Space–Time Computational Methods and Ram-Air ...

TAFSM!

Symposium on Stabilized, Multiscale, and Isogeometric Methods in CFD, 19th International Conference on Finite Elements in Flow Problems, Rome, Italy, April 2017 (Keynote Lecture).

M S F A F T

Space–Time Computational Methods and Ram-Air Parachute Aerodynamics With the ST Isogeometric Analysis Kenji Takizawa

Tayfun E. Tezduyar

Takuya Terahara

Waseda University

University of Tokyo Rice University

Waseda University

TAFSM! Deforming-Spatial Domain/Stabilized Space–Time (DSD/SST) Method “ST-SUPS”

M S F A F T Summer 1994

Large Ram-Air Parachute 60 ft × 180 ft

First 3D parachute computation with the ST-SUPS method

One of the earliest 3D computations with the ST-SUPS method

TAFSM! Flare Maneuver of a Large Ram-Air Parachute ST-SUPS

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T.E. Tezduyar, V. Kalro, and W. Garrard, “Parallel computational methods 3D simulation of a parafoil with prescribed shape changes”, Parallel Computing, 23 (1997) 1349–1363

TAFSM! Fluid–Structure Interactions of a Large Ram-Air Parachute December 1997

M S F A F T ST-SUPS

ALE-SUPS

V. Kalro and T.E. Tezduyar, “A parallel finite element methodology for 3D computation of fluid–structure interactions in airdrop systems”, Proceedings of the 4th Japan-US Symposium on Finite Element Methods in Large-Scale Computational Fluid Dynamics, Tokyo, Japan (1998)

V. Kalro and T.E. Tezduyar, “A parallel 3D computational method for fluid–structure interactions in parachute systems”, Computer Methods in Applied Mechanics and Engineering, 190 (2000) 321–332

TAFSM! DSD/SST Method “ST-SUPS”

M S F A F T ST slab

TAFSM! ST-SUPS and ST-VMS

M S F A F T Z

✓

◆ Z h @u h h h h w ·⇢ + u · ru f dQ + " (wh ) : (uh , ph )dQ @t Qn Z Z Z Qn h + wh · hh dP + q hr · uh dQ + (wh )+ (uh )n d⌦ n · ⇢ (u )n (Pn )h

XZ

Qn

(nel )n

+

e=1

XZ

⌦n

✓ ✓ h ◆ ◆ @w ⇢ + uh · r wh + r q h · rM (uh , ph )dQ @t

Qen

⌧SUPS ⇢

Qen

⌫LSICr · wh ⇢rC (uh )dQ

(nel )n

+

e=1

XZ

Terms existed in ST-SUPS

(nel )n

e=1

XZ

Qen

⌧SUPS wh · rM (uh , ph ) · r uh dQ

Qen

2 ⌧SUPS rM (uh , ph ) · r wh · rM (uh , ph )dQ = 0 ⇢

(nel )n

e=1

Terms added in ST-VMS

K. Takizawa, and T.E. Tezduyar, “Multiscale space–time fluid–structure interaction techniques”, Computational Mechanics,

48 (2011) 247–267

TAFSM! ST-SUPS and ST-VMS Milestones and Key Players in the Development

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1990

James Liou

ST-SUPS

Implementation

1997

Vinay Kalro

ST-SUPS  FSI

Implementation

2004

Sunil Sathe

ST-SUPS  FSI+

Development and Implementation

2010

Kenji Takizawa

ST-SUPS  FSI++ ST-VMS ST-VMS  FSI++ + ST-SI ST-TC ST-SI-TC ST-IGA ST-SI-TC-IGA

Development and Implementation

TAFSM! Mesh Update No reason to be afraid of…

M S F A F T

25-year history of development…

Starting from Jacobian-Based Stiffening (JBS) in 1992…

To ST NURBS Mesh Update Method (STNMUM) in 2011…

To Element-Based Mesh Relaxation (EBMR) in 2013…

TAFSM! Fluid–Particle Interactions Reaching 1000 Spheres ST-SUPS

M S F A F T ST-SUPS was the first in 3D FPI… … (1994)

… reaching 100 spheres (1996)

•  Large displacements •  Near contact •  Near topology changes

June 1998

… reaching 1000 spheres (1998) … in tri-periodic domains (1999)

•  “Nearness” is sufficiently “near” for the purpose of solving the problem

TAFSM! ST Topology Change Method ST-TC (2013)

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•  A moving-mesh method that can handle an actual TC •  High-resolution flow representation near solid surfaces

Heart valve (2014)

Mechanical valve (2014)

Wing clapping (2014)

Tire aerodynamics (2016)

+ (Pn )SI

Z

TAFSM!

