STAR-CCM+ Samir Muzaferija & Milovan Peri Contents - - PowerPoint PPT Presentation

VOF-Technology in STAR-CCM+

Samir Muzaferija & Milovan Perić

Contents

 Introduction to multiphase flows  Theoretical background for VOF-method  High-Resolution Interface-Capturing (HRIC) scheme  Accounting for surface tension effects  Extensions of VOF-method  Waves: generation, propagation, damping…  Free surface flows: application examples  Future development

Introduction to Multiphase Flows

VOF-approach is suitable, when the grid is fine enough to resolve the interface between two immiscible fluids. Sometimes not all parts of the flow are suited for VOF-treatment… Examples: Atomization nozzle flow and jet break-up (right) and flow around a hydrofoil (below)

Interface Conditions, I

• Conditions at an interface between two immiscibe fluids:



Kinematic condition: No flow through interface.



Dynamic conditions: Balance of normal and tangential stresses (surface tension forces):

VOF: Theory, I

• VOF considers a single effective fluid whose properties vary

according to volume fraction of individual fluids:

• The mass conservation equation for fluid i reads:
• It can be rearranged into an equation in integral form:

This equation is used to compute the transport of volume fraction αi.

VOF: Theory, II

• The mass conservation equation for the effective fluid is
• btained by summing up all component equations and

using the condition:

• The integral form of mass conservation equation (used to

compute pressure correction) reads:

• The properties of effective fluid are computed according to

volume fractions:

VOF: Theory, III

• All fluids (liquids and gases) can be compressible.
• If density is a function of pressure and temperature, we have:
• For an ideal gas, the following relations hold:
• The source term due to compressibility is then:

Interface-Capturing Method, I

• For sharp interfaces, special discretization for convective

terms in the equation for volume fraction αi is needed (to avoid excessive spreading).

• The method must produce bounded solutions, i.e. each

volume fraction must lie between 0 and 1 and the sum of all volume fractions must be 1 at each control volume.

• Bounded schemes must fall within a certain region of the

normalized variable diagram; the normalized variables are defined as:

Interface-Capturing Method, II

• The boundedness requirement:

The normalized variable diagram and the proposed high-resolution interface- capturing (HRIC) scheme

HRIC-Scheme, I

• The HRIC-scheme defines the face value of the

normalized variable as follows:

• This value is corrected by the local Courant-number (CFLl

and CFLu are scheme parameters – default 0.5 and 1):

HRIC-Scheme, II

• Another correction is introduced to account for the
• rientation of interface relative to cell face:
• This correction reduces the tendency of interface to align

with the grid…

• Cθ is the scheme parameter (default value: 0.05)

HRIC-Scheme, III

• The convected cell-face value of volume fraction is finally

determined as:

• The face value can also be expressed as a blend of

upwind and downwind values:

• The blending factor is a function of normalized face

variable and volume fraction values at U, C and D nodes:

Surface Tension Effects, I

• The kinematic interface condition is implicitly accounted

for by the transport equation for volume fraction.

• The dynamic interface conditions require additional forces

in the momentum equations in cells containing free surface…

• Surface tension forces are converted to volume forces:

Since the gradient of volume fraction is zero away from interface, these terms are equal to zero everywhere except along interface…

Surface Tension Effects, II

• The unit vector normal to interface is obtained from the

gradient of volume fraction:

• The curvature of free surface is obtained from the

divergence of the unit vector normal to interface:

• The volume fraction field needs to be smoothed before

the curvature is computed (sharp interface leads to a non- smooth curvature field).

Surface Tension Effects, III

• The so called „parasitic currents“ can develop, if the fluid

moves only slowly or not at all, and the surface tension effects dominate (high curvature or surface tension coefficient)...

• The reason: pressure and surface tension forces must be

in equilibrium when fluid is at rest – but the numerical approximations do not guarantee that (one term is linear and the other is non-linear):

• There are many partial solutions to this problem in

literature, but none works in all situations…

Surface Tension Effects, IV

• Where free surface is in contact with wall, contact angle

needs to be prescribed.

Surface Tension Effects, IV

• One can distinguish between:

 Static contact angle  Dynamic advancing contact angle on dry surface  Dynamic advancing contact angle on wet surface  Dynamic receding contact angle

• The contact angle is enforced as:

nfs = - nw cos θw + tw sin θw

Surface Tension Effects, V

• Contact angle and dynamic contact line at a moving wall (e.g. in

a coating process)...

Extensions of VOF-Method

• One can add additional models in the equation for volume

fraction (diffusion, sources) in order to model effects like non-sharp interfaces, phase change etc.

• This is the main advantage of this approach compared to

level-set and similar schemes...

• VOF-framework is already used in STAR-CCM+ for the

following models:

 Cavitation  Boiling  Evaporation and condensation at free surface  Melting and solidification

• STAR-CCM+ provides several wave models:

– For initialization of volume fraction, velocity and pressure fields; – For a transient inlet boundary condition.

