Simulation of Free Surface Flow Cheng LIU chengliu@sjtu.edu.cn - - PowerPoint PPT Presentation

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Simulation of Free Surface Flow Cheng LIU chengliu@sjtu.edu.cn - - PowerPoint PPT Presentation

Aug 13, 2023 200 likes •623 views

The 3rd Symposium on Computational Marine Hydrodynamics, Shanghai, China Recent Advancement for High-Fidelity Simulation of Free Surface Flow Cheng LIU chengliu@sjtu.edu.cn State Key Laboratory of Ocean Engineering, School of Naval

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Recent Advancement for High-Fidelity Simulation of Free Surface Flow

Cheng LIU

chengliu@sjtu.edu.cn

State Key Laboratory of Ocean Engineering, School of Naval Architecture, Ocean and Civil Engineering,

Shanghai Jiao Tong University

The 3rd Symposium on Computational Marine Hydrodynamics, Shanghai, China

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

OUTLINE

Motivation Numerical Method for Large Density-Ratio Flow

  • Geometric Method
  • Algebra Method

Surface Tension Model

  • Continuum Surface Force Model
  • Sharp Surface Force Model

Numerical Simulation for Breaking Wave Conclusion and Ongoing Work

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Motivation

Water Entry Wave Breaking

Vincent L et al, 2018 Rojas & Loewen (2010) Delaware air–sea interaction tank

High Speed Camera PIV

  • Void fraction
  • Energy dissipation
  • Bubble/Droplet distribution

Ocean Exp. Sphere Wedge

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Motivation

Challenge

Physical Numerical

  • Large density ratio
  • Micro-bubbles/droplets

(𝟐𝟏 − 𝟐𝟏𝟏𝝂𝒏)

  • Turbulent Flow

Number of bubbles

Scale

𝑃(1𝜈𝑛) 𝑃(1𝑛𝑛) 𝑃(1𝑛) Bubble Size Distribution

Wide-Range of Scales

  • Fine mesh resolution
  • Robust two-phase model

Bubble Flows generated by Wave Breaking (Fraser, 2017)

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Motivation

Numerical Strategy

Interface Capturing Scheme Surface Tension Model SSF Model CSF Model Curvature Estimation Coupled LS-VOF √ √ HF function (SDF field) VOF-PLIC √ HF function (VOF field) THINC/SW √ HF function (VOF field)

Block-Structured AMR High-Resolution Scheme Fractional Step Method Two-Phase Treatment

BAMR Ex. Straight Liquid Jet Spray

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Numerical Method for Large Density-Ratio Flow

Problem Description

Numerical Instability comes from

  • Discretization of pressure gradient
  • Decoupling of pressure-velocity
  • Inconsistent advection of

Mass/momentum

  • Small density-ratio
  • Large physical viscosity
  • Surface tension dominated

Maybe covered by

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Numerical Method for Large Density-Ratio Flow

Momentum-Mass Consistent Scheme Solution 1 : Geometric Method Interfacial cells Single-phase cells

Collocated grid Staggered grid Dual grid for VOF

+…

Corrected by mass flux

Solution 2 : Algebraic Method

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Numerical Method for Large Density-Ratio Flow

Present Momentum-Mass Consistent Scheme Original Scheme

Numerical Validation Case (2): Advection of Droplet

Initial volume-fraction field Initial velocity field 𝐯 = 0,0 𝑗𝑜 𝑕𝑏𝑡 𝑣𝑦

0, 𝑣𝑧

𝑗𝑜 𝑚𝑗𝑟𝑣𝑗𝑒 𝛽 = 0 𝑗𝑜 𝑕𝑏𝑡 1 𝑗𝑜 𝑚𝑗𝑟𝑣𝑗𝑒

Numerical Validation Case (1): Dam Breaking

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Numerical Method for Large Density-Ratio Flow

Numerical Validation Case (2): Advection of Droplet

Bussmann M et al. (2002) Fuster D, Arrufat T, S. Zaleski (2019)

Present Simulation Result 𝐸𝑀𝑗𝑟𝑣𝑗𝑒 𝐸𝑕𝑏𝑡 = 106 Final l Shape of f Drople let

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Numerical Method for Large Density-Ratio Flow

Numerical Validation Case (3): Two-Dimensional Jet Flow

Experimental Setup Park J , Huh K Y , Li X , et al. Experimental investigation on cellular breakup of a planar liquid sheet from an air-blast nozzle. Physics of Fluids, 2004, 16(3):625.

