BODY FITTED COORDINATES
DOCUMENTATION
• BFC phoenics online documentations:
– Introduction,
– Boundary Conditions and
– GCV (general colocated velocity method)
• Tutorials (look for BFC tutorials)
• Browse at the phoenics input library cases for:
BFC and Multblock
When To Use BFCs
• BFCs are particularly suitable for internal or external
flows with smoothly-varying non-regular boundaries.
• For such flows, BFCs provide:
• good geometric representation,
• possibility of economical grid refinement close to the
surface,
• good representation of surface boundary layers, and
hence of wall friction and heat transfer.
• BFCs can also be used to reduce numerical "falsediffusion" errors, by aligning the grid with the local
flow direction where possible, e.g., for angled jets
(inclined fan heater in a room)
• Columns of cells must continue from one
end of the grid to the other, i.e., the
mesh is structured.
• The cells are counted using the same
conventions as in Cartesian and polar
geometries:
• 1 to NX in the IX-direction
• 1 to NY in the IY-direction
• 1 to NZ in the IZ-direction
• The grid corner points must be
prescribed by the user, via a Cartesian
frame of axes, (XC, YC, ZC).
• The alignment of the Cartesian axes - and
the origin - can be chosen arbitrarily.
• NOTE: The Cartesian coordinates
(XC,YC,ZC) must NOT be confused with
the cell-indices (IX,IY,IZ).
• Note how the Cartesian and grid axes
only coincide for the first few cells.
Coordinate
Systems
Structure of the Grid File
• XC, YC and ZC are the Cartesian
co-ordinates of the nodes.
• Note that: I goes from West to
East, J goes from South to North,
and K goes from Low to High.
• I, J & K count nodes (cell corners),
• IX, IY & IZ count cells.
• NX, NY and NZ are the numbers
of cells in the I (IX), J (IY) & K (IZ)
directions.
WEST
EAST
I=6
I=1
IX=1
IX=5
Velocity Components
• Q is the total velocity vector.
• U1, V1 (and W1) are the
SOLVEd velocity resolutes.
• UCRT, VCRT (and WCRT) are
the deduced vector
components in the Cartesian
coordinate system.
• UC1, VC1 (and WC1) are the
deduced vector components
in the grid line directions (the
co-located velocities)
IY
IX
The Steps In BFC Grid Generation
1. Specify POINTS - provide the Cartesian coordinates of
key features of the geometry to be meshed
2. Specify LINES - join the points by lines, which are
divided into segments corresponding to the number
of cells which lie along the line. Lines may be straight,
arc segments, or spline curves through defined points.
3. Create FRAMES - link the lines to make 2-D FRAMES.
Frames always have four corners.
4. MATCH Grid to Frames - match the grid plane to
appropriate frames.
5. Form the 3-D Grid - link 2-D grid planes to form a 3-D
grid.
POINTS
LINES
EACH LINE IS DIVIDED IN POINTS WHICH
WILL FORM THE VOLUMES
EXTRUDING TO FORM VOLUMES
FORMING THE FRAMES
EACH FRAME HAS ALWAYS 4 CORNERS
SEE ADDITIONAL INFORMATION AT: Introduction,
WORKSHOP#1: SETTING A BFC GRID
5
5
5
Y
10
DIMENSION: NX = 15 & NY = 10
X
a. Set to view plane (XY);
b. click on mesh togle;
c. Select BFC grid
• Problem
data
WORKSHOP#1 – STEP2
Setting: points, lines, dimension and lines
RESCUE Q1
WORKSHOP#1 – Step 3
FRAMES always have 4 corners only
Frame#1: corners
Frame#2: corners
Frame#3: corners
Number of Cells on
each side of the Frame
has to match!
WORKSHOP#1 – Step 3
Setting a Frame
WORKSHOP#1 – Step 4 Match a grid
a. Pick the first corner of a Frame
b. Match the corner with the NODES coordinates
c. Specify the first corner direction to the next points. All frames
have right-handed axes. Ex: B->C +I & C->D +J
(I,J,K)
(1,6,1)
(I,J,K)
(1,1,1)
(I,J,K)
(6,1,1)
RESCUE Q1
WORKSHOP#1 – Step 4 Match a grid
WORKSHOP#1 – Step 5 Volume
a. Grid along (XY) plane
b. To create volumes is necessary to extrude the grid along the K
direction
Inlet Boundary Conditions
• It is a special b.c. because
the mass fluxes are related
to the U1, V1, W1 resolute
and not to the UCRT, VCRT
and WCRT.
• In general the required angles will vary from cell to cell.
• Subroutine GXBFC has been provided to calculate the inlet
conditions automatically, for the case of uniform inflow.
• UCRT, VCRT, WCRT and density is non-standard, and simply
provides a mechanism for transmission of UIN, VIN, WIN
and RHOIN to GXBFC
SEE ADDITIONAL INFORMATION AT: Boundary Conditions
Use Of Cyclic Boundaries
• The default setting in PHOENICS is no cyclic conditions, and a
symmetry condition is assumed.
