TFAWS August 21-25, 2017 NASA Marshall Space Flight Center MSFC - - PowerPoint PPT Presentation

TFAWS

MSFC · 2017

Presented By

Frederick Ferguson Evaluating the Performance of an Improved Finite Volume Method for Solving the Fluid Dynamic Equations

• F. Ferguson, J. Mendez, D. Amoo & M. Dhanasar

Mechanical Engineering Department, NCAT, Greensboro, NC 27411

Thermal & Fluids Analysis Workshop TFAWS 2017 August 21-25, 2017 NASA Marshall Space Flight Center Huntsville, AL

TFAWS AEROTHERMAL Paper Session

2

Presentation Outline

ü Introduction ü CFD: Its Importance & Challenges ü The NS System of Equations: Its Closure ü Expectations: Flow Physics Prediction Capabilities ü The NS Non-Dimensionalization Process ü The IDS Concepts: From Grids to Points, Cells & Control Volumes; Spatial & Temporal Cells ü The IDS – Solving the Integral form of the NS Equations ü IDS – An Explicit Numerical Method, its execution ü IDS Applications

• The Hypersonic Flat Plate, the Shock Boundary Layer

Interaction and the Cross Flow Injection Problems ü Conclusion

TFAWS 2017 – August 21-25, 2017

• Ref. 4 Data

The Importance of CFD

TFAWS 2017 – August 21-25, 2017

Final Product

• Ref. 4 Data

Long Cycle Times Due to

• 1. Grids Generation Req. &
• 2. Fidelity of Simulation Tools

Engineering Perspective: Analysis, Not Design

Potential Benefit Elimination of Complex Grids

CFD Challenges

TFAWS 2017 – August 21-25, 2017

!Use DNS/LES Data to Develop Turbulence Models for CFD Applications

Why Cartesian Grids?

• fast grid generation, numerical &

memory efficiency during parallelization Why Algebraic Turbulence Models?

• numerical & memory efficiency
• capture the basic physics of the process

State-of-the-Art in the CFD Industry

TFAWS 2017 – August 21-25, 2017

Industrial Applications vs CFD Models Computer Speed vs. Time (Year)

http://www.bcs.org/content/conBlogPost/2035

• Historically only Analytical Fluid Dynamics (AFD) and

Experimental Fluid Dynamics (EFD).

• CFD is the computer simulation of fluid dynamic systems through

the use of engineering models (mathematical formulation) and numerical methods (discretization methods and grid generations)

• CFD made possible by the advent of digital computer and advancing

with improvements of computer resources (1947, 500 Flops, à 2003 Teraflops, 2003 à 2015 Petaflops à 2020 Exaflops )

1947 - 500 flops Computer

2003 – 20 Teraflops Computer

Data, Ref. 2

Opportunity

Introduction

TFAWS 2017 – August 21-25, 2017

Plus the Boundary & Initial Conditions

NS Eqs: System of Conservations Laws

òòò òò

= + ¶ ¶

v s

s d V dv t r r

( )

s d s Pd V s d V dv V t

s s s v

òò òò òò òòò

+

• =

+ ¶ ¶ t r r ˆ .

òò òò òò òò òòò

+ +

• =

+ ¶ ¶

s s s s v

s d q s d V s d V P s d V E Edv t ! . ˆ . . t r r

Research Objective: To Solve the NS Equations

• Applicable to a wide Class of Fluid Dynamic Problems
• Accurate Flow Physics Capturing Capabilities
• Efficient Grid Generation & Solution Process

Introduction

TFAWS 2017 – August 21-25, 2017

÷ ÷ ø ö ç ç è æ ¶ ¶ + ¶ ¶ = = x v y u

yx xy

µ t t ÷ ø ö ç è æ ¶ ¶ + ¶ ¶ = = x w z u

zx xz

µ t t ÷ ÷ ø ö ç ç è æ ¶ ¶ + ¶ ¶ = = z v y w

zy yz

µ t t

x T k qx ¶ ¶

• =

! y T k q y ¶ ¶

• =

!

z T k qz ¶ ¶

• =

!

Viscous Relations

Equations and formulas from: J. D. Anderson(1995) : “Computational Fluid Dynamics-The basics with applications”, McGraw-Hill, Inc.