Present Simulation

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Numerical Method for Large Density-Ratio Flow

Numerical Validation Case (3): Two-Dimensional Jet Flow

Raessi M , Pitsch H . Consistent mass and momentum transport for simulating incompressible interfacial flows with large density ratios using the level set method. Computers & Fluids, 2012

From Park J et al. Exp. Present Simulation

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Surface Tension Model (CSF)

Continuum Surface Force (CSF) Model 𝑞 = 𝜏𝒧𝐨𝜀𝑡 = 𝜏𝒧𝛼𝐼𝜗 𝐲 − 𝐲𝑡 𝐼𝜗 ≡ 𝑤𝑝𝑚𝑣𝑛𝑓 𝑔𝑠𝑏𝑑𝑢𝑗𝑝𝑜 𝐷

𝑗𝑔 𝐷𝑗,𝑘,𝑙 − 𝐷𝑗−1,𝑘,𝑙 > 𝜗, 𝑣𝑗−1

2,𝑘,𝑙 = 𝑣𝑗−1 2,𝑘,𝑙 − ∆𝑢𝜏𝒧𝑗−1 2,𝑘,𝑙

𝐷𝑗,𝑘,𝑙 − 𝐷𝑗−1,𝑘,𝑙 ∆𝑦 ∙ 1 1 2 𝜍𝑗,𝑘,𝑙 + 𝜍𝑗−1,𝑘,𝑙 ,

  • Add ST force effect:
  • Solve pressure Eq. to recover pressure jump

averaged from 𝒧𝑗−1,𝑘,𝑙 and 𝒧𝑗,𝑘,𝑙

Smoothed

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

𝐼𝑡,𝑢 =

𝑛=𝑙−3 𝑛=𝑙+3

𝐷𝑡,𝑢,𝑛 𝒧𝑗,𝑘,𝑙 = 𝐼𝑦𝑦 + 𝐼𝑧𝑧 + 𝐼𝑦𝑦𝐼𝑧

2 + 𝐼𝑧𝑧𝐼𝑦 2 − 2𝐼𝑦𝑧𝐼𝑦𝐼𝑧

1 + 𝐼𝑦

2 + 𝐼𝑧 2 1.5

𝒧 = 2 𝑑1 𝑑5

2 + 1 + 𝑑2 𝑑4 2 + 1 − 𝑑3𝑑4𝑑5

𝑑5

2 + 𝑑4 2 + 1 1.5

𝐺 𝐲 = 𝑑1𝑦2 + 𝑑2𝑧2 + 𝑑3𝑦𝑧 + 𝑑4𝑦 + 𝑑5𝑧 + 𝑑6

  • Eq. (1):
  • Eq. (2):

True False Local curvature from Eq. (1) Identify the inactive cells Approximate quadratic interface Whether 𝐷𝑡,𝑢,𝑛 is monotonic in 𝑛 = [𝑙 − 3, 𝑙 + 3] Local curvature from Eq. (2)

𝜖𝒧 𝜖𝜐 + 𝐼 𝒧 𝐨 ∙ 𝛼𝒧 = 0

𝐼 𝒧 = 0 𝑗𝑔 𝑑𝑓𝑚𝑚𝑗,𝑘,𝑙 ∈ 𝕁 ∪ 𝕄 , 1 𝑗𝑔 𝑑𝑓𝑚𝑚𝑗,𝑘,𝑙 ∈ 𝐻,

MLS interface-fit

Disperse curvature values along anti/normal direction

Improved Height function method for curvature estimation

Surface Tension Model (CSF)

Continuum Surface Force Model (CSF)

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

△: smoothed VOF [28], ◇: re-distancing function based on VOF [28], □: height function (HF) method of S.J. Cummins et al., 2005, ●: present HF, – – –: second order, – ∙ – ∙ –: first order.

