GRIDS
OR
MESHES
Discretização das Equações
• As Equações de Transporte não são resolvidas analiticamente. Ao contrário, seu
domínio de cálculo é dividido em volumes onde se busca alcançar uma solução
numérica.
• A função da malha é definir a dimensão dos volumes, das áreas das faces e das
distâncias entre centros e vértices onde serão avaliados os fluxos e outros termos
fonte.
• Em contornos simples (cartesianos ou cilíndricos) é relativamente fácil criar uma
malha ortogonal que se adapte a este contorno
• O desafio reside em adaptar malhas em contornos complexos
Discretização das Equações
• Devido aos mais diversos motivos, a malha pode vir a ser modificada
 geometrias irregulares;
 localização / investigação de fenômenos em locais específicos;
 redução do número de volumes (rapidez de simulação, áreas mortas).
• Há diversas maneiras de se personalizar a malha (grid);
 técnicas como espaçamento em progressão geométrica ou segundo
uma power-law;
 malhas definidas por objetos (ver caso da biblioteca 290);
 finegrid.
Características das Malhas utilizadas nas
simulações do PHOENICS
• Malhas
estruturadas
hexaédrica):
1)
2)
(geometria
cartesiana / polar / cilíndrica –
todas ortogonais;
BFC (body-fitted coordinate) –
ortogonalidade variável.
Structured Mesh
•Hexahedral elements orderly spaced with orthogonal or
near orthogonal faces require three coordinates to locate
each corner point, or 3*(I+1)*(J+1)*(K+1) values for the entire
grid, which is much larger than the I+J+K values needed for
rectangular grids.
•In addition, other three-dimensional arrays are usually kept, such
as their face areas and volumes, so these quantities don't have to
be constantly recomputed.
•This uses a large amount of stored memory and increases memory
retrieval times. Although memory is becoming inexpensive, the
amount of memory to be retrieved is becoming an important
consideration in parallel computing.
•The distortion of elements away from a purely rectangular shape
has several consequences. For one thing, distortion may reduce
numerical accuracy because numerical approximations are no
longer centered (or symmetric) about the centroid of the volume
element. This drawback, however, may be balanced by the
increase in local grid resolution
Grades Cartesianas e Polares
Uniforme
Cartesiana
Uniforme
Polar
Não-Uniforme
Power
Não-Uniforme
duas regiões
Não-Uniforme
Fine Grid Embedding
O sistema polar de coordenadas do PHOENICS
• O Sistema cilíndrico polar está implementado no PHOENICS e seus
termos fontes associados: centrífugo e coriolis para as equações de
quantidade de movimento.
• No sistema polar é necessário definir o Raio Interno, RINNER.
• As demais especificações de domínio são coincidentes com
aquelas do sistema cartesiano.
• A direção X do cartesiano
corresponde a direção tangencial.
• A direção Y do cartesiano
corresponde a direção radial.
• A direção Z do cartesiano
corresponde a direção axial.
Body Fitted Coordinates
Hexahedral elements with orthogonal or near orthogonal
faces which adapt to the body profile.
Access link to PHOENICS tutorial: BFC
Tratamento Sólido - Parede
• PARSOL: partial solid – por default ativado
Modelo implementado no PHOENICS que permite distinguir
sólido de fluido em um mesmo volume de controle.
Malha cartesiana com
volumes bloqueados pelo
sólido
Malha BFC
Outros Exemplos de PARSOL com Fine-Grid
IMPORTAÇÃO & GERAÇÃO DE
OBJETOS
• AutoCAD – export format: STL
or DXF format files
• Shapemaker
• AC3D
Outros Recursos
• interpolação para malhas mais refinadas: PINTO (ver tutorial)
• refinamentos dinâmico (time-varying) – exemplo: pistão de motor;
• Observações:
 evitar
distorções nas malhas (> 1:3 pode ser perigoso)
 sempre
malhas eulerianas;
Grades BFC e Mult-Block para Geometrias
Complexas Multi-Block
Body Fitted Coordinates - BFC
Ortogonal ou Não Ortogonal
Ortogonal ou Não Ortogonal
Grade Cartesiana com Objetos Imersos:
• Iteração volume a volume tipo ‘escada’ ou;
• Iteração via software com algoritmo PARSOL
Unstructured grids
Unstructured Meshing of Control Volumes
Unstructured grids have the advantage of
generality in that they can be made to
conform to nearly any desired geometry. This
generality, however, comes with a price. The
grid generation process is not completely
automatic and may require considerable user
interaction to produce grids with acceptable
degrees of local resolution while at the same
time having a minimum of element
distortion. Unstructured grids require more
information to be stored and recovered than
structured grids (e.g., the neighbor
connectivity list), and changing element types
and sizes can increase numerical
approximation errors.
Optimization of Alumina Refinery Isolation
Valves
WORKSHOP: Fine Grid Application
• Fine grid increases the grid
fineness in specific regions while
on other regions the domain
employs a coarse grid. This
strategy can reduce the
computational time.
coarse grid
fine grid
• Observe on the figure that at the grids’ interface a single coarse
grid cell face shares two fine grid cell faces.
• The have success on fine grid applications avoid:
• placing the grid interface at regions with strong gradient,
• introducing fineness greater than 3. Prefer the use of
double or tripling fineness in multiple of 2 instead
WORKSHOP: Fine Grid Application
• This workshop models the laminar flow
around a circular cylinder in a free stream.