÷ ÷ ø ö ç ç è æ ¶ ¶

• ¶

¶

• ¶

¶ = z w y v x u

xx

2 3 2 µ t

÷ ÷ ø ö ç ç è æ ¶ ¶

• ¶

¶

• ¶

¶ = z w x u y v

yy

2 3 2 µ t ÷ ÷ ø ö ç ç è æ ¶ ¶

• ¶

¶

• ¶

¶ = y v x u z w

zz

2 3 2 µ t

TFAWS 2017 – August 21-25, 2017

The Closed System of the Equations

Ø The closed system of the equations has only five unknowns

( )

T w v u , , , , r

Ø Additional relations § Equation of state § Internal energy § Sutherland’s law for viscosity § Prandtl number

RT P r =

T C e

v

= ( )

T k k =

110 110

5 . 1

+ + ÷ ÷ ø ö ç ç è æ =

¥ ¥ ¥

T T T T µ µ

TFAWS 2017 – August 21-25, 2017

10

!Examples of Problems to be solved Shock/Boundary Layer Interaction Flow Over Blunt Body

Capability: Predicted Flow Physics

TFAWS 2017 – August 21-25, 2017

TFAWS 2017 – August 21-25, 2017

11

Computational Flow Physics@Caltech

• Ref. Y. You, et al: Flow physics of a low momentum jet in supersonic crossflow

Capability: Predicted Flow Physics

!Examples of Problems to be solved

IDS: Non-Dimensionalization Process

Geometric Variables L x x =

L y y = L z z =

¥

= µ µ µ

¥

= k k k

Fluid Properties

¥

= r r r

¥

= u u u

¥

= u v v

¥

= T T T

¥

= u w w Fluid Parameters/IDS Solution Variables

air

R k T V L , , , , , , , g µ r

¥ ¥ ¥ ¥ ¥

IDS Code Inputs: + Grids & I&B Cdts

TFAWS 2017 – August 21-25, 2017

13

( ) ( )

¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥

= = =

• =
• =

RT V M k C L V R C R C

p air p air v

g µ µ r g g g ; Pr , Re , 1 , 1

Non-Dim Properties to be Computed

( )

¥ ¥ ¥

+ + = = T T T T 110 110 . 1

5 . 1

µ µ µ

Properties Computed from Inputs

( ) ( ) ( ) ( )

¥ ¥ ¥ ¥ ¥ ¥

+ + + = = k C T T C T T C T T C k T T k k

k k k k 1 2 2 3 3

IDS: Non-Dimensionalization Process L t u u L t t t t

¥ ¥ ¥ ¥

= = = =

T RT RT a a a = = =

¥ ¥

g g

2 ¥ ¥

= u P P r

Derived No-Dim Variables

TFAWS 2017 – August 21-25, 2017

14

( )

T M V e e

2 2

1 1

¥ ¥

• =

= g g

T M P r g

2

1

¥

=

( ) ( ) ( )

2 6 5 4 2 3 2 2 2 1

1 Pr 1 Re 1 1 1 ; Re 1 Re 1 3 2 ; 1 1 ; 1 ; 1 1

¥ ¥ ¥ ¥ ¥ ¥ ¥ ¥

• =

= =

• =

=

• =

M C C C M C M C M C

NS NS NS NS NS NS

g g g g g

e k h H e k e E

Total Total

+ = + = ;

( )

T M V h h

2 2

1 1

¥ ¥

• =

= g

( )

2 2 2 2 2

2 1 w v u V V e k + + = =

¥

Non-Dim Properties to be Computed IDS NS Coefficients

IDS: Non-Dimensionalization Process

15

IDS - Solving the Integral Equations on Cartesian Grids

òòò òò

= + ¶ ¶

v s

s d V dv t r r

( )

s d s Pd V s d V dv V t

s s v

òò òò òò òòò

+

• =

+ ¶ ¶ t r r ˆ .

