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P age 2 of 8
To overcome difficulties using RANS, Large
Eddy Simulation (LES) is proposed that r esolves
the main turbulent structure instead of modeling
it . In LES onl y sub- grid sc al e turb ulence smaller
than local grid resolut i on, is modeled. In addition
no wall f unc tion is used, instead, wall lay er is
cap t ur ed. R esol v ed (u nsteady large scal es) are
capable to predict transition, cor r ect flow b ehavior
and accu rat e heat transfer co efficient . The
dra wb acks are computa tional i nte nsity a s we ll as
exploring turbulent friendly boundary conditions.
This work repr esents the first attempt to
investigat e effectiveness of LES simulation tool in
board level analysis. Areas emp hasized are: 1)
finding required mes h resolution for accurate the
boar d level simu lation, 2) investiga ting proper
boundar y conditions, a nd 3) Deeper understanding
of physics in boar d level analys is.
R e quired mes h resolu ti on f or LES is a f unct ion
of numeric al s c h e me. Most c o mmercial co d es are
used in thermal management industr y emp loy fir st
or second order accurate met hods. First or der
methods are tw o diffu si ve and a re not
recommended for LES. To det ermine the requ ired
mesh resolution for a second order scheme a
benchma rking pr oblem ha d to be sought.
Turbulent cha nnel flow, (i.e. turbulent flow
betw een two parallel plates) is ext ensivel y us ed
for this pur p ose. T his problem is s imula ted L E S
using F luent CFD code. S ub-grid model of
S magorinsky [1] and periodi c boundary
conditions are implement ed. Sma gorinsl y model
in an algebra ic eddy vis cos ity model that
dissipa tes sub-grid eddies such that correct
balance b et ween turbulen ce produc tion and
dissipa ti o n rea c hes. In reality, this b alanc e is a lso
fu nc tio n of numerical dissipation o f the s ch e me
(i.e. lower ord er sc hemes hav e s u c h numerical
dissipa tion tha t over sha dows effect of turbulenc e
model) [4] . To minimiz e this, tur bulent intensive
regi ons are fu lly res olved an d Smagor insk y’ s
constant, Cs, is set to be 0.1 that is common for
channel f low simulation wit h higher order non-
dissipa tive schemes.
Since LES is inherently transient, flow
st atist ics are collected for ev er y ti me step s . At the
end of the simulation, they a r e time/space
averaged and compared wit h experimental data.
Fina lly, following channel flow simulation,
two pr oblems were investigated. First a typical
air-cooled el ect ronic board with thr ee chips in a
row, and a h eat - si nk p rob lem in fre e s tream
turbulenc e.
Turbulent Channel flow
As men t ioned, this problem is sought as benchmarking
to es timate the required mes h resolu tion fo r ac curate
sim ulati on us i ng s e c ond order fin it e volume method
that is implemented in Fluent CFD code.
Channel is made of two infinite parallel plates
0.0445m (2 inches) apart. Air velocity between plates
is adjusted ar oun d 2 m/s. This correspon ds to Re=2800
based on channel mean velocity. Channel length and
width are 0.31 and 0.1 m resp ectively. This resembles a
typical air-cooling problem between electronic boards
used in telecommunication chassis. To mimic infinite
size of these plates, stream-wise and span-wise
periodic velocity conditions are implemented. This
means the same velocity profile that exits from one
face en t er s the ot h er fa ce of t h e ch ann el. Im pl emen tin g
periodic boundary condition is essential in that flow
instabilities evolve by exiting and entering back into
domain, growing overtime, hence leading to fully
turbulent flow.
Since the Reynolds number is known, extent of
laminar, buffer, and logarithmic sub-layers are
estimated. To capture the wall layer, ten cells are
allocated for the laminar sub-layer. Mesh is then
expanded into buffer zone to capture production of
stream-wise vortices responsible for boundary layer
turbulence as well as mixing. Mesh is then
geometrically expanded toward channel center. To
capture near wall streak y behavi ors of the fl o w i n span-
wise direction near walls (see [4]) more cells are used
in the span-wise direction than in stream-wise
direction. In total there are about 64 cell used in each
direction. Second order implicit time stepping method
is used. Ti me step is chosen such that, with in a step, a
fluid particle, with mean chann el velocity, could travel
one strea m -wise cell forwa rd. Figure 1 shows geom etr y
of the probl em.
To start turbulence a destabilizing mechanism is
required. In reality it comes from board roughness,
acoustic noise or other factors. Here two trips were
used (one for each surface) to initiate instability.
Figure 2 shows the effect of the trip located at the
lower surface on velocity vectors. Fairly large
separation is seen behind the trip. Flow is then
reattached down stream. Figure 3 illustrates speed
contours in a plane cut 1 mm above the lower plate.
Start of instabilities is clearly seen after flow
reattachment. At this time stream-wise and span-wise
periodic boundary conditions were activated to allow
instabilities re-enter the domain, hence, amplify. Over
time they evolve to self-sustaining turbulence and trip
was r emoved. Th en soluti on marched forward ti ll ful ly
turbulent ch annel flow realized.
Fi g ur e 4 sh ows a sn a p sh ot of sp ee d c on t ou r s wi th i n
the channel domain when flow is fully turbulent.
Figure 5 and 6 represent statistics for this