Coupling of STAR-CCM+ to Other Theoretical or Numerical Solutions - - PowerPoint PPT Presentation

Coupling of STAR-CCM+ to Other Theoretical or Numerical Solutions

Milovan Perić

• The need to couple STAR-CCM+ with other theoretical or

numerical solutions

• Coupling approaches: surface and volume coupling
• Examples of surface and volume coupling
• Future developments

Contents

• Eliminate reflections from boundaries (especially inlet)
• Reduce the size of 3D simulation domain (reduce

computing cost, especially for long-lasting transient simulations)

• Enable simulation of wave propagation over long

distance (wake signature, shore impact etc.)

Need for Coupling

Source: Wikipedia

• An example of surface coupling is Fluid-Structure-

Interaction (FSI): the solutions in fluid and structure are coupled at the contact surface…

• The same approach can be applied to two fluid domains,

whereas in each domain different equations (potential flow, Euler- or Navier-Stokes equations) can be solved with different methods (boundary element, finite element

• r finite volume).
• There are many different options (implicit or explicit

coupling, solving simultaneously for the whole domain or using solution in one subdomain to impose boundary conditions in another subdomain, one- or two-way…).

Surface Coupling, I

• An example of surface coupling represents also the

imposing of theoretical solution (Stokes 5th-order wave, Pierson-Moskwoitz or Jon-Swap irregular long-crested waves, superposition of linear waves…) at an inlet boundary.

• The imposed inlet values can also come from another

numerical solution in the upstream subdomain.

• The problem: reflection of upstream-traveling waves at

such an inlet boundary if the coupling is only one-way.

Surface Coupling, II

• An example of two-way surface coupling:

 The upstream domain imposes at interface inlet condition for the downstream domain;  The downstream domain imposes at interface pressure-

• utlet condition for the upstream domain.
• The most comprehensive approach:

 Solving for the same variables in the whole domain simultaneously (as we do with overset grids)…  This fully-implicit approach requires exchange of information at each iteration within a time step…  … and imposes some compatibility conditions…

Surface Coupling, III

• Instead of using contiguous subdomains and coupling at

a common surface interface, one can also use

• verlapping subdomains and enforce coupling over a

volume zone…

• The forcing is realized via a source term of the form:

S* = - µf (ϕ - ϕ*) where µf is the forcing coefficient.

• A large number is used when the variable value is to be

fixed to ϕ* (e.g. dissipation rate at a near-wall cell).

Volume Coupling, I

• A smoothly varying forcing coefficient provides also a

damping function…

• The volume coupling can also be either one-way or two-

way (the forcing zones usually do not coincide)…

Volume Coupling, II

µf

3D Navier-Stokes 2D Euler Forcing zone

• If the grids do not coincide, volume coupling requires

interpolation of one solution to the other grid (mapping).

• If the grid moves, this mapping has to be done in each

time step…

• … or even in each iteration, in the case of DFBI…
• Volume mapping can thus be expensive!

Volume Coupling, III

Example from Technip, I

t = -17.33 s t = 0 s t = 1.16 s

Solution domain for 3D RANSE computation Solution domain for 2D Euler computation

• 3D-RANSE computation is performed only over the time

0 – 1.5 s in a domain 2 m long and 1 m wide around the cylinder.

• 2D solution of Euler equations to obtain the desired wave

at the cylinder position is performed over a 20 times longer solution domain (> 100 m) and over 20 times longer time period (ca. 20 s).

• 2D Euler solution is used to initialize RANSE computation

at the desired time, ignoring the obstacle (as we do with theoretical wave solutions).

• Mapping 2D solution to 3D domain is much less

expensive than 3D to 3D…

Example from Technip, II

• Theoretical solutions can also be used for volume

coupling…

• Instead of specifying inlet conditions based on theory,
• ne can use a forcing zone to impose theoretical solution

in any part of the solution domain.

• The advantage of this approach is that it provides

damping both upstream and downstream of obstacles.

• The disadvantage is that theory may not be a good

representation of the solution of Navier-Stokes equations (e.g. linear wave theory)…

Coupling to Theory, I

• Example: Stokes 5th-order wave theory imposed at both inlet

and outlet over forcing zones of different length…

• Note: The computed wavelength is slightly shorter than

theoretical, but the solution is forced to theory over a short distance (the forcing coefficient is too strong).

