Example 57

November 2011 57.1 Version 14.0.0

EXAMPLE 57

2D ELASTIC REMESHING

DESCRIPTION

This example illustrates the use of the elasticity remeshing technique. The flow domain is depicted in figure 1. It consists of 2 domains: the inner one corresponds to a fluid with a viscosity of 1[Poises] and a density of 1 [gr/cm3], while the outer one is related to a fluid a 0.5 [Poises] for the viscosity and 1.23 [gr/cm3] for the density. The boundary set 1 represents a rotating rod.

SD1

SD2

BS1

BS2

Interface

10 cm

6 cm 4 cm

2 cm

Fig. 1. Geometry, sub-domains, boundary sets and mesh.

KEYWORDS

remeshing technique: elastic, multi-fluid

FILENAMES

remelas2d.msh, remelas2d.dat, remelas2d.cons, remelas2d.cfx.res and remelas2d.res

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November 2011 57.2 Version 14.0.0

SYSTEM OF UNITS

centimeter-gram-second

MATERIAL DATA

The flow is isothermal and the physical and material properties have been chosen as follows: Fluid 1 - constant viscosity = 1.[Poise],

- density: [g/cm3], - inertia is taken into account, - gravity is neglected. Fluid 2 - constant viscosity = 0.5.[Poise],

- density: [g/cm3], - inertia is taken into account, - gravity is neglected.

BOUNDARY CONDITIONS

The boundary conditions are: - BS1 (Rotating rod): Vn = 0, Vs = 10 [cm] * f(t) with f(t) = t if t < 1 [s] f(t) = 1 if t > 1 [s] - BS2 (Wall): Vn = VS = 0 - Along the intersection of the sub-domains, we define a moving interface.

ELASTIC REMESHING

As we can see in figure 1, there is no regularity in the mesh and there is only 2 boundaries for each sub-domains, therefore we must use the elastic remeshing. This remeshing technique needs boundary conditions defined as follows: On BS1: No displacement. On BS2: No displacement. On intersection between SD1 and SD2: Moving interface. In order to use a remeshing technique such as Thompson, we ought to define, at least, 4 sub-domains and 5 boundary-sets.

SPECIAL COMMENT

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November 2011 57.3 Version 14.0.0

This problem must be solved with a transient scheme, a steady state problem requiring a boundary condition for the free surface or an equation expressing the mass conservation in each sub-domain. Therefore, we will simulate the problem as far as the steady state is reached.

POLYDATA SESSION

- Read a mesh file: remelas2d.msh - Create a new task: F.E.M task, transient - Create a subtask: Generalized Newtonian isothermal flow problem Domain: S1 Material data: Constant viscosity: 1 [Poise] Density: 1 [gr/cm3] Inertia taken into account. Flow Boundary Conditions: Along SD2: Interface Moving interface BS1: Vn,Vs imposed EVOL Vn = 0 Vs = 10 *f(t) f(t): ramp function a = 0.0 b = 0.0 c = 1.0 d = 1.0 EVOL Global remeshing Domain: SD1 Elastic remeshing Condition on displacement along borders Along SD2: Moving interface BS1: No displacement - Create a subtask: Generalized Newtonian isothermal flow problem Domain: S2 Material data: Constant viscosity: 0.5 [Poise] Density: 1.23 [gr/cm3] Inertia taken into account. Flow Boundary Conditions: Along SD1: Interface Moving interface BS2: Vn = Vs = 0 Global remeshing

Example 57

November 2011 57.4 Version 14.0.0

Domain: SD2 Elastic remeshing Condition on displacement along borders Along SD1: Moving interface BS2: No displacement Numerical parameters: Transient iterative parameters: Upper time limit: 100 Max time-step: 25 - Filename syntax: New prefix: remelas2d Outputs - Default output : CFD-Post - System of units for CFD-POST: metric_cm/g/s/A+Celsius - listing: max. - Save and Exit: - mesh file: remelas2d.msh - data file: remelas2d.dat - result file: remelas2d.res - CFD-Post: remelas2d.cfx.res

RUNNING POLYFLOW

The input file for POLYFLOW is 'remelas2d.dat'. POLYFLOW generates a result file 'remelas2d.res', and result files for CFD-Post.

polyflow < remelas2d.dat > remelas2d.lst

GRAPHIC POST-PROCESSING

As we can see in the listing file, we have reach the steady state because, for the last steps, the time-step increases until 25[s] while the last step converges with 1 iteration only and the relative changes are of the order of magnitude of 10-6.

The figure 2 shows the interface position and the mesh for the steady state solution (last step: 100 [s]).

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November 2011 57.5 Version 14.0.0

Fig. 2. Interface position (left) and mesh (right) for steady state (t = 100 [s])

The figure 3, 4 and 5 present the velocity vectors colored by the velocity magnitude, the iso-values of velocity magnitude and the iso-values of pressure respectively.

Fig. 3. Velocity vectors colored by the velocity magnitude for steady state solution.

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Fig. 4. Iso-values of velocity magnitude for steady state solution.

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Fig. 5. Iso-values of pressure for the steady state solution.

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The table 1 gives the mass conservation for the first step and for the last one. The mass conservation is quantified by the surface of the fluid domain. At the end of the simulation, after 47 steps, the error over the mass conservation is only 0.22% This is acceptable. Step Surface SD1 Error SD1 [%] Surface SD2 Error SD2 [%] Exat 37.70 0.00% 41.73 0.00% 1 37.71 0.03% 41.77 0.10% 47 37.65 0.13% 41.82 0.22%

Table 1. Mass balance: error over the surface of the flow domain.