òò òò òò òò òòò

+ +

• =

+ ¶ ¶

s s s s v

s d q s d V s d V P s d V E Edv t ! . ˆ . . t r r

The conservation of mass , momentum, and energy equations

TFAWS 2017 – August 21-25, 2017

An IDS Cell != Control Volume

TFAWS 2017 – August 21-25, 2017

• It’s A Physics based Approach
• It consists of points, cells & surfaces

Consider a rectangular Prism …

Point Surface Cell

IDS Control Volume Representation

TFAWS 2017 – August 21-25, 2017

• The Spatial & Temporal Cells
• The 2D Control Volume

An IDS Control Volume

i,j,k z x y üPoints üCells üControl Volume Key Features

TFAWS 2017 – August 21-25, 2017

TFAWS 2017 – August 21-25, 2017

19

a Flow enters from the lower side 1 2 4 3 Flow leaves from the upper side Flow enters from the left side Flow leaves from the right side dy dx dz 2’ 1’ 3’ 4’

òòò òò

= + ¶ ¶

v s

s d V dv t r r

( ) ( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) [ ]

ï þ ï ý ü ï î ï í ì + + +

• +

+ + D ï þ ï ý ü ï î ï í ì + + +

• +

+ + D ï þ ï ý ü ï î ï í ì + + +

• +

+ + D = ÷ ø ö ç è æ ¶ ¶

¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ ¢ plus us plus us plus us average cell

w w w w w w w w z v v v v v u v v y u u u u u u u u x t

4 3 2 1 min 4 3 2 1 4 3 2 1 min 4 3 2 1 4 3 2 1 min 4 3 2 1

4 1 4 1 4 1 r r r r r r r r r r r r r r r r r r r r r r r r r

The Mass Conservation Equation in an IDS Cell

dxdydz t

Center Cell

ú û ù ê ë é ¶ ¶r

òòò òò

= + ¶ ¶

v s

s d V dv t r r

( ) ( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) [ ] ( ) ( ) ( ) ( ) [ ]

ï þ ï ý ü ï î ï í ì + + +

• +

+ + D + ï þ ï ý ü ï î ï í ì + + +

• +

+ + D + ï þ ï ý ü ï î ï í ì + + +

• +

+ + D = ÷ ø ö ç è æ ¶ ¶

plus us plus us plus us average cell

w w w w w w w w z v v v v v u v v y u u u u u u u u x t

4 3 2 1 min 4 3 2 1 4 3 2 1 min 4 3 2 1 4 3 2 1 min 4 3 2 1

4 1 4 1 4 1 r r r r r r r r r r r r r r r r r r r r r r r r r

Example of the IDS –Spatial Scheme

TFAWS 2017 – August 21-25, 2017

( )

( ) ( )

...

6

+

• =

×

• +

= =

å

dydz u dydz u ds n V

Avg nx Avg nx i Surface i Surface s s

i i

r r r ! !

1 2 4 3

a dy dx dz =1

2’ 1’ 3’ 4’

( )minus

u r

( )plus

v r

( )plus

u r

( )minus

v r

( )minus

w r

( )plus

w r

The Mass Conservation Equation in an IDS Cell

TFAWS 2017 – August 21-25, 2017

21

Mass Conservation in an IDS Cell/2D Concept

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

ú û ù ê ë é D +

• +

+ ú û ù ê ë é D +

• +

= ÷ ø ö ç è æ ¶ ¶ y 2 v v v v x 2 u u u u t

4 3 2 1 3 2 4 1 average

r r r r r r r r r

a 1 2 4 3 2’ 1’ 3’ 4’

u r

v r

u r

v r

Assumptions for 2D IDS Concept

• 2 Planes are identical
• dz = 1.0

TFAWS 2017 – August 21-25, 2017

22

Momentum Conservation in an IDS Cell/2D Concept

( )

( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

( )

( )

( )

( )

ú ú ú û ù ê ê ê ë é D

• +

D

• ú

û ù ê ë é D +

• +

+ ú û ù ê ë é D +

• +

+ ú ú û ù ê ê ë é D +

• +

= ÷ ø ö ç è æ ¶ ¶

¥

y x 1 x 2 T T T T M 1 y 2 vu vu vu vu x 2 u u u u t u

upper xx lower xy right xx left xx L 3 2 4 1 2 4 3 2 1 3 2 2 2 4 2 1 2 average

t t t t r r r r g r r r r r r r r r Re

( )

( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

( ) ( )

( )

( ) ( )

( )

ú ú ú û ù ê ê ê ë é D

• +

D

• ú

û ù ê ë é D +

• +

+ ú û ù ê ë é D +

• +

+ ú ú û ù ê ê ë é D +

• +

= ÷ ø ö ç è æ ¶ ¶

¥

x y 1 y 2 T T T T M 1 x 2 uv uv uv uv y 2 v v v v t v

right xy left xy upper yy lower yy L 4 3 2 1 2 3 2 4 1 4 2 3 2 2 2 1 2 average

t t t t r r r r g r r r r r r r r r Re

TFAWS 2017 – August 21-25, 2017

23

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) ( ) ( )

