CERN Intensive Course on CFD 1st, March 2007
Hands on computer session:
6. Flow behind a bluff body
[Time: 1 h 30’]
Objects
• choice of computational domain and definition of simple boundary conditions
• techniques to obtain a smooth meshing of a “complex” domain, near wall refinement for wall
layer approximation and modelling;
• identification of reference data, calculation of quantities to verify simulation accuracy (drag
and lift coefficients, vortex shedding frequency and Strouhal number);
• calculation of heat transfer coefficients, comparison with available correlations from the liter-
ature;
Physical problem
Upflow of incompressible/compressible (buoyant) fluid around an object coupled to heat transfer
between object and flow:
• velocity field around the body depends on flow regime (steady or unsteady wake forms behind);
• velocity field around the body determines forces acting (drag and lift);
• the wake is modified for fluid heated by the object (thermal instability due to buoyancy is added
to fluid instability);
• heat transfer coefficient changes depending on the flow regime (thermal instability due to
buoyancy is added to fluid instability).
Low Reynolds High Reynolds
T out T out
Fdrag
F drag F lift
V in T in V in T in
Centro Interdipartimentale di Fluidodinamica e Idraulica 1
CERN Intensive Course on CFD 1st, March 2007
Data
cylinder diameter D = 20mm
channel width W = 6D = 120mm
channel lenght L = 12D = 240mm
channel height H = 2mm
Reynolds number Re = 160
fluid inlet temperature Tin = 293K
cylinder temperature Tcyl = 293 ÷ 300K
Worksheet
Mesh generation • evaluate thickness of wall layer around the cylinder to fully resolve the
flow;
→ use cylinder fitted SPLINE to generate a block of cells (half domain)
→ use CGEN-REFLECT to replicate subdomain regions
Boundary conditions → use symmetry B.C. to set up a bidimensional simulation
→ use Dirichelet B.C. (inlet) to fix the velocity and temperature of the
approaching fluid
→ use Pressure B.C. (outlet) at the downstream section
→ use Wall B.C.(slip option) to simulate the outer domain (free stream)
→ use a Table to increase the temperature at the cylinder wall
Initial conditions initial velocity field (V = cost) (or use fluid at rest)
Solution method • steady state simulation at Re=160 with fixed wall temperature, solve for
V , P, T
• transient simulation at Re=160 using a table for wall temperature, solve
for V , P , T
→ choice of relaxation factor
→ choice of differencing scheme
Results considerations over Strouhal number and buoyancy effect
use of tracers to represent streamlines
calculation of pressure coefficient over the cylinder
calculation of drag and lift coefficient
calculation of heat transfer coefficient / Nusselt number
animation of transient development of vortex shedding
References
Patnail, B. S. V., Narayana, P. A. A., and Seetharamu, K. N., (1999), “Numerical simulation of
vortex shedding past a circular cylinder under the influence of buoyancy”, Heat and Mass Transfer,
42, 3495-3507.
Zdravkovich, M.M., (1996), “Different modes of vortex shedding: an overview”, Journal of fluids
and structures, 10, 427-437.
Van Steenhoven, A. A., and Rindt, C. C. M., (2003), “Flow transition behind a heated cylinder”,
Heat and fluid flow, 24, 322-333.
Centro Interdipartimentale di Fluidodinamica e Idraulica 2
CERN Intensive Course on CFD 1st, March 2007
Geometry and Experimental results
127 128 129 131
60
125 124
126 1 2 X 123 130
10
20
40
200
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CERN Intensive Course on CFD 1st, March 2007
Figure 1: Drag coefficient vs. Reynolds number
Figure 2: Strouhal number vs. Reynolds number
Centro Interdipartimentale di Fluidodinamica e Idraulica 4
CERN Intensive Course on CFD 1st, March 2007
MACROS
!****************
! Geometry.MAC *
!****************
!———————————
!*** generation of points and splines
!———————————
csys 1
v 1 -20 0 0
csys 2
v 2 10 180 0
vset news vlist 2
vgen 121 1 vset vset 1 ,,-1.5,,
csys 1
v 123 20 0 0
v 124 20 20 0
v 125 -20 20 0
spl 1 vran 2 42 1
spl 2 vran 42 82 1
spl 3 vran 82 122 1
csys 1
v 126 -40 0 0
v 127 -40 60 0
v 128 -20 60 0
v 129 20 60 0
v 130 200 0 0
v 131 200 60 0
!————————————-