• Currently available models:

– 1st-order linear wave theory – Non-linear 5th-order Stokes wave theory (Fenton, 1985) – Pierson-Moskowitz and JONSWAP long-crested wave spectra – Superposition of linear waves with varying amplitude, period and direction of propagation (can be set-up via Excel-file)

Wave Models

w w

• Vertical motion is damped by introducing smoothly

increasing resistance…

• The method proposed by Choi and Yoon (Costal Engineering,
• Vol. 56, pp. 1043-1060, 2009) has been implemented into

STAR-CCM+:

Wave Damping

xsd – Starting point for wave damping (propagation in x-direction) xed – End point for wave damping (boundary) f1 , f2 and nd – Parameters of the damping model

w – Vertical velocity component

• Accurate wave propagation requires 2nd-order time-

integration method.

• Second-order method (quadratic interpolation in time)

requires that the wave propagates less than half a cell per time step.

• First-order scheme is always stable but less accurate…
• Test case:

– Stokes 5th-order wave – Wavelength 102.7 m – Wave height 5.8 m – Wave period 8 s – Solution domain 4 wavelengths long…

Time-Accurate Wave Propagation, I

Time-Accurate Wave Propagation, II

Wave damping was applied over the last 100 m before outlet... 41 cells per wave length, 11.5 cells per wave height (Δx = 2.5 m, Δz = 0.5 m) 1st-order scheme, 100 Δt/T (CFL = 0.41), after 4 periods 2nd-order scheme, 100 Δt/T (CFL = 0.41), after 4 periods 5 cells 10 cells

• Droplet impact on a wall
• Flow in a slot coater
• Micro-gravity free surface re-orientation
• Flow around ships
• Wave impact on offshore structures
• Flow over a weir
• Simulation of pouring

Application examples

Drop Impact on a Wall, I

• A water droplet with a diameter D = 2.7 mm hits a wall with a

speed of 4.551 m/s.

• Wall surface is waxed: contact angle is 105° for advancing

interface and 95° for receding interface.

• Surface tension coefficient: σ = 0.073 N/m
• Weber number: We = ρu2D/σ = 763
• Mesh size at wall: 6 µm
• Time step: 0.2 µs
• Comparison with experiments by S. Sikalo and E. Ganic

(Phenomena of droplet-surface interactions, Experimental Thermal and Fluid Science, 2006)

Animation showing droplet impact on the wall and rebound due to non-wetting contact angle...

Drop Impact on a Wall, II

Drop Impact on a Wall, III

Comparison of predicted and measured spreading of liquid droplet on the wall Comparison of predicted and measured height of liquid above wall at the impingement location...

Simulation of Slot Coating, I

Prediction of stable operation window of a slot coater as a function of vacuum level Stable region predicted well on very coarse grid

Simulation of Slot Coating, II

Effects of grid refinement (web speed 0.8 m/s, under-pressure 500 Pa):

Coarse grid Refined grid

Simulation of Slot Coating, III

Effects of grid refinement: Flow rates at inlet and outlet

Coarse grid Refined grid

Web speed: 0.5 m/s Vacuum: 2000 Pa On a coarse mesh,

• utlet flux oscillates

strongly, on a fine mesh much less…

Micro-Gravity Free Surface Shape, I

Symmetry axis Wall

Silicon oil in a cylindrical container subjected to a sudden reduction in gravity (to 1e-6 m/s^2) changes free surface shape to spherical… Fluid is at rest both initially and at the end

• f simulation –

parasitic currents require reduced CFL- limits for HRIC…

Micro-Gravity Free Surface Shape, II

Comparison of predicted and experimentally observed position of free surface during transition process at symmetry axis and at wall (experiments by Michaelis and Dreyer, in Multiphase Science and Technology, Vol. 16, pp. 219-238, 2004) Symmetry axis Wall

Flow Around Ships, I

Comparison of predicted and measured wave profiles around container ship at Froude number 0.26

Flow Around Ships, II

Comparison of measured and predicted wave profiles around a military vessel (destroyer DTMB 5415)…

Wave Impact on Offshore Structures, I

Simulation of wave impact on a platform in shallow water by DNV (published at OMAE2012 Conference) Simulation of wave impact on a jack-up platform in shallow water by GL (published at OMAE2009 Conference)

Wave Impact on Offshore Structures, II

Coupled simulation of flow using STAR-CCM+ and deformation of platform structure using ABAQUS.

Simulation by CD-adapco Engineering Services for

• Chevron. Published at

OMAE2012 Conference.

Evidence of damage on a platform after it was hit by a hurricane Deformation in a simulation: good agreement with field

• bservation…

Flow Over a Weir

Simulation of Pouring, I

• Improvements to computation of free surface curvature

(to reduce the parasitic currents)

• Transition to other multiphase models:

– VOF to Lagrangian and vice-versa – Fluid film to VOF and vice versa

• Eulerian or Lagrangian multiphase models within VOF

phases

Future Developments