𝑴𝟑 and 𝑴∞ error Example : Curvature estimation of a circular interface Interfacial cells

Surface Tension Model (CSF)

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

𝑴𝟑 and 𝑴∞ error

  • Fig. Curvature estimation errors ( L∞ ) of interfacial cells and

extrapolation cells (as shown in Fig. 3) with (●) or without (○) curvature populating, – – –: second order, – ∙ – ∙ –: first order. Example : Curvature estimation of a circular interface Interfacial/neighbor cells

Surface Tension Model (CSF)

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

  • Domain 𝑦, 𝑧, 𝑨 ∈ [−1,1].
  • Water/air density & viscosity ratio:

𝜍𝑚/𝜍𝑕 = 1000.0/1.2, 𝜈𝑚/𝜈𝑕 = 1.0 × 10−3/1.8 × 10−5

  • Initial free surface profile: cylindrical

interface with sinusoidal perturbation, 𝑠 𝑦 = 𝑠

0 1 + 𝜁 sin 𝑙𝑦 ,

𝑠

0 = 0.2, 𝜁 = 0.02 and 𝑙 = 𝜌.

  • Periodical b. c. for pressure and

velocity Pa Para ramet eters ers Rep Repeat eat th the e th theor eoret etica ical study by L. l study by L. Ra Raylei yleigh(1 gh(1892 892)* )* and and C. . Weber Weber(19 (1931 31)** )**  Three cases with Laplace number: 2000, 238.34, 23.834. 𝜓𝑛𝑏𝑦 = 𝑠

𝑛𝑏𝑦 − 𝑠0

𝜁𝑠0 , 𝜓𝑛𝑗𝑜 = 𝑠0 − 𝑠𝑛𝑗𝑜 𝜁𝑠0 𝑠

𝑛𝑏𝑦 , 𝑠𝑛𝑗𝑜 : 最大，最小半径

**Weber C. Zum zerfall eines flüssigkeitsstrahles. ZAMM‐Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 1931, 11(2): 136-154. *Rayleigh L. XVI. On the instability of a cylinder of viscous liquid under capillary force. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 1892, 34(207): 145-154.

Example : Capillary Breakup of Liquid Jet

Surface Tension Model (CSF)

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

(a) (b)

  • Fig. Comparison of relative deformations of the interface. (a). Maximum radius

variation 𝜓𝑛𝑏𝑦, (b). Minimum radius variation 𝜓𝑛𝑗𝑜. – – –: L. Rayleigh [45] (𝑀𝑏 = 2000), ∙∙∙∙∙: C. Weber [46] (𝑀𝑏 = 238.34), ∙–∙–∙: C. Weber [46] (𝑀𝑏 = 23.834), ○: present BAMR (𝑀𝑏 = 2000), △: present BAMR (𝑀𝑏 = 238.34), □: present BAMR (𝑀𝑏 = 23.834). Example : Capillary Breakup of Liquid Jet

Surface Tension Model (CSF)

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

𝑆𝑓 = ) 𝜍𝑚𝐸(2𝑉0 𝜈𝑚 , 𝑋𝑓 = 𝜍𝑚𝐸 2𝑉0 2 𝜏 ,

  • Table. Fluid properties for present droplet collisions.

Rep Repeat eat th the e exper experim iment ental s al stu tudy dy by by Qian Qian and Law, 1 and Law, 1997 997 *  Four collision mode.  Two equal-sized droplets 𝜇 = 𝑐 𝐸 , 𝜃 = 𝑥 𝐸 Example : Droplet Collisions

Surface Tension Model (CSF)

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Fig. Comparisons

  • f

collision regimes from experimental analysis and simulated results. ○: case-I, □: case-II, △: case-III, ◇ : case-IV. Different collision modes are divided by lines as demonstrated in Ref.

  • Table. Parameters for different cases of the droplet collisions.