(Pn )SI Z ST Slip Interface Method

ST-SI

h nB · wBh + nA · wA

wBh

ACI

1 h pB + phA dP 2

h ˆ B · µ " (uhB ) + " (uhA ) wA · n h ˆ B · µ " wBh + " wA n

· uhB

M S F A F T Z Z

(Pn )SI

qBh nB

qAh nA

1 h · u 2 B

uhA

dP

+

Z

(Pn )SI

(Pn )SI

µC wBh h

1 FBh FBh uhB FBh FBh uhA dP 2 (P ) Z n SI h 1 ⇢wA · FAh FAh uhA FAh FAh uhB dP 2 (P ) Z n SI h 1 + nB · wBh + nA · wA phB + phA dP 2 (P ) Z n SI h ˆ B · µ " (uhB ) + " (uhA ) dP wBh wA · n (Pn )SI Z h ˆ B · µ " wBh + " wA n · uhB uhA dP ACI (Pn )SI Z µC h + wBh wA · uhB uhA dP (Pn )SI h ⇢wBh ·

h wA · uhB

uhA dP

FBh = nB · uhB

vBh

FAh = nA · uhA

h vA

A: above

B: below

K. Takizawa, T.E. Tezduyar, H. Mochizuki, H. Hattori, S. Mei, L. Pan, and K. Montel, “Space–time VMS method for flow computations with h h h slip interfaces (ST-SI)”, Mathematical ModelsFand Methods 2377–2406

nB · inuApplied vSciences, 25 (2015) B = B B

ST version of…

FAh = nA · uhA

h vA

Y. Bazilevs, and T.J.R. Hughes “NURBS-based isogeometric analysis for the computation of flows about rotating components”, 

Computational Mechanics, 43 (2008) 143–150

dP

uhA dP

TAFSM! Vertical-Axis Wind Turbine VAWT

M S F A F T Blade

Support column

Shaft

Arm

Rotor

Turbine model

Blade chord length

1.5

Blade length

18

Arm chord length

1.35

Arm length

7

Rotor diameter

16

Tower height

45

Dimensions (m)

TAFSM! 2D Fluid Mechanics Computations Tip-Speed Ratio = 3

M S F A F T 1.0 0.8

CPOW

0.6 0.4 0.2 0.0

0.2 0

Velocity magnitude m/s

0.0

Low

10.0

High

Velocity magnitude

90

Three-airfoils model Three-airfoils model (average) Betz theory

180

()

270

360

Full-machine model Full-machine model (average)

TAFSM! ST-SI Weakly-Imposed Dirichlet Boundary Condition

M S F A F T Z

+

Z

(Pn )SI

qBh nB · uhB dP

(Pn )SI

⇢wBh ·

(Pn )SI

wBh · nB ·

(Pn )SI

µC h wB · uhB hB

Z

+

Z

1 2

Z

⇢wBh · FBh uhB dP +

(Pn )SI

FBh + FBh h B

dP

uhB + FBh Z

ACI

(Pn )SI

gh dP

FBh

Z

(Pn )SI

qBh nB · gh dP

gh dP

nB · 2µ"" wBh · uhB

gh dP

g: given

B: boundary

K. Takizawa, T.E. Tezduyar, H. Mochizuki, H. Hattori, S. Mei, L. Pan, and K. Montel, “Space–time VMS method for flow computations with slip interfaces (ST-SI)”, Mathematical Models and Methods in Applied Sciences, 25 (2015) 2377–2406

