Unsteady CFD Simulations of Moving Flow-Control … · Unsteady CFD Simulations of Moving Flow-Control Valves by an Unstructured Overset-Grid Method ... lift and drag forces on a

Unsteady CFD Simulations of Moving Flow-Control Valves by an Unstructured Overset-Grid Method

Ph.D. Prelim Exam Presentation

Jingxin LiuJingxin Liu

Advisory Committee:

Dr Akin Ecer (co chair)Dr. Akin Ecer (co-chair)Dr. Steve Frankel (co-chair)Dr. Hasan U. AkayDr. Gregory A. BlaisdellDr. Jayathi Y. Murthy

Department of Mechanical EngineeringIUPUI/Purdue UniversityIUPUI/Purdue University

January 31, 2008

Outline

• Research Motivation and Approach

• Methodology

• CFD Solver Equations and Boundary Conditions

• Case Studies

• Conclusions

Jingxin Liu's Prelim Exam, Jan. 31, 2008, IUPUI

MotivationMotivation

• Danhan and Solliec has studied flow-control valves experimentally and stated the complexity of such flows (ASME Journal of Fluid Engineering, Vol. 122, pp.337-344 , 2000)

• Silvester has developed a simple analytical model for predicting the aerodynamic torque of flow-control valves (Proceedings Institute of Mechanical Engineering, Vol. 196, pp. 229-237, 1982)

• Leutwyler and Dalton used the commercial CFD code Fluent to predict steady aerodynamic torque, lift and drag forces on a 2-D butterfly valve model (ASME Journal of Fluid Engineering, Vol. 128, pp. 1074-1082, 2006)

• The flow field of compressible fluid in a flow-control valve with pmovements is quite complex and can be rather challenging for any CFD algorithm (R. Morita, ASME Journal of Fluid Engineering, Vol. 129, pp. 48-54, 2007)

• No detailed CFD simulations of 3D, unsteady compressible flows around moving valves were found existing in the literature.


Approach: Leading TechniquesApproach: Leading Techniques

Three leading techniques for treatment of grids surrounding movingbodies exist in the literature:

D f i id A bit L i E l (ALE) f l ti d Th• Deforming grids: Arbitrary Lagrangian-Euler (ALE) formulation are used. These guarantee conservation and a smooth variation of grid size. They need re-meshing and smoothing techniques.

Ad ti C t i G id Th d t i hi h t• Adaptive Cartesian Grids: These do not require re-meshing or mesh movement (ALE is not used). They need to detect the location of boundaries with respect to the mesh to refine/coarsen the mesh as the bodies move.

O t G id D t i hi ll f i d d t id f• Overset Grids: Do not require any re-meshing, allow for independent grids for components and the body. ALE techniques are required for moving the bodies.


Approach: Proposed Solution with an Unstructured Overset Grids Method

• While structured overset grid methods have been well developed,While structured overset grid methods have been well developed, unstructured overset grid algorithms have been not as popular.

• In conventional CFD unstructured overset grid methods,• Establishing inter-grid communication between sub-grids is not trivialEstablishing inter grid communication between sub grids is not trivial,• Usually manual hole cutting and inefficient searching algorithms are

used,• Considerable modifications flow solvers are required.

• Proposed unstructured overset grid method provides,• A systematic and automated hole-cutting process,• An efficient searching algorithm,• One-cell overlapping width reducing the computational effortOne cell overlapping width reducing the computational effort,• Ease in integration to the CFD solver with very few changes• Ease in modeling complex geometries and movements. Once an

unstructured mesh around a moving body (minor grid) is generated, it is coupled with a background grid for the entire flow domain for anycoupled with a background grid for the entire flow domain for any specified motion.


Methodology: Definition of overset gridMethodology: Definition of overset grid

Each body has its own attached grid independently generated. Due to the y g p y garbitrary position of the different bodies/grids, some nodes can be located in thesolid regions, namely non-flow/non-computational domains. These nodes have to be removed from the flow calculations.