• The objective is to compare the use of FG
(50x50) against regular grid (100x100) with
equivalent FG cell sizes to estimate the wake
length behind the cylinder and the CPU time.
Flow visualization at the wake
of a cylinder at Re of 41
Experimental data: laminar flow regime
Problem Data
Domain Properties: RHO1=1 & ENUL = 0.015
outlets
Model
Inlet
Cylinder
U=1,025 m/s
D=0.6m
6m
Fine
Grid
10m
OBJ
SIZE
IN
PLACE
SIZE
EOUT
PLACE
SIZE
SOUT
PLACE
RELAX
X
Y
Z
0
6
1
0
0
10
10
0
0
6
0
0
0
0
1
0
1
0
AUTO
ATRIBUTES
OBJ
U = 1,025
CYL
P=0
P=0
X
Y
Z
ATRIBUTES
0,6
0,6
1
SOLID WITH
FRICTION
3,7
2,7
0
5
3
1
FG
FINENES = 2
2,5
1,5
0
10
0
1
NOUT
P=0
0
6
0
XMON YMON ZMON
5,62
3
0,5
Grid Check: 51 x 51 with FG x 2
• Use the auto-mesh and adjust the init-cell-factor to get a
51x51 grid.
• Place the pointer downstream saddle point, choose: (x,y,z)
= (5.62, 3, 0.5)
• In Numerics box set sweeps to 3200.
• It is ready to run
Wake length: numerical x experimental
51 X 51 with FG X2
CPU time of run 30 s
Rescue q1
100 X 100
without FG
CPU time of run 60 s
Rescue q1
Wake length: numerical x experimental
100 X 100 with FG X2
CPU time of run 390 s
200 X 200
without FG
CPU time of run 500 s
Comments I
• The reduction on the CPU time with the use of FG is of 50%
for a 50 x 50 grid. The prediction on the wake length is
equivalent for a uniform grid although not coincident with the
experimental value.
• A 100 x 100 grid with FG makes it hard to get a solution
satisfying the residuals. The relaxation factors have to be
reduced and the CPU time increases. There is still a reduction
in CPU time but it is less than the 50%. Perhaps a search of
optimum relaxation factor is necessary.
• The use of FG is more appropriate for problems where flow
changes more quickly in a specific region while in others it
remains fairly behaved.
Comments II
Unbounded domain
Symmetric domain
• The use of outlets to the
North and South faces of
the domain is necessary
to simulate the flow
around a cylinder in an
unbounded fluid, i.e., like
the atmosphere.
• When one uses the
symmetry condition, i.e.,
just leave these frontiers
to the default condition,
it is like having mirror
images of the cylinder.
• The confinement of the
mirror images of the
cylinders increases the
maximum velocity
Further Simulations
• Just get the 50 x 50 FG case and double the
inlet velocity, 2,050 m/s. The Re number now
should be of 82.
• Try run this case and comment your results.
Comments
• When the inlet velocity changed to 2,050 the solution did not
converged. On the contrary, the monitor spot was periodic. The
residuals were high after 2000 sweeps.
Comments
• The X velocity field was quite distinct from the Re 41.
• The question is: this discrepancy is due to a numerical
problem or the physics of the phenomena has been changed
Comments
• The physics of the phenomenon has been changed!
• The flow above Re 47 is periodic.
• A flow instability develops at the separated regions
shedding wall vorticity to the wake flow.
• See further information on the following links
– Reference 1
– Reference 2
Drag & Flow visualization at
different Re
Re=104
Further references
Go to POLIS and visit:
• Documentation...
Hard-copy documentation
> Starting with PHOENICS-VR; TR 324
> The PHOENICS-VR reference guide; TR 326
FLOW WITH ANGLED INLET/OUTLET
• Air distribution inside a 2D ware-house
• The case shows a 2D cross-section through a long warehouse.
An ANGLED-IN object is used to inject air at 2m^3/s normal to
the roof, and an ANGLED-OUT object is used to create an
opening on the sloping roof.
Settings
• Models:
– Velocity ON; Turbulence: KECHEN; Energy: OFF
• Properties
– Air (material 0)
• Numeric:
– 500 sweeps
Objects settings
SET DOMAIN: X = 10M, Y = 1M & Z = 4M
OBJ
X
Y
Z
2
1
1
PLACE
1,5
0
SIZE
2
SIZE
PLACE
SIZE
PLACE
CRATE1
CRATE2
ROOF1
ATRIBUTES
OBJ
X
Y
Z
ATRIBUTES
BLOCKAGE
ROOF2
5
1
1
0
10
0
4
BLOCKAGE,
WEDGE
1
1
1
1
0,75
6,5
0
0
2
0
5
5
1
1
1
1
0,75
0
0
4
7
0
4
BLOCKAGE
IN
BLOCKAGE,
WEDGE
OUT
XMON YMON ZMON
RELAX
FALSDT, U1 =V1=100 & 100; KE=EP=-0,5
5
0,5
2
ANGLED IN,
Q=2m3/s &
k=5%
ANGLED OUT
Comments
• The angle in object was set to give volumetric
flow rate normal to the aperture of roof1.
• It is also possible specify a velocity. For
example, try set a velocity of 2m/s directed at
45o to the left of the vertical.
U1  2  Sin45  1.414 m/s
W1
45o
U1
W1  2  Cos45  1.414 m/s