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Board level thermal analysis via Large Eddy
Simulation (LES) tool
Farzam Roknaldin
Applied Thermal Tec hnologies
3255 Kifer Road
Santa Clara, CA 95051 USA
E-mail: roknald i@ app lied.f luent.com
Arunima Panigrahy
Departmen t of Mechanical En gin eer ing
San Jose Sta te University
ABSTRACT
Large Eddy Simulation (LES) is a step beyond widely
used Reynol d s A veraged Navi er Stok es f orm u lation
(RANS) with tur bulence model. LES is un steady,
ther efore, predicts evol u tion of tur bu lent ed d ies in
time. Th e only physic that is not resolved is the
evol u tion of so-ca lled s u b- g ri d ed d ies [1,2], these are
turbulent eddies smaller th en local grid resolution.
These edd ies are mod eled m ainly b y increas in g local
dissipation via so-called sub-grid model [1]. LES has
wi del y used as r esearch t ool rather then desi gn tool due
to its computational intensity. Ther e ar e two factors
that make LE S appealin g as design t ool in air-cooling
thermal m anagement . First, th ose flow pr oblems that
occu r in thi s indus try are consi d ered to be lo w
Reynolds number beca use of board size and air speed
when com p ared t o problem s in aerosp ace or p ower -
generation industries. Thi s is a solid advantage since
required mesh resolution , cost of LES, is directly
proportional to Re ynol ds number. S e cond, with new
high- s p eed (2- 3 GHz ) wor k stations in the mark et, th e
phrase ,“ int ensive computation” , has been
redefin ed. Other factors include employi ng non -
conformal grid that allows local mesh refinement
inside regions of inter est and existence of faster
solvers. Th is work is an attempt to introduce LES to
electronics cooling industr y. First portion of this paper
i s devoted to ex pl ore /invent build i ng block s for
reasonable simulation. They in clude mesh requir ement
study, implementin g per iodic boun dar y condition s,
fin ding ways to filter pre-heated flow enter ing periodic
condition, and examine an effective way to induce flow
instability to create turbulence. Second por tion of this
paper is devoted to employ LES for better
understanding of flow/ thermal physi cs that occur in
boar d level analysis and h eat sink modelin g.
INTRODUCTION
Most CFD simulation tools are ba sed on stea dy
state Reynolds aver a ged ver sion of Navier Stokes
equa tions (RANS ) with augmented turbulence
model. T here ar e l imitat ions in us ing RANS that
a re u sua lly n ot a ddressed. R AN S t urbule nc e
models are applied everywhere over entire fl ow
assumi ng fully turbulent boundary layer over
entire sur face. Experi ments show that boundar y
layer over a typical size board might be partially
laminar/partially turbulent depending on fan
l oc ation a nd averag e roug hness of th e board.
Applying turbulence model over the entire surface
over pr edicts the heat transfer coefficient, r esults
in lower than true sur face tempera ture.
Other main issue is rela ted to embed ded wall
funct i ons used in turbulenc e models. Wa ll
funct ions are used to curve-fit turbulent boundary
la yer gradi e nt betwee n th e s ur f ac e of interest and
the first gr i d point a way fr om it [5]. Their s ole
advantage is to avoid r esolving the wall layer that
other wise results in la rg e mesh cou nt. H ow e ver
they ar e accurate if the f irst grid point is located
inside the logarithmic la yer. If the first gr id point
is below the logar ithmic la yer (inside
laminar/buffer layer) layer, velocity gradients and
heat transfer coefficient are over predicted,
differences up to 15 °C lower than true sur face
t empera tures a re r ealiz e d. F or a typic al board
l e v e l si mula tion, a-pr iori es tima te of extent of
logarithmic la yers for elevated surfaces such as
component/heat sinks, is practically impossible.
The f inal draw back of turbulence models is
their flow dependency. Different tur bulent flows
have different coher ent structur es (mainly large
eddies). No single model can fit them a ll.
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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