Original grids Grids after hole cutting

Methodology: Hole Cutting ProcessMethodology: Hole-Cutting Process

St 1 H l C tti f Mi G idStep 1. Hole Cutting for Minor Grid1.1 Check if boundary of background grid overlap with that of minor grid by using

a recursive searching algorithm by building a data tree of bounding box, (if not, go to Step 2).

Valve in 30-degree position (no intersection between boundaries)

Valve in 60-degree position (Intersection occurs between boundaries)

Methodology: Hole Cutting Process (cont’d)Methodology: Hole-Cutting Process (cont d)

Step 1. Hole Cutting for Minor Grid1.2 Remove inactive cells which have inactive vertexes and form new boundaries by an

improved vector intersection algorithm.

Minor grid before hole cutting Minor grid after hole cutting

Methodology: Hole Cutting Process (cont’d)Methodology: Hole-Cutting Process (cont d)

Step 2. Hole Cutting for background grid2.1 Remove inactive cells which have inactive vertexes and form new boundaries by an

improved vector intersection algorithm.

Minor grid after hole cutting Background grid after hole cutting

Methodology: Searching and Interpolation gy g

Step 3: Donor cell searching and interpolation stencil building: Get donor cell from background grid for fringe boundary points of minor grid.

3.1 Build Alternate-Digital Tree (ADT) for all background grid cells,3.2 Build recursive searching algorithm,3.3 Get donor cell and interpolation coefficients using volume rate linear

interpolationinterpolation.

Methodology: Searching and Interpolation (cont’d)

Ill t ti f th ADT S hi Al ithIllustration of the ADT Searching Algorithm

Methodology: Searching and Interpolation ( t’d)(cont’d)

Step 4: Get donor cell from minor grid for fringeStep 4: Get donor cell from minor grid for fringe boundary points of background grid

4.1 Build Alternate-Digital Tree (ADT) for all background grid cells,4 2 B ild i hi l ith4.2 Build recursive searching algorithm,4.3 Get donor cell and interpolation coefficients by using volume rate

linear interpolation.


Integration to the CFD Solver: SunFlo

The CFD solver, SunFlo, is an IUPUI CFD Lab version of an external flow code, (USM3D), developed at NASA. It is based on a cell-centered, finite volume Euler and Navier-Stokes flow solver for viscous/inviscid, compressible flows (Frink, 1990)

Modifications made to SunFlo for this research:1. Internal flow boundary conditions based on Riemann invariants were

implemented,implemented,

2. Overset griddling algorithm was developed,

3. A boundary type added for interpolating between overset grids..

Grid Generator: All the meshes used in this research were generated by using VGRIDns, developed by S. Pirzadeh (AIAA Journal, Vol. 32, No. 8, pp.1735-1737, August 1994)g )


CFD Solver: Flow EquationsC So e o qua o s

• Flow equations (Arbitrary Lagrangian-Euler (ALE) formulation)• Flow equations (Arbitrary Lagrangian Euler (ALE) formulation)