Coupling to Theory, II

Blue: Stokes theory (5th order) Red: Computed Forcing zone Forcing zone

Coupling to Theory, III

• 3D example: Flow around a vertical cylinder
• The cylinder disturbs the free surface; disturbances propagate in

all directions.

• Inlet is relatively near cylinder – reflections can be better
• bserved…
• The solution domain is 9.2 m long and 6.4 m wide; cylinder

diameter is 1 m and its axis is 3.8 m away from inlet.

• Stokes wave parameters: wavelength 3.2 m, wave height 0.2 m,

wave period 1.4043 s

• The mesh is locally refined in free-surface zone and around

cylinder (80 cells per wavelength and 20 cells per wave height). Forcing is applied all around cylinder…

Coupling to Theory, IV

Grid in the free surface and the value of the forcing coefficient µ0: red means RANS-zone, blue means maximum forcing to Stokes 5th-order theory. Outside zone around cylinder, the grid is only fine in x- and z-direction to resolve free surface variation – in y-direction it is coarse since the wave is long-crested. 2.4 m 1.2 m 1.6 m 1.6 m

Coupling to Theory, V

Grid in the longitudinal section through the solution domain, also showing volume fraction distribution after 4 periods.

Coupling to Theory, VI

Volume fraction of water in the longitudinal section through the solution domain, also showing the free surface shape from Stokes 5th-order theory, after 4 periods. Note that the computed free surface position corresponds to the theory within forcing zones. Forcing Forcing

Coupling to Theory, VII

Volume fraction of water in the symmetry plane (upper) and side boundary (lower), also showing the free surface shape from Stokes 5th-order theory, after 4 periods. Note that the computed free surface near inlet does not correspond to the theory, due to reflections. Computation using standard approach in STAR-CCM+ (inlet + damping at outlet, symmetry conditions at sides)

Coupling to Theory, VIII

Computation using inlet, damping at outlet, symmetry at sides Computation using forcing (at inlet, sides and outlet) Free surface after 4 periods (around cylinder it looks the same) Disturbances due to reflections at symmetry and inlet

No obvious

disturbances

Coupling to Theory, IX

Animation of simulated free surface motion during the 3rd and the 4th period (using forcing). Along boundaries the free surface position corresponds to Stokes 5th-order wave theory.

Coupling to Theory, X

Animation of simulated free surface motion during the 3rd and the 4th period using the standard approach (inlet condition from Stokes 5th-order theory, side boundaries are symmetry planes, outlet is pressure boundary set to represent flat free surface and damping is applied over 2.4 m towards outlet).

Coupling to Other Solutions, I

• 2D example: Laminar flow of water around a circular cylinder in a

channel, Reynolds number 200.

• Boundary conditions: steady uniform flow at inlet, constant

pressure at outlet.

• Vortices are shed by the cylinder; pressure-outlet boundary

condition is not optimal for outgoing vortices – disturbances

• ccur…
• The solution is forced into channel flow without obstacle over

some distance towards outlet.

• The aim of coupling to undisturbed channel flow is to avoid

disturbances at outlet, i.e. to obtain an almost steady flow at

• utlet.

Coupling to Other Solutions, II

2D grid for the computation of unsteady laminar flow around cylinder in a channel (only part of the solution domain is shown – it is longer both upstream and downstream, with grid structure similar to what is seen here at both ends). The grid has 180 cells along cylinder perimeter and the thickness of the first cell next to wall is 1/166th of the cylinder diameter. The time step was set to 120 steps per period of lift oscillation (on average 60 steps per period of drag oscillation). Under- relaxation factors were 1.0 for all transport equations and 0.5 for pressure.

Coupling to Other Solutions, III

No forcing Forcing

Drag force on cylinder: the result is practically identical, i.e. the forcing of the flow far away from cylinder does not influence the flow around cylinder (as far as drag and lift are concerned).

Coupling to Other Solutions, IV

Animation of pressure variation: no forcing (upper) and with forcing (lower)

Coupling to Other Solutions, V

Animation of velocity variation: no forcing (upper) and with forcing (lower)

Future Developments

• Future developments of STAR-CCM+ will include:

 The possibility to apply the method described in this

presentation as a feature rather than field function coding:

• Coupling to theories available in STAR-CCM+ over some

distance to boundary (as is the case with wave dumping currently);

• Coupling to 2D simulations of undisturbed flow running

simultaneously in another region (providing the solution without

• bstacle).



Generic API for surface coupling at selected boundaries;



Generic API for volume coupling over selected zone(s).