( ) ( )

( )

( ) ( )

( )

ú ú ú û ù ê ê ê ë é D

• +

D

• +

ú û ù ê ë é ÷ ÷ ø ö ç ç è æ D +

• ÷

÷ ø ö ç ç è æ D +

• ú

ú û ù ê ê ë é ÷ ÷ ø ö ç ç è æ D +

• ÷

÷ ø ö ç ç è æ D +

• ú

ú û ù ê ê ë é ÷ ÷ ø ö ç ç è æ D +

• ÷

÷ ø ö ç ç è æ D +

• ú

û ù ê ë é ÷ ÷ ø ö ç ç è æ D +

• ÷

÷ ø ö ç ç è æ D +

• ú

ú û ù ê ê ë é ÷ ÷ ø ö ç ç è æ D +

• ÷

÷ ø ö ç ç è æ D + + ú û ù ê ë é ÷ ÷ ø ö ç ç è æ D +

• ÷

÷ ø ö ç ç è æ D + + ú ú û ù ê ê ë é ÷ ÷ ø ö ç ç è æ D +

• ÷

÷ ø ö ç ç è æ D + + ú û ù ê ë é ÷ ÷ ø ö ç ç è æ D +

• ÷

÷ ø ö ç ç è æ D + = ÷ ø ö ç è æ ¶ ¶

¥ ¥ ¥

y q q x q q M 1 x 2 u u x 2 u u 1 y 2 v v y 2 v v 1 y 2 v v y 2 v v 1 x 2 u u x 2 u u 1 y 2 Tv Tv y 2 Tv Tv M 1 x 2 Tu Tu x 2 Tu Tu M 1 y 2 Ev Ev y 2 Ev Ev x 2 Eu Eu x 2 Eu Eu t E

upper yy lower yy right xx left xx 2 L 4 1 right xy 3 2 left xy L 2 1 upper yy 4 3 lower yy L 2 1 upper xy 4 3 lower xy L 4 1 right xx 3 2 left xx L 4 3 2 1 2 3 2 4 1 2 4 3 2 1 3 2 4 1 average

! ! ! ! Pr Re Re Re Re Re t t t t t t t t r r r r g r r r r g r r r r r r r r

Energy Conservation in an IDS Cell/2D Concept

IDS Control Volume Representation

TFAWS 2017 – August 21-25, 2017

• The Spatial & Temporal Cells
• The 2D Control Volume

IDS Implementation Steps for Control Volume

ú ú ú ú ú ú û ù ê ê ê ê ê ê ë é = ú ú ú ú ú ú û ù ê ê ê ê ê ê ë é = E w v u U U U U U U m r r r r

5 4 3 2 1

t dt dU U U

k j i m t k j i m t t k j i m

D ÷ ø ö ç è æ + =

D + , , , , , ,

) ( ) (

Construct the solution using Taylor Series Expansion

Ø Control volume of center i,j,k; surrounded by 8 cells-3D/4 cells-2D. Evaluate the generic function U as an arithmetic average.

( )

å

=

=

8 1 , ,

8 1

cell average cell t k j i

U U

Ø The time derivative at node i,j,k is obtained as an arithmetic average of the time derivatives at the cell centers.

å

=

÷ ø ö ç è æ = ÷ ø ö ç è æ

8 1 , ,

8 1

cell cell m k j i m

dt dU dt dU

TFAWS 2017 – August 21-25, 2017

( )

1 2 2 2 , , ' 2 2 2 , , , , , , , , ,

1 1 1 Re 2 1 1 1

• ú

ú ú ú ú û ù ê ê ê ê ê ë é ÷ ÷ ø ö ç ç è æ D + D + D + D + D + D + D + D + D = D z y x z y x a z w y v x u t

k j i L j i k j i k j i k j i k j i CFL

n

Ø Use the following CFL Criterion to evaluate the time step

( )

ú ú ú ú û ù ê ê ê ê ë é =

k j i k j i k j i k j i , , , , , , , , '