∫ Ω∂ =⋅−+∂

∂ 0ˆ)()( dSnFFtVQ

i ν

rrr

)(V

dVqQ ∫Ω=

rr

jpWvv

Wvu

Wv

iWuvpWuu

Wu

F y

y

y

x

x

x

iˆ)(

)(

)(

ˆ)()(

)(

⎥⎥⎥⎥⎤

⎢⎢⎢⎢⎡

+−

−

−

+⎥⎥⎥⎥⎤

⎢⎢⎢⎢⎡

−+−

−

= ρ

ρ

ρ

ρρρ

r jiF yy

xy

yx

xx

vˆ

0

ˆ

0

⎥⎥⎥⎥⎤

⎢⎢⎢⎢⎡

+⎥⎥⎥⎥⎤

⎢⎢⎢⎢⎡

= ττ

ττ

r

Ww

pWWvpE

WvwpWWupE

Wuw

z

yy

y

y

xx

x

)(

))((

)())((

)(

⎤⎡ −

⎥⎥⎥⎥

⎦⎢⎢⎢⎢

⎣ +−+

−⎥⎥⎥

⎦⎢⎢⎢

⎣ +−+−

ρ

ρρqwvuqwvu yyzyyyx

zy

xxzxyxx

zx

0⎥⎤

⎢⎡

⎥⎥⎥

⎦⎢⎢⎢

⎣ −++⎥⎥⎥

⎦⎢⎢⎢

⎣ −++ ττττ

ττττ

kpWww

WwvWwu

z

z

z

z

ˆ

)()()(

)(

⎥⎥⎥⎥⎥⎥⎤

⎢⎢⎢⎢⎢⎢⎡

+−−−

+ρρρρ

k

zz

yz

xz

ˆ

⎥⎥⎥⎥⎥⎥

⎢⎢⎢⎢⎢⎢

+τττ

pWWwpE zz))(( ⎥⎦⎢⎣ +−+ qwvu zzzzyzxx⎥⎦⎢⎣ −++ τττ


CFD Solver: Boundary Conditions

Moving boundary:

For moving boundaries, wall boundary conditions are modified by taking into account the mesh movementsaccount the mesh movements,

]ˆ)[(ˆ.._ nWVnVV fluidfluidCBoutter ⋅−⋅−=

where, W is the grid moving velocity., g g y

For no-slip wall boundary condition, it becomes, .WVwall =

The wall pressure is calculated from the normal momentum equation asThe wall pressure is calculated from the normal momentum equation as,

wannp

⋅−=∂∂ ρ

where, wa is the acceleration of the body wall.


CFD Solver: Turbulence Model• Spalart-Allmaras (S-A)

jiuuρ−The Reynolds stress tensor ( ) is related to the mean strain rate through an apparent turbulent viscosity called eddy viscosity :

)( ji uu ∂∂ ~νρµ f)(i

j

j

itji xx

uu∂

+∂

=− µρ 1ννρµ ft =

where 33

3

1ν χχ

Cf

+= νχ

~:=,

,

where1νχ C+ ν

χ,

The PDE, which is solved separately from the flow equations , is in the following form:

2221

~

]~)~[(1~~]1[)~(~

C

CSfCuxt btbj

j

−∇+∇+⋅∇+−=∂∂

+∂∂

ν

ννννσ

ννν

21

222

11 )]([ Uf

df

kCfC tt

bww ∇+−

ν


Case Studies: Inviscid Steady Flow around aNACA 0012 Ai f ilNACA 0012 Airfoil

Grid ComparisonGrid Comparison

Multi-cell overlapping width One-cell overlapping width

Case Studies: Inviscid Steady Flow around aNACA 0012 Ai f il

2D Case Studies (cont’d):Comparison of Results with Different Levels of Overlapping

NACA 0012 Airfoil8.0=∞M

Comparison of Results with Different Levels of Overlapping

P1.68541.63131.57731.52321.4692

P1.68541.63131.57731.52321.4692

1.41511.36101.30701.25291.19891.14481.09081.0367

1.41511.36101.30701.25291.19891.14481.09081.0367

0.98260.92860.87450.8205

0.98260.92860.87450.8205

Multi-cell overlapping width One-cell overlapping width


2D Case Studies (cont’d):

NACA 0012 Airfoil

8.0=∞MComparison of Results

P1.68541.63131.57731.52321 4692

P1.68541.63131.57731.52321.46921.4692

1.41511.36101.30701.25291.19891.14481.09081 0367

1.46921.41511.36101.30701.25291.19891.14481.09081.03671.0367

0.98260.92860.87450.8205

0.98260.92860.87450.8205

One-cell overlapping width Single grid solution


Unsteady Flow Results: 80=M

NACA 0012 Airfoil

y

Sinusoidal pitching solution.