• Cyclic (or periodicity) boundary conditions applies only along the east
and west boundaries of XZ plane.
• The provision for BFCs is intended for turbomachine (and airfoil)
applications in which cyclic conditions are needed at the entrance to
and exit from the blade passage.
• To activate x-cyclic boundaries: Group 6, Q1 file:
• XCYIZ(1,NZ,T) (switches XCYCLE on for all IZ slabs)
• XCYIZ(1,9,T)
(switches XCYCLE on for IZ=1 to 9)
case B523 exemplifies the use
of x-cyclic boundary conditions
for the flow through a cascade
of wedges
• Models:
– elliptic GCV and,
– solution for Vel & P
– KECHEM
• Numerics: 200 iter.
• Props: Fluid: air(0)
• Create objects:
– inlet size: (10,1,1) & -2 m/s,
– outlet size (5,1,1)
– blocakge.
• Note: case B116 has 15x15
volumes.
RESCUE Q1
plate
plate
outlet
inlet
plate
WORKSHOP#1: SET UP A CASE USING BFC
Real world is not so simple
Automatic Block Links
• The GCV solver uses
overlapping cells at block
joints. These cells must exist
in the individual block grid
files.
• Link automatic is when the
blocks blocks share the same
IJK orientation and same
number of cells
A Natural Link
• A natural link is when the blocks share the same IJK orientation but
not the same number of cells
B2
S
N
B1
• B1 share the
north face of L3
with the south
face of B2
Basic steps for Multi-Block Setup
a. Plan the decomposition of domain
into individual blocks. A possible
configuration is shown above. Block
1 is to be 5 x 15 x 1, and Block 2 is to
be 15 x 5 x 1.
b. Generate the grid for each individual
block. The grid for each block will be
generated in a separate meshgenerator session.
c. Combine the grids to form the multiblock grid and define inter-block
links. This step involves hand-editing
the input Q1 file.
d. Define remainder of the problem
(variables, boundary conditions,
B2
B1
Block links
a. The GCV solver uses overlapping
cells at block joints. These cells must
exist in the individual block grid files.
b. Only the linked faces of a block
require an extra layer of dummy cells.
c. Block B1 has an extra plane of nodes
at J =17 with thickness DY=0.
J=6
B2
J=2
J=1
J=17
f. See further examples at GCV
DY=0
J=16
(16,5)
d. Similarly B2 has an extra plane of
nodes at J = 1 with thickness DY =0
e. These extra nodes are most
conveniently copied exactly from the
'real' edge nodes, so that they are
invisible to any viewing program.
(15,6)
B1
J=1
Linking the blocks in Q1
•
•
•
•
•
•
TALK=T;
RUN( 1, 1)
BFC=T
NUMBLK=2
READCO(GRI+)
MPATCH(1,MBL1-2,
NORTH,1,NX,NY-1,NY-1,1,NZ,1,1)
• MPATCH(2,MBL2-1,
SOUTH,6,10,2,2,1,NZ,1,1)
• STOP
• See additional information on
linking blocks at GCV
J=6
B2
(15,6)
J=2
J=1
J=17
DY=0
J=16
(16,5)
B1
Y
J=1
X
WORKSHOP#2 –
Flow in a bifurcation; a natural link
• Each block’s grid is developed
and then linked together.
WORKSHOP#2 - Flow in a bifurcation;
• We will follow the
workshop on how to
assemble natural links in a
pipe bifurcation: wksh
multiblock 1.
• To short the drilling time,
please download the q1
file which contains the
Points and Lines.
• After UPLOADING the file
start from section: ‘Set
grid for first block’ on
wksh multiblock 1.
WORKSHOP#2 – Blocks’ construction;
• Hint: before building MGRID2 (left) erase: the volume, the frame
and the cells of MGRID1 (right) leaving only the lines.
• Rescue q1 files at the links: MGRID1 and MGRID2.
WORKSHOP#2 – Assembling the case
• Rescue q1 files at the links: MGRID3, GRI1, GRI2. Save these files
at your working directory.
Unnatural Block Links
• Link is unnatural when the blocks do not share the same IJK
orientation
W
N
Y
B3
N
S
B2 W E
B1
X
Blocks 1&2 and 1&3 are linked 'naturally' - West to East and South to
north, whilst the link between 2&3 is 'unnatural' - a North face is linked
to a West face.
The instructions are in the tutorial: workshop multblock-2; also visit the
links: READCO , MPATCH and link the three blocks.
Basic steps for Multi-Block Setup
a. Plan the decomposition of domain
into individual blocks. A possible
configuration is shown above.
Each block is to be 5 x 5 x 1.
b. Generate the grid for each
individual block. The grid for each
block will be generated in a
separate mesh-generator session.
c. Combine the grids to form the
multi-block grid and define interblock links. This step involves
hand-editing the input Q1 file.
d. Define remainder of the
problem (variables,
boundary conditions, etc).
WORKSHOP#3 - Flow in a disk sector;
• We will follow the workshop on
how to assemble un-natural
links in a disk sector: workshop
multblock-2
• To short the drilling time, please
download the q1 file which
contains the Points and Lines.