Pr / , 3 4 max r gµ µ n

t dt dU U U

k j i m

• ld

k j i m new k j i m

D ÷ ø ö ç è æ + =

, , , , , ,

) ( ) (

Ø Update the solution Ø Decouple the new variables

( )

new k j i new k j i

U

, , 1 , ,

= r

new k j i new k j i

U U u

, , 1 2 , ,

÷ ÷ ø ö ç ç è æ =

new k j i new k j i

U U v

, , 1 3 , ,

÷ ÷ ø ö ç ç è æ =

new k j i new k j i

U U w

, , 1 , ,

4 ÷ ÷ ø ö ç ç è æ =

( )

2 , , 2 2 2 1 5 , ,

1 2

¥

• ÷

÷ ø ö ç ç è æ + +

• =

M w v u U U T

new k j i new k j i

g g

TFAWS 2017 – August 21-25, 2017

IDS Implementation Steps

Test Case 1: The Inviscid-Viscous Interaction Problem: Illustrative Physics of the Inviscid-Viscous Interaction Flow field

TFAWS 2017 – August 21-25, 2017

M =8.6, Re=4.37861*10.0E+5, Pr=0.70, γ= 1.4

Test Case 1: The Inviscid-Viscous Interaction Problem: Grid Independence: Validation Flow Parameters

Non-Dimensional Density y-axis 1 1.05 1.1 1.15 1.2 1.25 1.3 1.35 1.4 1.45 1.5 1.55 1.6 0.005 0.01 0.015 0.02 Leading Edge Density for Grid 1001 by 1001 Leading Edge Density for Grid 801 by 801 Leading Edge Density for Grid 601 by 601 Leading Edge Density for Grid 401 by 401 Leading Edge Density for Grid 201 by 201 Non-Dimensional Temperature y-axis 0.95 1 1.05 1.1 0.005 0.01 0.015 0.02

Non-Dimensional uVelocity y-axis 0.8 0.85 0.9 0.95 1 0.005 0.01 0.015 0.02 Leading Edge uVelocity for Grid 1001 by 1001 Leading Edge uVelocity for Grid 801 by 801 Leading Edge uVelocity for Grid 601 by 601 Leading Edge uVelocity for Grid 401 by 401 Leading Edge uVelocity for Grid 201 by 201 Non-Dimensional vVelocity y-axis 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.005 0.01 0.015 0.02 Leading Edge vVelocity for Grid 1001 by 1001 Leading Edge vVelocity for Grid 801 by 801 Leading Edge vVelocity for Grid 601 by 601 Leading Edge vVelocity for Grid 401 by 401 Leading Edge vVelocity for Grid 201 by 201

M =8.6, Re=4.37861*10.0E+5, Pr=0.70, γ= 1.4

TFAWS 2017 – August 21-25, 2017

Test Case 1: The Inviscid-Viscous Interaction Problem: Illustrative Physics of the Inviscid-Viscous Interaction Flow field

M =8.6, Re=4.37861*10.0E+5, Pr=0.70, γ= 1.4

TFAWS 2017 – August 21-25, 2017

Test Case 2: Shock Boundary Layer Interaction: General Physics of the flow

http://archives.limsi.fr/RS2005/meca/aero/aero3/

TFAWS 2017 – August 21-25, 2017

x-axis y-axis

0.45 0.475 0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2

0.932 0.867 0.860 0.857 0.853 0.850 0.849 0.848 0.848 0.848 0.847 0.796 0.730 0.728 0.660 0.457 0.253 0.136 0.049 0.005

• 0.019
• 0.037
• 0.044
• 0.051
• 0.062
• 0.070
• 0.080

Test Case 2: Shock Boundary Layer Interaction: IDS Numerical Results u- Velocity

TFAWS 2017 – August 21-25, 2017

x-axis y-axis

0.45 0.475 0.5 0.525 0.55 0.575 0.6 0.625 0.65 0.025 0.05 0.075 0.1 0.125 0.15 0.175 0.2

0.137 0.121 0.105 0.089 0.073 0.056

• 0.057
• 0.074
• 0.090
• 0.106
• 0.122
• 0.138
• 0.155
• 0.171
• 0.187
• 0.203
• 0.220
• 0.236
• 0.252
• 0.268
• 0.285

Test Case 2: Shock Boundary Layer Interaction: IDS Numerical Results u- Velocity

TFAWS 2017 – August 21-25, 2017

Injector

14http://www.stanford.edu/group/psaap/heat_release_modeling/Jet_cross-flow.html.