8.0∞M

Angle of attack varies as

Movie


Case Studies: Moving Grids for a Flow-Control Amplifier with a Moving Disc

Moving Grid Animation


Case Studies: 3D Steady Flow inside a Butterfly Valve

Experimental setup of Morris and DuttonExperimental setup of Morris and Dutton(Morris, Ph.D. Dissertation, University of Illinois, Urbana, IL. 1987.)

Butterfly valve testing section

rectangular pipe tunnelheight/depth: 2.67 Section of the arc valve geometry

Case Studies: 3D, Inviscid, Steady Flow inside a Butterfly Valve (cont’d)

Sections of the Valve Grids at Different Angles:Sections of the Valve Grids at Different Angles:

0 degree 5 degree 10 d0 degree 5 degree 10 degree

15 degree 30 degree 60 degree

Case Studies: 3D, Inviscid, Steady Flow inside a Butterfly Valveinside a Butterfly Valve

Specified Boundary Conditions, (for all cases, total temperature, T0 = 300K):


Case Studies: 3D, Inviscid, Steady Flow inside a Butterfly Valvey

Y X

Z

P0.7334050 6902630.6902630.6471220.603980.5608390.5176980.4745560.4314150.3882730.3451320.301990.2588490.2157070.1725660.1294240.08628290.0431415

Z

Y X

Mach0.7867230.7573380.7279530.698568 Flow results and experimental validation0.6691840.6397990.6104140.5810290.5516440.5222590.4928740.463490.4341050.404720 375335

Flow results and experimental validation for fully-opened valve position (0 degree).

0.375335



Y X

Z

P

surface pressure data comparison of arc valve flow at 5 degree

simulationresults on

P0.7641170.7131760.6622350.6112940.5603530.5094110.458470.4075290.3565880 305647 0 4

0.6

0.8

1

1.2

sure ratioa

upstream facingsurfaceexperimentaldata onupstream facingsurfaceexperimental0.305647

0.2547060.2037650.1528230.1018820.0509411

Z

0

0.2

0.4

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

Arc Surface Coordinate (x/D)

press p

date ondownstreamfacing surfacesimulationresults ondownstreamfacing surface

Y X

Mach0.8577290.804090.750450 696811 Flow results and experimental validation

facing surface

0.6968110.6431720.5895330.5358930.4822540.4286150.3749760.3213370.2676970.2140580.160419

Flow results and experimental validation for 5-degree open valve position.

0.10678


Case Studies: 3D, Inviscid, Steady Flow inside a Butterfly Valves de a u e y a e

Y X

Z

P0.7593740.712802

surface pressure comprison of arc valve at 10 degree position numerical

simulation onupstream facing0.712802

0.6662310.619660.5730890.5265170.4799460.4333750.3868030.3402320.2936610.247089

0 4

0.6

0.8

1

1.2

sure ratioa

upstream facing surface

experimatnal dataon upstream facingsurface

experimental data0.2005180.1539470.107376

Z

0

0.2

0.4

-0.6 -0.4 -0.2 0 0.2 0.4 0.6

Valve surface coordinate X/D

Press

on downstreamfacing surface

numericalsimulation ondownstream facingsurface

Y X

Mach1.96191.831551.701191.570841 44048

surface

Flow results and experiment validation of1.440481.310131.179771.049410.9190580.7887030.6583470.5279910.3976350.267280.136924

Flow results and experiment validation of 10-degree open valve position.