!*** generation of patches and 2D geometry
!————————————-
ctab 4 shell 6
patch 125 42 2 1 25 10
patch 124 82 42 125 25 10
patch 123 122 82 124 25 10
patch 127 128 1 126 5 30
patch 128 129 124 125 10 20
patch 129 131 130 123 50 30
vmer all
c
cset all
!—————————————————-
!*** extrusion of 2D geometry and creation of 3D mesh
!—————————————————-
vcextrude 1,mini,cset,cset,1,local,,,-2,both
get voff mxve
cset news fluid
!—————————-
!*** reflection around y-axis
!—————————-
cgen,2,voff,cset,,,vref,1,2
vmer all
n
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CERN Intensive Course on CFD 1st, March 2007
vcomp all
y
cset news shell
cdel cset
ccomp all
y
!————————————-
!*** refining the cylinder cells
!————————————-
cset news fluid
vset news edge
cset news vset any
cset subset gran -11.1,11.1,,,,,2
vset news cset
cset news vset any
crefine,2,1,1,cset,0,0,merge,nocouple
cset all
cplo
vcomp all
y
ccomp all
y
cset news type 5
ctype 1
cmod cset
ctdelete,2,5,1
vset none
cset all
cplo
!——————
!*** save the model
!——————
save exe6.mdl
!****************
! animation.MAC *
!****************
trload,exe6.pstt,nomvgr,,c
cset news fluid
csca,20,auto,reverse
set it 900 1
DEFI
STOR iter it
getv,stre
PLTB ON
REPLOT
PLTB OFF
END
LOOP 1 500
Centro Interdipartimentale di Fluidodinamica e Idraulica 6
CERN Intensive Course on CFD 1st, March 2007
!**************
! cp-time.MAC *
!**************
!—————————————–
!*** resume model, load transient solution
!—————————————–
resume exe6.mdl
trload,exe6.pstt,nomvgr,,c
pldi,off,all
!———————————
!*** setting time, loop definition
!———————————
set time 14 0.1
set frm 2001 1
defi noex
greset
y
sens dele all
store time,time
oper,getv,p,1,relative
oper,smul,165.9751,1,4
gpost,spline,4,50,next
frame,1,xreg,init,3
frame,1,xrange,-10,10
frame,1,xtick,0,0,real,noindent,bottom
frame,1,xtitle,6,0.5
X LOCATION
frame,1,yreg,init,9
frame,1,yrange,-5,1
frame,1,ytitle,12.0,5.5
CP
term,,x
scdu,gif,frm
gdraw,1
end
loop 1 10
!**************
! Nusselt.MAC *
!**************
!————————————
!*** resume model and load the *.pstt
!————————————
resume exe6.mdl
trload,exe6.pstt,nomvgr,,c
pldi,off,all
!———————–
!*** identification time
Centro Interdipartimentale di Fluidodinamica e Idraulica 7
CERN Intensive Course on CFD 1st, March 2007
!———————–
set tm 19
greset
y
sens dele all
!———————————————-
!*** load solution and computing Nusselt number
!———————————————-
store time,tm
getc,dens
getw,nearwall
psys,2
oper,getw,sfxyz,3
oper,mult,4,3,3
oper,sqrt,3,3
oper,getw,yplus,4
oper,smul,1.81e-5,4,4
oper,divi,4,3,3
oper,getw,hflu,1
oper,getw,temp,2
oper,smul,0.02637,2,2
oper,mult,1,3,1
oper,divi,1,2,4
cave all
!————————–
!*** creating registers
!————————–
gpost,spline,4,31,next
!——————-
!*** customize graph
!——————-
frame,1,xreg,init,3
frame,1,xrange,-10,10
frame,1,xtick,0,0,real,noindent,bottom
frame,1,xtitle,6,0.5
X LOCATION
frame,1,yreg,init,9
frame,1,ytitle,12.0,5.5
NUSSELT
gdraw,1
!*********
! CD.MAC *
!*********
resume exe6.mdl
trload,exe6.pstt
c
store,time,20
getwall,ftot,p,relative
cset news type 3
cset subset gran ,,11,,,,,2
acoeff,drag,0.12,1.205,4e-5,0.02,0,0,0,,
Centro Interdipartimentale di Fluidodinamica e Idraulica 8
CERN Intensive Course on CFD 1st, March 2007
!********************
! film-4windows.MAC *
!********************
!——————————————————-
!*** resume model, setting time, load transient solution
!——————————————————-
resume exe6.mdl
macro execute new-color.MAC
SET,TIME,9,0.1
TRLOAD,,
N
window,0,0,12,10
plme,off
pldi,off,all
title
FLOW BEHIND A BLUFF BODY - Re=160 - Twall=293/300
pldi,on,title
window,divi,2,2
POPT,CONT
PLTY EHID
CSET NEWS FLUID
TRINTERPOLATE,ON,CAVER CSET
!———————–
!*** Loop over timesteps
!———————–
SET FRM 1001 1
DEFI NOEX
greset
y
STOR TIME TIME
window,activate,1,1
getc,vmag
CSCA,20,user,0,0.16,,
CPLO
window,activate,1,2
oper,getv,su,1
oper,getv,sv,2
oper,getv,sw,3
oper,rotor,no,1
CAVER CSET
csca,20,user,0,50,,
CPLO
window,activate,2,1
getc,T
csca,20,user,293,300,,
CPLO
window,activate,2,2
getv,stre
csca,20,auto
CPLO
SCDU,GIF,FRM
Centro Interdipartimentale di Fluidodinamica e Idraulica 9
CERN Intensive Course on CFD 1st, March 2007
REPLOT
END
LOOP,1,20,1
Centro Interdipartimentale di Fluidodinamica e Idraulica 10