ST version of…

Y. Bazilevs, and T.J.R. Hughes “NURBS-based isogeometric analysis for the computation of flows about rotating components”, 

Computational Mechanics, 43 (2008) 143–150

TAFSM! 3D Fluid Mechanics Computation Vorticity Magnitude

M S F A F T 0.1

157.0

1/s

TAFSM! ST-SI Between a Thin Porous Structure and the Fluid on Its Two Sides

M S F A F T Z

Z

(Pn )SI

qBh nB · uhB dP 1 2

(Pn )SI

⇢wBh · FBh uhB dP +

Z

(Pn )SI

qBh uhPORO + uhS · nB dP

FBh + FBh uhB + FBh FBh (nB nB ) · uhA + (I nB nB ) · uhS dP (P ) Z n SI Z + wBh · nB phB dP (nB nB ) · wBh · nB · µ " (uhB ) + " (uhA ) dP (P ) (Pn )SI Z n SI (I nB nB ) · wBh · nB · 2µ""(uhB ) dP (Pn )SI Z nB · µ"" wBh · (nB nB ) · uhB uhA dP ACI (P ) Z n SI nB · 2µ"" wBh · (I nB nB ) · uhB uhS dP ACI (Pn )SI Z A: above µC + (nB nB ) · wBh · uhB uhA dP h (P ) S: structure Z n SI µC + (I nB nB ) · wBh · uhB uhS dP B: below (Pn )SI h +

⇢wBh ·

Z

K. Takizawa, T.E. Tezduyar, H. Mochizuki, H. Hattori, S. Mei, L. Pan, and K. Montel, “Space–time VMS method for flow computations with slip interfaces (ST-SI)”, Mathematical Models and Methods in Applied Sciences, 25 (2015) 2377–2406

TAFSM! Ram-Air Parachute Geometry and Flow Conditions

M S F A F T 8m×3m

18 air cells

19 ribs

Glide speed = 12.5 m/s

α = −2°, 0°, 2°, 4°, 6°, 8°, 10°, 12°

K. Takizawa, T.E. Tezduyar, and T. Terahara, “Ram-air parachute structural and fluid mechanics computations with the space–time isogeometric analysis (ST-IGA)”, Computers & Fluids, 141 (2016) 191–200

TAFSM! Ram-Air Parachute Structural Mechanics Control Mesh

M S F A F T

•  NURBS mesh enables increased accuracy in representing the parafoil geometry •  Special-purpose mesh generation technique enables complex-geometry representation

K. Takizawa, T.E. Tezduyar, and T. Terahara, “Ram-air parachute structural and fluid mechanics computations with the space–time isogeometric analysis (ST-IGA)”, Computers & Fluids, 141 (2016) 191–200

TAFSM! Ram-Air Parachute Fluid Mechanics Mesh

M S F A F T

•  Surface mesh = canopy structure mesh •  Volume mesh both inside and outside •  Challenging near the trailing edge

NURBS mesh enables…

•  Increased accuracy in representing the parafoil surface •  Increased accuracy in obtaining the flow solution

•  Reasonable element density near the trailing edge

•  Special-purpose mesh generation technique enables complex-geometry representation

K. Takizawa, T.E. Tezduyar, and T. Terahara, “Ram-air parachute structural and fluid mechanics computations with the space–time isogeometric analysis (ST-IGA)”, Computers & Fluids, 141 (2016) 191–200

TAFSM! Ram-Air Parachute Fluid Mechanics Control Mesh

M S F A F T First deform at α = 0°

α = 0°

α = 0°

Next deform from α = 0° to other α values

K. Takizawa, T.E. Tezduyar, and T. Terahara, “Ram-air parachute structural and fluid mechanics computations with the space–time isogeometric analysis (ST-IGA)”, Computers & Fluids, 141 (2016) 191–200

TAFSM! Ram-Air Parachute Vorticity

M S F A F T α = 0°

α = 12°

TAFSM! Ram-Air Parachute α = 0°

M S F A F T Porosity modeling

TAFSM!

M S F A F T Japanese Translation"

TAFSM!

M S F A F T Thank you!