• After UPLOADING the file start
from section: ‘Set grid for first
block’ on workshop multblock-2
WORKSHOP#3 – Blocks’ extrusion parameters
B3
W
N
S
B2
N
E W
B2
B1
B3
B1
UGRID1.q1
BLOCK #
Direction K 
Direction J 
Direction I 
B1
plane
from/to
1 to 2
6 to 7
2 to 1
UGRID2.q1
B2
plane
from/to
1 to 2
6 to 7
6 to 7
B3
plane
from/to
1 to 2
2 to 1
2 to 1
UGRID3.q1
Length
dZ = 1
dY = 0
dX = 0
WORKSHOP#3 Matching Blocks
q1 code lines
B3
W
S
N
B2
N
E
W
B1
TALK=T;RUN(1,1)
BFC=T
GCV=T
NUMBLK=3
READCO(UGRI+)
MPATCH(1,MBL1.2,WEST,2,2,1,NY-1,1,NZ,1,1)
MPATCH(2,MBL2.1,EAST,NX-1,NX-1,1,NY-1,1,NZ,1,1)
MPATCH(1,MBL1.3,NORTH,2,NX,NY-1,NY-1,1,NZ,1,1)
MPATCH(3,MBL3.1,SOUTH,2,NX,2,2,1,NZ,1,1)
MPATCH(2,MBL2.3,NORTH,1,NX-1,NY-1,NY-1,1,NZ,1,1)
MPATCH(3,MBL3.2,WEST,2,2,2,NY,1,NZ,1,1)
SPEDAT(SET,GCV,MBL3.2,C,WNL)
STOP
• If the blocks are rotated relative to each other in IJK space (B3 to B2),
the block alignment must be specified through SPEDAT command.
• This string defines how the N, E and H faces of the first block link to
the second block. The default, natural, link would be S W L; i.e. North
to South, East to West and High to Low, see B1 to B3 and B2 to B1.
WORKSHOP#3 - SPEDAT COMMAND & BLOCK ROTATION
N
B3
y
W
N
W
B2
y
E
Blocks’
Linkages
E
N
S
B3
S
W
x
B3 is
rotated 90º
from B2
N
W
B1
B2
S
E
E
N
B3
S
W
x
SPEDAT(SET,GCV,MBL3.2,C,WNL)
BLOCK#3 -> N E H
  
BLOCK#2 -> W N L
The string defining the block rotation consists of three letters, which
may be any of E W N S H L. The individual characters define the relative
orientation between the N, E and H faces of the first block (B2) of the
pair of blocks, and the current block (B3) respectively.
WORKSHOP#3 – Case setting;
• Properties: air (0)
• Model: laminar, activate
velocities, CGV
• Numerics: 100 iteractions
• Objectcs: Inlet (V = 1,0 m/s)
& Outlet
WORKSHOP#3 – Results
•
Rescue q1 files at the links: UGRID123, UGRI1, UGRI2, UGRI3. Save these files at your
working directory.
Multblock Application in Complex Geometry
• The selected figures come from
the cases available in the phoenics
input library ( Multiblock)
Phoenics BFC Generator
• The Phoenics built-in BFC Generator is helpful for
simple problems.
• If one application demands several ‘natural or
unnatural’ links the mesh generation process
becomes very complex.
• In this scneario phoenics BFC generator is not
recommended. There are specific software for mesh
generation recommended such as: ICEM,
Airfoil Grids
http://courses.cit.cornell.edu/fluent/airfoil/step1.htm
• The domain size is expressed in terms
of the airfoil thickness.
• Airfoil with finite thickness (present
illustration) require Natural and/or
Unnatural links, unfortunately. It is not
an easy task to do using Phoenics BFC
grid generator!
C Grids for Finite Thicknes Airfoil
( represent the frames’ corners)
finite thickness trailing edge
zero thickness trailing edge
x
(G)
(F)
(E)
y B3
B4
(L)
B1
y
(A) x
•
•
•
•
•
y
(B)x
(F)
(G)
(E)
B3
(H)
y
x
(D)
B4
B1
B2
(C)
Blocks B1, B2, B3 have natural links
B4 is 180o rotated in regard to B1.
Multi Block grid.
Provide extra Y cells to B1 and B4
SPEDAT(SET,GCV,MBL4.1,C,NEL)
(A)
•
•
•
•
•
(D)
(L)
B2
(B)
(C)
Blocks B1, B2, B4 have natural links
B3 is 180o rotated in regard to B4.
Multi Block grid.
Provide extra Y cells to B4 and B3
SPEDAT(SET,GCV,MBL4.3,C,NEL)
Finite x Small Thickness Airfoil
• The small thickness airfoil is gives an approximated solution.
• The thin airfoil consists
of a line and it is easily
setup on the BFC mesh
generator in phoenics.
Natural links for airfoil: frames
Natural links for airfoil: grid
This grid would be a 2nd choice for the C grid. It still can be improved
by changing the inclination of lines L23 & L24 an designing a better
number of cells to result in a more orthogonal mesh. One can also
design a similar grid for a zero thickness airfoil