Case Studies: 3D, Inviscid, Steady Flow inside a Butterfly Valves de a u e y a e

surface pressure comprison of arc valve at 30 degree position

1

numericalsimulation onupstream facingsurface

Y X

Z

P0.7593740.712802

0 2

0.4

0.6

0.8

ressure ratioa experimatnal data

on upstream facingsurface

experimental dataon downstreamfacing surface

0.6662310.619660.5730890.5265170.4799460.4333750.3868030.3402320.2936610.2470890.200518

Z

0

0.2

-0.6 -0.4 -0.2 0 0.2 0.4 0.6


Pr facing surface

numericalsimulation ondownstream facing surface

0.2005180.1539470.107376

Y X

Mach1.96191.831551.701191.570841.440481 31013 Flow results and experiment validation of1.310131.179771.049410.9190580.7887030.6583470.5279910.3976350.267280.136924




surface pressure comprison of arc valve at 60 degree position numerical

simulation onupstream facing

0 4

0.6

0.8

1

1.2

sure ratioa

upstream facingsurface

experimatnal dataon upstream facingsurface

experimental data

Z

0

0.2

0.4

-0.6 -0.4 -0.2 0 0.2 0.4 0.6


Press

on downstreamfacing surface

numericalsimulation ondownstream facingsurface

Y X

Z

Mach0.5048880.4712990.4377110 404122 Flow results and experiment validation of

surface

0.4041220.3705340.3369460.3033570.2697690.236180.2025920.1690030.1354150.1018260.0682377


0.0346492


Proposed Unsteady Flow Case Study for an Air Pulsating Valvean Air Pulsating Valve

An air pulsation valve for a pulse detonation engine with supersonic parametric inlettest section will be analyzed, (experiments by R Tornabene NASA TM-2005-test section will be analyzed, (experiments by R. Tornabene, NASA TM 2005

213893, 2005).

Pulsed radial flow through the shaftPulsed radial flow through the shaft

Pulsation valve concept showing inlet and discharge

ConclusionsConclusions

1. An unstructured grid method has been developed with features of simplicity and high automation of hole cutting and efficient searching process.

2. The main advantage of the method is that it guarantees the one-cell overlapping grid width leading to less computational time and less numerical errors; there is no need to perform any post-processing or optimizations for the after-hole-cutting grids, contrary to other algorithms in the literature.

3 The developed overset unstructured grid method has been applied to internal3. The developed overset unstructured grid method has been applied to internal inviscid flow computations of a 3D circular-arc-shape butterfly valve at different fixed positions. For these cases, steady state simulations results are validated with the experimental data with good accuracy.


Significant Features of the Developed Approach

• Proposed/developed method provides:

• A systematic and automated hole-cutting process,• An efficient searching algorithm• An efficient searching algorithm,• One-cell overlapping width reducing the computational effort,• Ease in integration to the CFD solver with very few changes• Ease in modeling complex geometries and movements. Once an

unstructured mesh around a moving body (minor grid) is generated, it is coupled with a background grid for the entire flow domain for any specified motion.

• Capability to analyze unsteady flows inside valve bodiesCapability to analyze unsteady flows inside valve bodies with complex geometries and moving bodies. The efficiency and accuracy of this capability will be documented in the thesis.


Future Work and Schedule

1 Complete implementation of ALE for unsteady flow1. Complete implementation of ALE for unsteady flow solutions

• (February 2008)2 Calculate proposed unsteady flow case for a valve2. Calculate proposed unsteady flow case for a valve

• (March 2008)3. Perform viscous and turbulent flow computations for a

valvevalve • (April and May 2008)

4. Perform mesh size refinement for accuracy studies• (June 2008)( )

5. Prepare dissertation and journal papers • (June thru’ August 2008)


Acknowledgements

Advisory Committee:Dr. Hasan U. AkayDr. Akin Ecer (co-chair)Dr. Steve H. Frankel (co-chair)Dr. Gregory A. Blaisdell Dr. Jayathi Y. Murthy

IUPUI CFD Lab Colleagues:Dr Erdal YilmazDr. Erdal YilmazMr. Resat U. PayliMs. Cai Shen


Thank you all very much

for your time and patience!


Documents

Unsteady CFD Simulations of Moving Flow-Control … · Unsteady CFD Simulations of Moving Flow-Control Valves by an Unstructured Overset-Grid Method ... lift and drag forces on a