Example : Droplet Collisions

Surface Tension Model (CSF)

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

  • Fig. Off-center collisions of hydrocarbon droplet (case-I), the predictions of

VOF/PLIC and VOF/APPLIC are presented for comparison. (c) Exp. (b) VOF/APPLIC (a) VOF/PLIC Example : Droplet Collisions

Surface Tension Model (CSF)

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

  • Fig. Off-center collisions of hydrocarbon droplet (case-II), only the predictions of

VOF/APPLIC are given. Exp. VOF/APPLIC Example : Droplet Collisions

Surface Tension Model (CSF)

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

  • Fig. Off-center collisions of hydrocarbon droplet (case-III), only the predictions of

VOF/APPLIC are given. Exp. VOF/APPLIC Example : Droplet Collisions

Surface Tension Model (CSF)

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

  • Fig. Off-center collisions of hydrocarbon droplet (case-IV), only the predictions of

VOF/APPLIC are given. Exp. VOF/APPLIC Example : Droplet Collisions

Surface Tension Model (CSF)

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Surface Tension Model

Continuum Surface Force (CSF) Model Application: Simulation of Breaking Wave CSF Model

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Surface Tension Model

Application: Simulation of Breaking Wave CSF Model Continuum Surface Force (CSF) Model

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Surface Tension Model

Application: Simulation of Breaking Wave CSF Model Continuum Surface Force (CSF) Model

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Surface Tension Model

Application: Simulation of Breaking Wave

Capillary Effect

  • f Liquid Filament
  • Accurate SF model

in Coarse mesh Liquid Filament

Continuum Surface Force (CSF) Model

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Surface Tension Model

Sharp Surface Force Model

Liu C, Hu C. A second order ghost fluid method for an interface problem of the Poisson equation. Communications in Computational Physics, 2017, 22(4): 965-996. Jump Condition for Pressure:

Step function

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Surface Tension Model

Sharp Surface Force (SSF) Model

Liu C, Hu C. A second order ghost fluid method for an interface problem of the Poisson equation. Communications in Computational Physics, 2017, 22(4): 965-996. Multi-Dimensional

Extension:

Sighed Distance Field is Preferred

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Surface Tension Model

Validation (1): Simulation of Breaking Wave Sharp Surface Force (SSF) Model SSF Model

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Surface Tension Model

Validation (1): Simulation of Breaking Wave Sharp Surface Force (SSF) Model SSF Model

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Surface Tension Model

Validation (1): Simulation of Breaking Wave Sharp Surface Force (SSF) Model SSF Model

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Surface Tension Model

Validation (1): Simulation of Breaking Wave Sharp Surface Force (SSF) Model SSF Model

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Surface Tension Model

Validation (1): Simulation of Breaking Wave Sharp Surface Force (SSF) Model SSF Model

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Surface Tension Model

Validation (1): Simulation of Breaking Wave Sharp Surface Force (SSF) Model SSF Model

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Numerical Simulation for Breaking Wave

Steepness=0.35 Steepness=0.4 Steepness=0.47 Steepness=0.5

Sharp Surface Force (SSF) Model

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Numerical Simulation for Breaking Wave

Steepness=0.35 Steepness=0.4 Steepness=0.47 Steepness=0.5

Sharp Surface Force (SSF) Model

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Conclusion and Ongoing Work

  • For coarse computational mesh, Sharp Surface

Tension (SSF) model is more robust than Continuum Surface Tension(CSF) model

  • For a sharp interface VOF method, consistent

mass-momentum advection scheme is helpful to maintain the numerical stability

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Conclusion and Ongoing Work

 for bow wave  for bubble collapse High-fidelity Simulation

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High-Fidelity Numerical Simulation for Free Surface Flow —— Cheng LIU

Conclusion and Ongoing Work

DNS of Incompressible Flows

Fluid Structure Interaction Free Surface Flows

Interfacial Flows

Multi-medium flows

Wing Flows

Compressible Turbulence Flow Shock-boundary layer interaction

Incompressible Flows Compressible Flows

Framework for Block-structured AMR

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http://dcwan.sjtu.edu.cn

Than hank k You

  • u !

Cheng LIU

chengliu@sjtu.edu.cn