n d E P Crossnb face nb face

F D D P V 1

.

( ) [ ] ( )n n np p e e p

nb face

a a S P V

Interim velocity u, v

MIM

Pressure-Correcton Equation

.

.

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

up e e nb nb e u e P E e

nb face

vp e e nb nb e v e P E e

nb face

a u a u S P P y

a v a v S P P x

.

.

( ) ( )

( )( ) ( )

( ) ( )

( )( ) ( )

nb nb e u enb face e

e P Eu up e p e

nb nb e v enb face e

e P Ev vp e p e

a u Sy

u P Pa a

a v Sx

v P Pa a

' ' '

' ' '

( )( )

( )( )

ee P E u

p e

ee P e v

p e

yu P P

a

xv P P

a

* * ' '

1

[( ) ( ) ( ) ( ) ] 0Nb

e e e ee

u y v x u y v x

Continuity Equation, assume u=u’+u*

2 2' ' ' '

1

[( )( ) ( ) ( ) ] 0Nb

P E e eu ve P P

y xP P u y v x

a a

' '

1

( ) . . . . .Nb

P P E Ee

a P a P Mass imbalance in to cell P

Momentum Interpolation Method

1. Used after interim velocity is achieved after solving momentum equations.

2. Applied in order to eliminate oscillating pressure field. Sometimes called ‘pressure smooth term’.

3. Used to calculate mass imbalance into each cell in this code.

Least Square Method

Backup slide: A failed try using LSM

Covergence Criteria

• The ratio of Maximum imbalance rate into a single cell over the inlet mass flow rate

Validation & Verification

1. Straight pipe flow

2. Jet flow

3. Flow around a cube

4. Z-pipe flow

Test Case 1: Flow in a straight channel

Case 1: FLUENT solution

U(max)=1.47

Test Case 1: Flow in a straight channel

U(max)=1.46

Test Case 2: Sudden Expansion-Jet Flow

Case 2: FLUENT solution: Velocity vector

U(max)=1.33

Case 2: FLUENT solution: Vortex pattern

Test Case 2: My code solution

U(max)=1.34

Case 2: Comparison of vortex length

Test case 3: Flow in a Z-pipe

Case 3: FLUENT solution: Velocity vector

U(max)=1.44

Case 3: FLUENT solution: Vortex pattern

Test case 3: My code solution

U(max)=1.44

Case 3: Comparison of vortex length

Test case 4: Flow past a square cylinder

Case 4: FLUENT solution: Velocity vector

U(max)=1.43

Case 4: FLUENT solution: Vortex pattern

Test case 4: My code solution

U(max)=1.41

Case 4: Comparison of vortex length

Case 4: Comparison of Cd

FLUENT My Code

Pressure Force 1.275 1.299

Viscous Force 0.601 0.541

Total Force 1.876 1.840

Cd 3.752 3.680

Density =1, viscosity =0.05, Frontal area =1, U=1

Backup slide: Case 4 FLUENT report

Futher Development• 1. Optimization• 2. Different methods to dicretized the momentum euqation.• 3. Different methods to calculate the pressure gradient.• 4. Different methods to do the iteration.• 5. Parallel computation.• 6. Mesh generator.• 7. More advanced models.• 8. Advanced post-processor.• 9. Commercialize the code, sell it to MATLAB :-D