• 15R. S. Amano and D Sun, ‘Numerical Simulation of Supersonic Flowfield with Secondary Injection’, 24th International Congress of the Aeronautical Sciences, ICAS 2004

MR Gruber, AS Nejad, JC Dutton, An experimental investigation of transverse injection from circular and elliptical nozzles into supersonic crossflow. wright lab technical report, WL-TR (1996), pp. 96–2102

Mach Disk Separation induced shock

Test Case 3: The Mach Jet Flow Interaction Problem/ Stanford Experimental Result

x-axis Non-Dim Pressure, Density and Temperature 0.7 0.725 0.75 0.775 0.8 10 20 30 40 50 60 70 80 90 100

Density Pressure Temperature

Test Case 3: The Mach Jet Flow Interaction Problem: Input Values for Jet Injection

TFAWS 2017 – August 21-25, 2017

Test Case 3: The Mach Jet Flow Interaction Problem: IDS Numerical Result: Mach Contours

. 9 2 3 9 6 9 0.999312 0.962082 0.999312

x-axis y-axis 0.7 0.72 0.74 0.76 0.78 0.8 0.01 0.02 0.03 0.04 0.05 0.06

5.625 5.250 4.875 4.500 4.125 3.750 3.375 3.000 2.625 2.250 2.164 2.130 2.087 2.034 1.875 1.761 1.500 1.265 1.125 0.999 0.962 0.924 0.902 0.750 0.375 0.175 0.164 0.148 0.119 0.083 0.061 0.054 0.047 0.033 0.022 0.013 0.004

Mach Disk Injector

MR Gruber, AS Nejad, JC Dutton, An experimental investigation of transverse injection from circular and elliptical nozzles into supersonic crossflow. wright lab technical report, WL-TR (1996), pp. 96–2102

TFAWS 2017 – August 21-25, 2017 M =6.0, Re=1.086*10.0E+7, Pr=0.042, γ= 1.4

uVelocity Contours with Velocity-vector Overlayed

Test Case 3: The Mach Jet Flow Interaction Problem: IDS Numerical Result: u-Velocity

x-axis y-axis

0.7 0.72 0.74 0.76 0.78 0.8 0.01 0.02 0.03 0.04 0.05 0.06

0.965 0.894 0.823 0.752 0.682 0.611 0.540 0.469 0.399 0.328 0.257 0.222 0.151 0.080 0.010

• 0.001
• 0.005
• 0.011
• 0.026
• 0.035
• 0.061
• 0.132

M =6.0, Re=1.086*10.0E+7, Pr=0.042, γ= 1.4

TFAWS 2017 – August 21-25, 2017

vVelocity Contours with Velocity-vector Overlayed

Test Case 3: The Mach Jet Flow Interaction Problem: IDS Numerical Result: v-Velocity

x-axis y-axis

0.7 0.72 0.74 0.76 0.78 0.8 0.01 0.02 0.03 0.04 0.05 0.06

0.414 0.390 0.367 0.343 0.320 0.296 0.273 0.250 0.226 0.203 0.179 0.156 0.133 0.109 0.086 0.062 0.039 0.015 0.004 0.000

• 0.000
• 0.003
• 0.008
• 0.016
• 0.031
• 0.055
• 0.078

M =6.0, Re=1.086*10.0E+7, Pr=0.042, γ= 1.4

TFAWS 2017 – August 21-25, 2017

Conclusions

Ø A IDS for solving the Q1D/2D/3D forms of the system of the Navier- Stokes equations was developed and tested. Ø The capability of the IDS with respects to predicting the flow physics for wide class of problems (Q1D flows, incompressible flows, compressible external flows and compressible internal flows) was evaluated. Ø In all cases the results showed very good agreement with the physical expectation of the flow fields, and with available experimental data. Ø The IDS 2D FORTRAN code is capable of running on multiple HPC platforms (with OpenMP and MPI capability). Ø Extension of IDS to Arbitrary Geometries is currently being explored. Ø The IDS 3D is being updated to run of HPC, with OpenMP & MPI capablilty. Ø An Error Analysis of the IDS Concept is in progress.

TFAWS 2017 – August 21-25, 2017

Questions?

TFAWS 2017 – August 21-25, 2017